%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.165", %%% date = "02 February 2026", %%% time = "06:30:19 MDT", %%% filename = "benfords-law.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "30540 43288 189744 1916005", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Benford's Law; %%% Bradford's Law; First Digit Phenomenon; %%% Gibrat's Law; Gibrat's Rule of Proportionate %%% Growth; Hall--Petch effect; Heaps' Law; %%% Herdan's Law; Law of Anomalous Numbers; %%% Lotka's Law; Pareto Distribution; Pareto Law; %%% Pareto Principle; power law; Significant %%% Digit Law; Simon--Yule model of text %%% generation; Stigler's Law; Yule process; %%% Zipf's Law", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography about a numerical %%% curiousity variously known as Benford's Law %%% (see particularly entries Newcomb:1881:NFU, %%% Benford:1938:LAN, Pinkham:1961:DFS, %%% Logan:1978:FDP, Hill:1998:FDP, and %%% Block:2010:GEB, Nigrini:2012:BLA), the Law of %%% Anomalous Numbers, and the Significant Digit %%% Law: in a table of physical constants (and in %%% many other collections of measured numbers), %%% the leading digits do not have equal %%% probability of occurrence: the digit 1 is %%% more common than 2, which is more common than %%% 3, and so on. %%% %%% Publications recorded here appear in about %%% 480 different journals from accounting, %%% aerobiology, animal behavior, auditing, %%% astronomy, bible studies, biology, %%% biometrics, botany, business, chaos theory, %%% chemistry, colloid science, complexity, %%% computer science, conflict resolution, %%% cognitive science, criminology, critical %%% phenomena, demographics, drug design, %%% dynamics, earthquake detection, economics, %%% electoral studies, engineering, entropy, %%% expert systems, extinction, finance, %%% forensics, gambling, geography, geophysics, %%% human resources, hydrology, imaging science, %%% informetrics, language science, library %%% science, linguistics, marine systems, %%% marketing, mathematics, medicine, networking, %%% neuroscience, nuclear engineering, nuclear %%% medicine, nuclear science, operations %%% research, pathology, physics, plasticity, %%% political analysis, probability, psychology, %%% risk analysis, signal processing, simulation, %%% social sciences, sociology, statistical %%% mechanics, statistics, stock-market trading, %%% tax accounting, urban development, and urban %%% growth, reflecting the broad interest in the %%% unexpected phenomenon discovered and reported %%% first by the Canadian/American astronomer and %%% mathematician, Simon Newcomb, in a two-page %%% note in 1881, and then independently, and %%% with numerical evidence from much more %%% measured data, by American physicist Frank %%% Benford in 1938. %%% %%% In Benford's Law, the frequency of leading %%% decimal digit p is roughly log10(1 + (1 / %%% p)): that is, approximately 0.301, 0.176, %%% 0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and %%% 0.046 for digits 1 through 9, instead of the %%% expected 1/9 ~= 0.111 for values taken from a %%% uniform distribution of random numbers. %%% %%% Another common statement of Benford's Law is %%% that the probability that a decimal number %%% representing a measured value begins with a %%% nonzero digit not greater than p is log10(1 + %%% p), that is, approximately 0.301, 0.477, %%% 0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and %%% 1.000 for digits 1 through 9. %%% %%% A simple Benford-based rule of thumb is that %%% about half the values start with digit 1 or %%% 2, about 10 percent with 8 or 9, and 5 %%% percent with 9. %%% %%% For the second digits, the probabilities are %%% determined by the formula (see %%% Todter:2009:BLI) %%% %%% sum(q = 1:9) log10(1 + 1 / (10*q + p)), %%% %%% that is, approximately 0.120, 0.114, 0.109, %%% 0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and %%% 0.085, for second decimal digits p = 0 %%% through 9. %%% %%% Probabilities for later digits are even %%% closer: see entries Newcomb:1881:NFU, %%% Feldstein:1976:CED, and Todter:2009:BLI. %%% %%% Benford's Law is not restricted to decimal %%% numbers: for base b (as long as b is not %%% huge, according to entry Schatte:1998:BLV), %%% just change the 10 values to b in the %%% previous formulas. Here are some results for %%% selected bases commonly used in computers, %%% showing the probability of the first (D1) or %%% second (D2) digit (first index) for base b %%% (second index): %%% %%% P[D1, 2]: 1.000 %%% P[D2, 2]: 0.585, 0.415 %%% %%% P[D1, 4]: 0.500, 0.292, 0.208 %%% P[D2, 4]: 0.304, 0.261, 0.230, 0.206 %%% %%% P[D1, 8]: 0.333, 0.195, 0.138, 0.107, %%% 0.088, 0.074, 0.064 %%% P[D2, 8]: 0.151, 0.141, 0.133, 0.126, 0.120, %%% 0.115, 0.110, 0.105 %%% %%% P[D1, 10]: 0.301, 0.176, 0.125, 0.097, %%% 0.079, 0.067, 0.058, 0.051, 0.046 %%% P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100, %%% 0.097, 0.093, 0.090, 0.088, 0.085 %%% %%% P[D1, 16]: 0.250, 0.146, 0.104, 0.080, %%% 0.066, 0.056, 0.048, 0.042, 0.038, %%% 0.034, 0.031, 0.029, 0.027, 0.025, %%% 0.023 %%% P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066, %%% 0.065, 0.064, 0.062, 0.061, 0.060, %%% 0.059, 0.058, 0.057, 0.056, 0.055, %%% 0.054 %%% %%% A small filter applied to the 1990 US Census %%% data in the Project Gutenberg file %%% uscen902.txt reports these frequencies of %%% first and second digits for the 5148 integer %%% values with at least 3 digits: %%% %%% F[D1]: 0.298, 0.215, 0.113, 0.082, %%% 0.098, 0.056, 0.055, 0.034, 0.049 %%% F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100, %%% 0.122, 0.076, 0.073, 0.066, 0.130 %%% %%% For the 110 numbers in the atomic weights %%% section of the GNU units utility data file, %%% units.dat, we have %%% %%% F[D1]: 0.391, 0.309, 0.045, 0.036, %%% 0.055, 0.036, 0.036, 0.036, 0.055 %%% F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145, %%% 0.145, 0.055, 0.055, 0.091, 0.082 %%% %%% From a snapshot of the country-area section %%% of the US CIA World Factbook %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html %%% %%% taken at 18 November 2011, we find 1505 %%% numbers with these frequencies: %%% %%% F[D1]: 0.312, 0.275, 0.100, 0.067, %%% 0.058, 0.062, 0.046, 0.029, 0.050 %%% F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062, %%% 0.067, 0.075, 0.067, 0.083, 0.075 %%% %%% From the country-population section %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html %%% %%% of that book, including only the 163 values %%% of 1,000,000 or larger, we find %%% %%% F[D1]: 0.301, 0.202, 0.092, 0.135, %%% 0.055, 0.067, 0.055, 0.037, 0.055 %%% F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098, %%% 0.123, 0.086, 0.043, 0.049, 0.092 %%% %%% From the section with the infant mortality %%% rates per 1000 births, %%% %%% https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html %%% %%% there are 208 values with at least 4 digits, %%% with these frequencies: %%% %%% F[D1]: 0.361, 0.293, 0.043, 0.072, %%% 0.062, 0.087, 0.038, 0.014, 0.029 %%% F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077, %%% 0.077, 0.106, 0.067, 0.043, 0.053 %%% %%% In the 2010 annual financial report for IBM %%% Corporation (its hundredth year of business) %%% %%% ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf %%% %%% there are 6126 numbers of two or more digits %%% that do not look like year dates (19xx and %%% 20xx), and they have these digit frequencies: %%% %%% F[D1]: 0.333, 0.160, 0.163, 0.086, %%% 0.068, 0.053, 0.047, 0.045, 0.046 %%% F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085, %%% 0.095, 0.079, 0.074, 0.079, 0.068 %%% %%% For the first 100,000 primes, we have %%% %%% F[D1]: 0.311, 0.091, 0.090, 0.087, %%% 0.086, 0.085, 0.084, 0.083, 0.082 %%% F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078, %%% 0.078, 0.078, 0.079, 0.078, 0.078 %%% %%% For the Fibonacci numbers, f(n), which %%% satisfy the recurrence f(n) = f(n-1) + f(n-2) %%% with f(1) = f(2) = 1, using the first 10000 %%% such numbers (the last of which has 2091 %%% digits), we find for the 9994 f(n) values %%% with at least two digits these frequencies: %%% %%% F[D1]: 0.301, 0.176, 0.125, 0.097, %%% 0.079, 0.067, 0.058, 0.051, 0.046 %%% F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100, %%% 0.097, 0.094, 0.090, 0.088, 0.085 %%% %%% If we take the same set of Fibonacci numbers, %%% we find these frequencies for values output %%% in base 4: %%% %%% F[D1]: 0.500, 0.292, 0.208 %%% F[D2]: 0.303, 0.262, 0.230, 0.205 %%% %%% The Fibonacci numbers, and the members of %%% many other such sequences, can be proved %%% mathematically to obey Benford's Law exactly %%% (see entries Raimi:1976:FDP, Berger:2011:BLS, %%% and Berger:2011:BTB). %%% %%% Simon Newcomb made another significant %%% appearance in the history of science when he %%% proposed that the then-not-understood %%% perihelion advance of the planet Mercury %%% could be explained by modifying Newton's law %%% of gravitation from a $r^{-2}$ dependence to %%% $r^{-2.000\,000\,157\,4}$. His proposal was %%% later shown to contradict more accurate %%% measurements of the orbit of Earth's Moon. %%% That story is told on pages 93--95 of %%% Clifford M. Will's 1993 book, ``Was Einstein %%% Right?'' (ISBN 0-465-09086-9). %%% %%% Although many papers purport to explain %%% Benford's Law, a recent paper (entry %%% Berger:2011:BLS) argues that several of the %%% prior published explanations are flawed. An %%% earlier paper (entry Raimi:1976:FDP) examines %%% the literature on Benford's Law up to 1976, %%% and points out flaws in several previous %%% explanations of the law. That paper also %%% gives a bibliography of previous important %%% works on the problem. A recent survey (entry %%% Berger:2011:BTB) may provide stronger %%% mathematical grounds for Benford's Law. %%% %%% Benford's Law has been applied to the problem %%% of detection of fraud in data, elections, and %%% finance (see, among other entries, %%% Hill:1998:FDP, Nigrini:1992:DIE, %%% Swanson:2003:DPF, Durtschi:2004:EUB, %%% Geyer:2004:DFD, Bhattacharya:2005:CPA, %%% Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD, %%% Schneider:2006:RAS, Cho:2007:BBL, %%% Diekmann:2007:FDU, Hand:2007:DDD, %%% Todter:2009:BLI, Corazza:2010:CFM, and %%% Roukema:2014:FDA, and the cautionary view in %%% Diekmann:2010:BLF). %%% %%% Benford's Law also applies to floating-point %%% numbers in computer arithmetic (see entries %%% Konheim:1965:MDT, Hamming:1970:DN, %%% Tsao:1974:DSD, Feldstein:1976:CED, %%% Feldstein:1986:OUS, Schatte:1988:ASC), where %%% it has implications for the frequency of %%% significance loss in subtraction of %%% like-signed numbers. %%% %%% This bibliography also includes publications %%% about two related empirical laws: Heaps' Law %%% and Zipf's Law, because they often occur in %%% discussions of Benford's Law. %%% %%% Heaps' Law (see entry Heaps:1978:IRC) is an %%% empirical observation from linguistics that %%% the proportion of words from a vocabulary %%% grows exponentially (but with a small %%% exponent, often between 0.4 and 0.6) with the %%% number of words in the text of documents. %%% %%% Zipf's Law says that if S is some stochastic %%% (random) variable, the probability that S %%% exceeds s is proportional to 1 / s. The %%% variable S might be, for example, the %%% population of a city (small cities are more %%% numerous than large ones). Zipf's Law is %%% a special case of the Pareto distribution %%% (see remark in entry Pareto:1896:CEP). %%% %%% Zipf's law finds application in the design of %%% information retrieval systems (e.g., hash %%% tables, databases, filesystems, and Web %%% searches), as well as in astronomy, biology, %%% computer science, demography, earth science, %%% economics, and physics. See entry %%% Newman:2005:PLP for an outstanding survey %%% that deserves to be widely read by %%% scientists, and entry Baldi:2003:MIW for a %%% book-length treatment. %%% %%% There is an actively-maintained bibliography %%% of Benford's Law at %%% %%% http://www.benfordonline.net/ %%% %%% (see entry Berger:2009:BOB). It includes %%% material from entries Hurlimann:2006:BLB and %%% Nigrini:1992:DIE. Although BibTeX output is %%% mentioned, it may not yet be implemented. %%% %%% There is an online bibliography of Zipf's Law %%% at %%% %%% http://www.nslij-genetics.org/wli/zipf/ %%% %%% (see entry Li:2011:ZLB). %%% %%% There is a collection of several papers on %%% election-fraud detection, some of them using %%% Benford's Law analyses, at %%% %%% http://www-personal.umich.edu/~wmebane/ %%% %%% At version 1.165, the year coverage looked like %%% this: %%% %%% 1881 ( 1) 1930 ( 0) 1979 ( 6) %%% 1882 ( 0) 1931 ( 1) 1980 ( 8) %%% 1883 ( 0) 1932 ( 2) 1981 ( 12) %%% 1884 ( 0) 1933 ( 0) 1982 ( 10) %%% 1885 ( 0) 1934 ( 1) 1983 ( 6) %%% 1886 ( 0) 1935 ( 1) 1984 ( 16) %%% 1887 ( 0) 1936 ( 2) 1985 ( 10) %%% 1888 ( 0) 1937 ( 1) 1986 ( 16) %%% 1889 ( 0) 1938 ( 2) 1987 ( 18) %%% 1890 ( 0) 1939 ( 0) 1988 ( 12) %%% 1891 ( 0) 1940 ( 0) 1989 ( 14) %%% 1892 ( 0) 1941 ( 0) 1990 ( 9) %%% 1893 ( 0) 1942 ( 0) 1991 ( 11) %%% 1894 ( 0) 1943 ( 1) 1992 ( 15) %%% 1895 ( 0) 1944 ( 1) 1993 ( 11) %%% 1896 ( 1) 1945 ( 2) 1994 ( 12) %%% 1897 ( 0) 1946 ( 1) 1995 ( 19) %%% 1898 ( 0) 1947 ( 0) 1996 ( 23) %%% 1899 ( 0) 1948 ( 2) 1997 ( 17) %%% 1900 ( 0) 1949 ( 2) 1998 ( 21) %%% 1901 ( 0) 1950 ( 3) 1999 ( 28) %%% 1902 ( 0) 1951 ( 0) 2000 ( 22) %%% 1903 ( 0) 1952 ( 1) 2001 ( 26) %%% 1904 ( 0) 1953 ( 1) 2002 ( 34) %%% 1905 ( 0) 1954 ( 1) 2003 ( 42) %%% 1906 ( 0) 1955 ( 1) 2004 ( 46) %%% 1907 ( 0) 1956 ( 0) 2005 ( 68) %%% 1908 ( 0) 1957 ( 5) 2006 ( 60) %%% 1909 ( 0) 1958 ( 1) 2007 ( 49) %%% 1910 ( 1) 1959 ( 1) 2008 ( 54) %%% 1911 ( 0) 1960 ( 1) 2009 ( 78) %%% 1912 ( 1) 1961 ( 2) 2010 ( 97) %%% 1913 ( 1) 1962 ( 2) 2011 ( 88) %%% 1914 ( 1) 1963 ( 1) 2012 ( 59) %%% 1915 ( 1) 1964 ( 1) 2013 ( 47) %%% 1916 ( 1) 1965 ( 4) 2014 ( 52) %%% 1917 ( 1) 1966 ( 4) 2015 ( 79) %%% 1918 ( 0) 1967 ( 3) 2016 ( 25) %%% 1919 ( 0) 1968 ( 4) 2017 ( 12) %%% 1920 ( 1) 1969 ( 12) 2018 ( 13) %%% 1921 ( 0) 1970 ( 8) 2019 ( 8) %%% 1922 ( 1) 1971 ( 2) 2020 ( 16) %%% 1923 ( 0) 1972 ( 7) 2021 ( 13) %%% 1924 ( 0) 1973 ( 10) 2022 ( 10) %%% 1925 ( 1) 1974 ( 12) 2023 ( 12) %%% 1926 ( 1) 1975 ( 13) 2024 ( 10) %%% 1927 ( 1) 1976 ( 13) 2025 ( 11) %%% 1928 ( 2) 1977 ( 9) 2026 ( 1) %%% 1929 ( 1) 1978 ( 11) %%% 20xx ( 1) %%% %%% Article: 1189 %%% Book: 93 %%% InCollection: 54 %%% InProceedings: 64 %%% Manual: 1 %%% MastersThesis: 6 %%% Misc: 20 %%% PhdThesis: 8 %%% Proceedings: 8 %%% TechReport: 50 %%% Unpublished: 3 %%% %%% Total entries: 1496 %%% %%% Data for this bibliography have been %%% collected from %%% %%% * the University of Utah Mathematics %%% Department bibliography archives %%% %%% * the TeX User Group bibliography %%% archives %%% %%% * the Karlsruhe Computer Science %%% bibliography archives %%% %%% * the Karlsruhe virtual catalog at %%% http://www.ubka.uni-karlsruhe.de/kvk_en.html %%% %%% * the US Library of Congress catalog at %%% http://catalog.loc.gov/ %%% %%% * the author's cattobib utility, which %%% provides Z39.50 interfaces to many %%% large libraries around the world, at %%% https://www.math.utah.edu/pub/cattobib/ %%% %%% * the American Institute of Physics %%% Scitation database at %%% http://scitation.aip.org/search_scitation %%% %%% * the American Physical Society PROLA %%% database at %%% http://publish.aps.org/search %%% %%% * the American Mathematical Society %%% MathSciNet database at %%% http://ams.rice.edu/mathscinet/search.html %%% %%% * the Bulletin of the Atomic Scientists %%% (archives available, albeit inconveniently, %%% via http://books.google.com/ and %%% http://bos.sagepub.com/search) %%% %%% * the Canadian Journal of Physics %%% database at %%% http://www.nrcresearchpress.com/search/advanced %%% %%% * the European Mathematical Society %%% Zentralblatt fuer Mathematik database %%% at http://zb.msri.org/ZMATH/zmath/en/ %%% %%% * the Europhysics journal archive at %%% http://www.europhysicsnews.org/ %%% %%% * the JSTOR database at %%% http://www.jstor.org/ %%% %%% * the Nature journal archive at %%% http://www.nature.com/search/ %%% %%% * the journal archives of the National %%% Academy of Science at %%% http://www.pnas.org/ %%% %%% * the Project Euclid archives at %%% http://projecteuclid.org/ %%% %%% * the SAO/NASA Astrophysics Data System at %%% http://adsabs.harvard.edu/ %%% %%% * the Science journal archive at %%% http://www.sciencemag.org/search %%% %%% * the SPIRES high-energy physics %%% literature database at the Stanford %%% Linear Accelerator at Stanford %%% University at %%% http://www.slac.stanford.edu/spires/hep/search/ %%% %%% * the Springer journal database at %%% http://www.springer.com/?SGWID=0-102-13-0-0 %%% %%% * the Wiley journal database at %%% http://onlinelibrary.wiley.com/ %%% %%% * many online library catalogs, including %%% those of the British Library, the %%% Karlsruhe Virtual Library catalog, the %%% Oxford University Library, the University of %%% California library system, and the US %%% Library of Congress. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{ "\let \k = \c" # "\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" # "\ifx \undefined \circled \def \circled #1{(#1)}\fi" # "\ifx \undefined \cprime \def \cprime{$'$} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \polhk \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" # "\ifx \undefined \reg \def \reg {\circled{R}}\fi" # "\ifx \undefined \url \input{path.sty} \fi" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-mjn = "Mark J. Nigrini"} @String{ack-nhfb = "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"} %%% ==================================================================== %%% Journal abbreviations: @String{j-ACCOUNT-HIST-J = "Accounting Historians Journal"} @String{j-ACCOUNT-RES = "Accountability in Research"} @String{j-ACCOUNT-REV = "The Accounting Review"} @String{j-ACCOUNTANCY = "Accountancy: The journal of the {Institute of Chartered Accountants in England and Wales}"} @String{j-ACTA-ARITHMETICA = "Acta Arithmetica"} @String{j-ACTA-ASTRONAUT = "Acta Astronautica"} @String{j-ACTA-PHYS-POL-B = "Acta Physica Polonica B"} @String{j-ADV-APPL-STAT = "Advances and Applications in Statistics"} @String{j-ADV-COMPLEX-SYST = "Advances in Complex Systems"} @String{j-ADV-MATH = "Advances in Mathematics"} @String{j-ADV-QUANTUM-CHEM = "Advances in Quantum Chemistry"} @String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"} @String{j-AEROBIOLOGIA = "Aerobiologia"} @String{j-AM-DOC = "American Documentation"} @String{j-AM-J-APPL-SCI = "American Journal of Applied Sciences"} @String{j-AM-J-ECON-SOCIOL = "The American Journal of Economics and Sociology"} @String{j-AM-J-MATH = "American Journal of Mathematics"} @String{j-AM-J-MATH-MANAGE-SCI = "American Journal of Mathematical and Management Sciences"} @String{j-AM-SCI = "American Scientist"} @String{j-AMER-J-PHYSICS = "American Journal of Physics"} @String{j-AMER-J-PSYCHOLOGY = "The American Journal of Psychology"} @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-AMER-STAT = "The American Statistician"} @String{j-ANAL-APPL = "Analysis and Applications (Singapore)"} @String{j-ANALYST = "The Analyst"} @String{j-ANIM-BEHAV = "Animal Behaviour"} @String{j-ANN-APPL-PROBAB = "Annals of Applied Probability"} @String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical Mathematics (Tokyo)"} @String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"} @String{j-ANN-OPER-RESEARCH = "Annals of Operations Research"} @String{j-ANN-PHYS = "Annals of Physics"} @String{j-ANN-PROBAB = "Annals of Probability"} @String{j-ANN-STAT = "Annals of Statistics"} @String{j-APPL-ECON-LETT = "Applied Economics Letters"} @String{j-APPL-FINANC-ECON = "Applied Financial Economics"} @String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"} @String{j-APPL-STAT = "Applied Statistics"} @String{j-AQUAT-BOT = "Aquatic Botany"} @String{j-ARCH-HIST-EXACT-SCI = "Archive for History of Exact Sciences"} @String{j-ARKHIMEDES = "Arkhimedes"} @String{j-ASTA-ADV-STAT-ANAL = "AStA. 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Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-DOVER = "Dover Publications, Inc."} @String{pub-DOVER:adr = "New York, NY, USA"} @String{pub-ELSEVIER = "Elsevier"} @String{pub-ELSEVIER:adr = "Amsterdam, The Netherlands"} @String{pub-FARRAR = "Farrar, Strauss, and Giroux"} @String{pub-FARRAR:adr = "New York, NY, USA"} @String{pub-HARVARD = "Harvard University Press"} @String{pub-HARVARD:adr = "Cambridge, MA, USA"} @String{pub-HOUGHTON-MIFFLIN = "Houghton-Mifflin"} @String{pub-HOUGHTON-MIFFLIN:adr = "Boston, MA, USA"} @String{pub-IEEE = "IEEE Computer Society Press"} @String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-MATH-ASSOC-AMER = "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"} @String{pub-MCGRAW-HILL = "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr = "New York, NY, USA"} @String{pub-MIT = "MIT Press"} @String{pub-MIT:adr = "Cambridge, MA, USA"} @String{pub-MORGAN-KAUFMANN = "Morgan Kaufmann Publishers"} @String{pub-MORGAN-KAUFMANN:adr = "Los Altos, CA 94022, USA"} @String{pub-NORTH-HOLLAND = "North-Holland Publishing Co."} @String{pub-NORTH-HOLLAND:adr = "Amsterdam, The Netherlands"} @String{pub-OXFORD = "Oxford University Press"} @String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PH = "Pren{\-}tice-Hall"} @String{pub-PH:adr = "Upper Saddle River, NJ, USA"} @String{pub-PRINCETON = "Princeton University Press"} @String{pub-PRINCETON:adr = "Princeton, NJ, USA"} @String{pub-SPIE = "SPIE Optical Engineering Press"} @String{pub-SPIE:adr = "Bellingham, WA, USA"} @String{pub-SV = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr = "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-SV-CHAM = "Spring{\-}er-Ver{\-}lag"} @String{pub-SV-CHAM:adr = "Cham, Switzerland"} @String{pub-U-MICHIGAN = "University of Michigan Press"} @String{pub-U-MICHIGAN:adr = "Ann Arbor, MI, USA"} @String{pub-W-H-FREEMAN = "W. H. {Freeman and Company}"} @String{pub-W-H-FREEMAN:adr = "New York, NY, USA"} @String{pub-WILEY = "Wiley"} @String{pub-WILEY:adr = "New York, NY, USA"} @String{pub-WORLD-SCI = "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road, Singapore 9128"} @String{pub-YALE = "Yale University Press"} @String{pub-YALE:adr = "New Haven, CT, USA"} %%% ==================================================================== %%% Series abbreviations: @String{ser-LNAI = "Lecture Notes in Artificial Intelligence"} @String{ser-LNCS = "Lecture Notes in Computer Science"} @String{ser-LNM = "Lecture Notes in Mathematics"} %%% ==================================================================== %%% Bibliography entries, sorted by year, and then by citation label: @Article{Newcomb:1881:NFU, author = "Simon Newcomb", title = "Note on the frequency of use of the different digits in natural numbers", journal = j-AM-J-MATH, volume = "4", number = "1--4", pages = "39--40", year = "1881", CODEN = "AJMAAN", ISSN = "0002-9327 (print), 1080-6377 (electronic)", ISSN-L = "0002-9327", bibdate = "Thu Feb 15 16:35:24 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.jstor.org/stable/2369148", abstract = "That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones. The first significant figure is oftener 1 than any other digit, and the frequency diminishes up to 9.", acknowledgement = ack-nhfb, author-dates = "March 12, 1835--July 11, 1909", fjournal = "American Journal of Mathematics", journal-URL = "https://www.jstor.org/journal/amerjmath", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From p. 40: ``The law of probability of the occurrence of numbers is such that all mantissas of their logarithms are equally probable.''. The article contains no references to earlier work.", remark-2 = "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are the earliest citations of Newcomb's work that I have yet found in connection with Benford's Law.", xxURL = "http://en.wikipedia.org/wiki/Simon_Newcomb", } @Book{Pareto:1896:CEP, author = "Vilfredo Pareto", title = "Cours d'{\'e}conomie politique profess{\'e} a l'universit{\'e} de {Lausanne}. (French) [{Course} on political economy given at the {University of Lausanne}]", publisher = "F. Rouge", address = "Lausanne, Switzerland", pages = "????", year = "1896--1897", LCCN = "HB173 .P22", bibdate = "Wed Nov 16 08:41:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "French", remark = "Two volumes issued in successive years. The Italian economist and mathematician, Vilfredo Federico (born in Paris, France, and initially named Wilfried Fritz) Pareto (15 July 1848--19 August 1923), introduced the 80--20 rule in economics (80\% of the wealth is owned by 20\% of the people, which was true at the time in Italy, and found to be similar in other countries). He developed the Pareto distribution, in which a random variable $X$ has the property that the probability that it is greater than some number $x$ is given by $ {\rm Pr}(X > x) = (x_m / x)^\alpha $ for $ x > x_m $, and $ {\rm Pr}(X > x) = 1 $ otherwise. The positive value $ x_m $ is a cutoff, and as $ \alpha \to \infty $, the Pareto distribution approaches a Dirac delta function, $ \delta (x - x_m) $. When this models the distribution of wealth, the exponent $ \alpha $ is called the {\em Pareto index}.", } @Article{Doolittle:1910:SNF, author = "C. L. Doolittle", title = "{Simon Newcomb, F.R.S., LL.D., D.C.L.}", journal = j-PROC-AMER-PHIL-SOC, volume = "49", number = "197", pages = "iii--xviii", month = oct # "\slash " # dec, year = "1910", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Sat Aug 24 19:37:51 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/procamerphilsoc1900.bib", URL = "https://www.jstor.org/stable/984092", acknowledgement = ack-nhfb, ajournal = "Proc. Amer. Philos. Soc.", fjournal = "Proceedings of the American Philosophical Society", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", remark = "This obituary does not mention Newcomb's short paper on the leading-digit phenomenon now known as Benford's Law, but it does give an overview of Newcomb's humble origins, education, life, and scientific influence.", } @Book{Poincare:1912:CPL, author = "H. Poincar{\'e}", title = "Calcul des Probabilit{\'e}s: Le{\c{c}}ons profess{\'e}es pendant le deuxi{\`e} me semestre 1893--1894. ({French}) [{Calculation} of Probabilities: Lectures from the second semester 1893--1894]", publisher = "Gauthier-Villars", address = "Paris, France", pages = "ii + 274", year = "1912", LCCN = "QA273 .P75", bibdate = "Mon Nov 14 10:08:18 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, author-dates = "1854--1912", language = "French", remark = "See pp. 313--320.", } @Article{Auerbach:1913:GBG, author = "Felix Auerbach", title = "{Das Gesetz der Bev{\"o}lkerungskonzentration}. ({German}) [{The} law of population concentration]", journal = "{Petermann's Geographische Mitteilungen}", volume = "59", number = "1", pages = "74--76", month = "????", year = "1913", CODEN = "PGGMA3", ISSN = "0031-6229", ISSN-L = "0031-6229", bibdate = "Thu Nov 24 10:49:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper is reported in \cite{Newman:2005:PLP} to be the first discovery of {\em Zipf's Law\/} in connection with city populations (see \cite{Zipf:1932:SSP}). See also \cite{Estoup:1916:GSM}.", URL = "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122", acknowledgement = ack-nhfb, ajournal = "Petermanns Geogr. Mitteilung", ajournal-2 = "Petermanns Geogr. Mitt.", language = "German", } @Article{Stamp:1914:NIP, author = "J. C. Stamp", title = "A New Illustration of {Pareto}'s Law", journal = j-J-R-STAT-SOC, volume = "77", number = "2", pages = "200--204", month = jan, year = "1914", DOI = "https://doi.org/10.2307/2339802", ISSN = "0952-8385", ISSN-L = "0952-8385", bibdate = "Sat Jan 24 11:18:04 MST 2015", bibsource = "http://www.jstor.org/stable/i315805; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1910.bib", URL = "http://www.jstor.org/stable/2339802", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Weyl:1915:GZM, author = "Hermann Weyl", title = "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}. ({German}) [{On} the uniform distribution of numbers mod. one]", journal = j-MATH-ANN, volume = "77", number = "3", pages = "313--352", month = "????", year = "1915", CODEN = "MAANA3", DOI = "https://doi.org/10.1007/BF01475864", ISSN = "0025-5831 (print), 1432-1807 (electronic)", ISSN-L = "0025-5831", bibdate = "Sun Nov 13 10:54:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Math. Ann.", fjournal = "Mathematische Annalen", journal-URL = "http://link.springer.com/journal/208", language = "German", xxyear = "1916", } @Book{Estoup:1916:GSM, author = "J. B. Estoup", title = "Gammes St{\'e}nographiques: m{\'e}thode \& exercices pour l'acquisition de la vitesse ({French}) [Stenographic ranges: method and exercises for achieving speed]", publisher = "Institut St{\'e}nographique de France", address = "Paris, France", edition = "Fourth", pages = "151", year = "1916", LCCN = "????", bibdate = "Thu Nov 24 14:24:28 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This on shorthand writing is the earliest known publication of the power-law distribution of word frequencies, generally credited to \cite{Zipf:1932:SSP}.", acknowledgement = ack-nhfb, keywords = "Zipf's Law", language = "French", } @Article{Franel:1917:PTL, author = "J. Franel", title = "{{\`A}} propos des tables de logarithmes. ({French}) [{On} tables of logarithms]", journal = "Festschrift Naturforschenden der Gesellschaft in Z{\"u}rich Vierteljahrsschrift", volume = "62", number = "??", pages = "286--295", month = "????", year = "1917", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 10:09:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "French", } @Article{Boring:1920:LNL, author = "Edwin G. Boring", title = "The Logic of the Normal Law of Error in Mental Measurement", journal = j-AMER-J-PSYCHOLOGY, volume = "31", number = "1", pages = "1--33", month = jan, year = "1920", CODEN = "AJPCAA", ISSN = "0002-9556 (print), 1939-8298 (electronic)", ISSN-L = "0002-9556", bibdate = "Thu Dec 01 21:35:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/1413989", acknowledgement = ack-nhfb, fjournal = "The American journal of psychology", remark = "A citation search in Google Scholar on 1-Dec-2011 found this article as the only one citing Newcomb's work \cite{Newcomb:1881:NFU} before it was brought to wider view by Raimi's frequently-cited paper \cite{Raimi:1976:FDP}. Boring's article has only brief mention of Newcomb's work, and then solely in connection with the believed randomness of digits of transcendental numbers.", } @InCollection{Macaulay:1922:PLG, author = "F. R. Macaulay", editor = "W. C. Mitchell", booktitle = "Income in the {United States}: Its Amount and Distribution: 1909--1919", title = "{Pareto}'s law and the general problem of mathematical describing the frequency of distribution of income", publisher = "National Bureau of Economic Research", address = "New York, NY, USA", pages = "??--??", year = "1922", LCCN = "????", bibdate = "Fri Nov 25 09:06:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Yule:1925:MTE, author = "G. Udny Yule", title = "A Mathematical Theory of Evolution, Based on the Conclusions of {Dr. J. C. Willis, F.R.S.}", journal = j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI, volume = "213", number = "??", pages = "21--87", day = "14", month = may, year = "1925", CODEN = "PTRBAE", DOI = "https://doi.org/10.1098/rstb.1925.0002", ISSN = "0962-8436 (print), 1471-2970 (electronic)", ISSN-L = "0962-8436", bibdate = "Tue Nov 15 10:45:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rstb.royalsocietypublishing.org/content/213/402-410/21", acknowledgement = ack-nhfb, fjournal = "Philosophical transactions of the Royal Society of London Series B, Biological sciences", journal-URL = "https://royalsocietypublishing.org/loi/rstb", } @Article{Lotka:1926:FDS, author = "Alfred J. Lotka", title = "The Frequency Distribution of Scientific Productivity", journal = j-J-WASH-ACAD-SCI, volume = "16", number = "12", pages = "317--323", day = "19", month = jun, year = "1926", CODEN = "JWASA3", ISSN = "0043-0439", ISSN-L = "0043-0439", bibdate = "Thu Nov 24 14:36:11 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This is the earliest known publication on the phenomenon known as Zipf's Law, here applied to publication counts of chemists and physicists. Lotka's Law (a term possibly first used in \cite{Zipf:1949:HBP}) says that the number of authors producing $n$ publications is about $ 1 / n^2 $ of the number producing only one. This `law' seems to have been misunderstood and misapplied in other fields; see \cite{Potter:1981:LLR}.", URL = "http://www.jstor.org/stable/24529203", acknowledgement = ack-nhfb, fjournal = "Journal of the Washington Academy of Sciences", journal-URL = "http://www.jstor.org/journal/jwashacadscie", keywords = "Lotka's Law", } @Article{Yule:1927:RS, author = "G. Udny Yule", title = "On Reading a Scale", journal = j-J-R-STAT-SOC, volume = "90", number = "3", pages = "570--587", month = "????", year = "1927", ISSN = "0952-8385", ISSN-L = "0952-8385", bibdate = "Wed Nov 23 12:29:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See related later work \cite{Preece:1981:DFD}.", URL = "http://www.jstor.org/stable/2341205", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", remark = "This paper reports on human bias in the recording of last digits in measurements, or from roundings, or from later scale conversions.", } @Article{Condon:1928:SV, author = "E. U. Condon", title = "Statistics of vocabulary", journal = j-SCIENCE, volume = "67", number = "1733", pages = "300--??", day = "16", month = mar, year = "1928", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.67.1733.300", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Fri Nov 25 09:04:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", } @Article{Sun:1928:EFD, author = "C. P. Sun", title = "On the Examination of Final Digits by Experiments in Artificial Sampling", journal = j-BIOMETRIKA, volume = "20A", number = "1/2", pages = "64--68", month = jul, year = "1928", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2331941", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 13:38:07 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315380; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/biometrika1920.bib", URL = "http://www.jstor.org/stable/2331941", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://www.jstor.org/journals/00063444.html", } @Article{Zipf:1929:RFD, author = "George Kingsley Zipf", title = "Relative frequency as a determinant of phonetic change", journal = "Harvard Studies in Classical Philology", volume = "40", number = "??", pages = "1--95", month = "????", year = "1929", CODEN = "????", ISSN = "0073-0688", ISSN-L = "0073-0688", bibdate = "Fri Nov 25 09:02:14 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/journals/00730688.html; http://www.jstor.org/stable/310585", acknowledgement = ack-nhfb, } @Book{Gibrat:1931:IE, author = "Robert Gibrat", title = "Les In{\'e}galit{\'e}s {\'e}conomiques", publisher = "Librairie du Recueil Sirey", address = "Paris, France", pages = "286", year = "1931", LCCN = "HB251.GIB", bibdate = "Mon Feb 18 14:43:11 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; library.ox.ac.uk:210/ADVANCE", note = "Applications: aux in{\'e}galit{\'e}s des richesses, {\`a} la concentration des entreprises, aux populations des villes, aux statistiques des familles, etc. d'une loi nouvelle. La loi de l'effet proportionnel.", URL = "http://en.wikipedia.org/wiki/Gibrat%27s_law", acknowledgement = ack-nhfb, author-dates = "1904--1980", remark-1 = "According to at least one library catalog (SWB), this book may be the author's doctoral dissertation from l'Universit{\'e} de Paris in 1931.", remark-2 = "This book is cited as the origin of Gibrat's Law, or Gibrat's rule of proportionate growth, that ``the size of a firm and its growth rate are independent''.", } @Misc{Anonymous:1932:FL, author = "Anonymous", title = "Fishpole Lamp", howpublished = "Web site", day = "30", month = apr, year = "1932", bibdate = "Sat Feb 23 14:52:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This Web site reports that General Electric researcher Frank Benford invented the electric light pointer, the forerunner of the modern laser pointer.", URL = "http://scienceservice.si.edu/pages/012020.htm", acknowledgement = ack-nhfb, remark = "CD 2478048, E\&MP12.020, Electric Appliances \ Apparatus.", } @Book{Zipf:1932:SSP, author = "George Kingsley Zipf", title = "Selected studies of the principle of relative frequency in language", publisher = pub-HARVARD, address = pub-HARVARD:adr, pages = "51", year = "1932", LCCN = "P123 .Z5", bibdate = "Wed Nov 16 09:03:46 MST 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This book is the origin of {\em Zipf's Law}, but the phenomenon was apparently first reported two decades earlier in \cite{Auerbach:1913:GBG} for city populations, in \cite{Estoup:1916:GSM} for word frequencies, and in \cite{Lotka:1926:FDS} for researcher publication counts.", acknowledgement = ack-nhfb, author-dates = "1902--1950", subject = "Plautus, Titus Maccius; language and languages; semantics; comparative linguistics; Chinese language; phonology; Latin language; glossaries, vocabularies, etc; dialects; China; Beijing", } @Article{Bradford:1934:SIS, author = "Samuel C. Bradford", title = "Sources of Information on Specific Subjects", journal = "Engineering: An Illustrated Weekly Journal (London)", volume = "137", number = "??", pages = "85--86", day = "26", month = jan, year = "1934", CODEN = "????", ISSN = "????", bibdate = "Fri Nov 25 11:47:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper (reprinted in \cite{Bradford:1985:SIS}) introduces an observation later known as Bradford's Law: there are exponentially-diminishing returns of extending a search for references in journals.", URL = "http://en.wikipedia.org/wiki/Bradford%27s_law", acknowledgement = ack-nhfb, } @Book{Zipf:1935:PBL, author = "George Kingsley Zipf", title = "The psycho-biology of language: an introduction to dynamic philology", publisher = pub-HOUGHTON-MIFFLIN, address = pub-HOUGHTON-MIFFLIN:adr, pages = "ix + 336", year = "1935", LCCN = "P105 .Z5", bibdate = "Wed Nov 16 09:07:09 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; prodorbis.library.yale.edu:7090/voyager", acknowledgement = ack-nhfb, author-dates = "1902--1950", subject = "language and languages; semantics; comparative linguistics", } @Article{Keyser:1936:VFD, author = "C. J. Keyser", title = "{Vilfredo Federico Damaso Pareto}. {Mathematician}, economist, sociologist", journal = j-SCRIPTA-MATH, volume = "4", number = "??", pages = "5--23", month = "????", year = "1936", ISSN = "0036-9713", bibdate = "Thu Oct 26 11:15:25 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scripta-math.bib", acknowledgement = ack-nhfb, ajournal = "Scripta Math.", fjournal = "Scripta Mathematica: A Quarterly Journal Devoted to the Philosophy, History, and Expository Treatment of Mathematics", jfm = "62.0027.01", ZBmath = "2525107", } @Book{Moon:1936:SBI, author = "Parry Moon", title = "The Scientific Basis of Illuminating Engineering", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xi + 608", year = "1936", LCCN = "TH7703 .M65", bibdate = "Mon Nov 14 10:11:54 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "See pages 420ff.", } @Article{Bresciani-Turroni:1937:PL, author = "C. Bresciani-Turroni", title = "On {Pareto}'s Law", journal = j-J-R-STAT-SOC, volume = "100", number = "3", pages = "421--432", month = "????", year = "1937", DOI = "https://doi.org/10.2307/2980528", ISSN = "0952-8385", ISSN-L = "0952-8385", bibdate = "Sat Jan 24 11:18:08 MST 2015", bibsource = "http://www.jstor.org/stable/i349533; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib", URL = "http://www.jstor.org/stable/2980528", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society", journal-URL = "http://www.jstor.org/journals/09528385.html", } @Article{Benford:1938:LAN, author = "Frank Benford", title = "The Law of Anomalous Numbers", journal = j-PROC-AMER-PHIL-SOC, volume = "78", number = "4", pages = "551--572", month = mar, year = "1938", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Thu Feb 15 16:28:28 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See comments about Benford's biased rounding practices \cite{Diaconis:1979:RP}.", URL = "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G", ZMnumber = "JFM 64.0555.03; Zbl 0018.26502", abstract = "It has been observed that the first pages of a table of common logarithms show more wear than do the last pages, indicating that more used numbers begin with the digit 1 than with the digit 9. A compilation of some 20,000 first digits taken from widely divergent sources shows that there is a logarithmic distribution of first digits when the numbers are composed of four or more digits. An analysis of the numbers from different sources shows that the numbers taken from unrelated subjects, such as a group of newspaper items, show a much better agreement with a logarithmic distribution than do numbers from mathematical tabulations or other formal data. There is here the peculiar fact that numbers that individually are without relationship are, when considered in large groups, in good agreement with a distribution law---hence the name ``Anomalous Numbers.''\par A further analysis of the data shows a strong tendency for bodies of numerical data to fall into geometric series. If the series is made up of numbers containing three or more digits the first digits form a logarithmic series. If the numbers contain only single digits the geometric relation still holds but the simple logarithmic relation no longer applies.\par An equation is given showing the frequencies of first digits in the different orders of numbers 1 to 10, 10 to 100, etc.\par The equation also gives the frequency of digits in the second, third + place of a multi-digit number, and it is shown that the same law applies to reciprocals.\par There are many instances showing that the geometric series, or the logarithmic law, has long been recognized as a common phenomenon in factual literature and in the ordinary affairs of life. The wire gauge and drill gauge of the mechanic, the magnitude scale of the astronomer and the sensory response curves of the psychologist are all particular examples of a relationship that seems to extend to all human affairs. The Law of Anomalous Numbers is thus a general probability law of widespread application.", acknowledgement = ack-nhfb, author-dates = "1883--December 4, 1948", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From \cite{Logan:1978:FDP}: ``Benford's paper was published in 1938 in a journal of rather limited circulation and not usually read by mathematicians. It so happened that it was immediately followed in the same issue by a physics paper which became of some importance for secret nuclear work during World War II [H. A. Bethe, M. E. Rose, and L. P. Smith, `The Multiple Scattering of Electrons', Proc. Amer. Phil. Soc. 78(4), 573--585 (1938)]. That is why Benford's paper caught the attention of physicists in the early 1940's and was much discussed. This led to the notes in Nature by Goudsmit and Furry [3] and Furry and Hurwitz [4] containing an effort to explain Benford's law. We considered it at that time merely a welcome diversion and did not expect that over thirty papers would be devoted to this subject in subsequent years.'' The 2006 bibliography \cite{Hurlimann:2006:BLB} cites 325 publications about Benford's Law.", xxURL = "http://en.wikipedia.org/wiki/Frank_Benford", } @Article{Bethe:1938:MSE, author = "H. A. Bethe and M. E. Rose and L. P. Smith", title = "The Multiple Scattering of Electrons", journal = j-PROC-AMER-PHIL-SOC, volume = "78", number = "4", pages = "573--585", month = mar, year = "1938", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Wed Nov 23 14:27:52 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "This paper, which immediately follows Benford's \cite{Benford:1938:LAN} in this journal issue, is reported in \cite[p. 197]{Logan:1978:FDP} to have been of considerable interest to scientists involved in secret nuclear physics work in World War II. That is how Benford's paper ``in a journal of rather limited circulation and not usually read by mathematicians'' came to be noticed by physicists.", URL = "http://www.jstor.org/stable/984803", acknowledgement = ack-nhfb, author-dates = "Hans Albrecht Bethe (1906--2005)", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", remark = "Biography supplement in \cite{Lee:2007:HAB} has this as Proc. Am. Philos. Soc., 89, 373--383 (1938), but that seems to be wrong: check??", } @Article{Benford:1943:PAG, author = "Frank Benford", title = "The Probable Accuracy of the General Physical Constants", journal = j-PHYS-REV, volume = "63", number = "5--6", pages = "212--212", month = mar, year = "1943", CODEN = "PHRVAO", DOI = "https://doi.org/10.1103/PhysRev.63.212", ISSN = "0031-899X (print), 1536-6065 (electronic)", ISSN-L = "0031-899X", bibdate = "Mon Nov 21 21:52:58 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRev.63.212", acknowledgement = ack-nhfb, fjournal = "Physical Review", journal-URL = "http://prola.aps.org/browse/PR", } @Article{Goudsmit:1944:SFN, author = "S. A. Goudsmit and W. H. Furry", title = "Significant Figures of Numbers in Statistical Tables", journal = j-NATURE, volume = "154", number = "3921", pages = "800--801", day = "23", month = dec, year = "1944", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/154800a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Sun Sep 18 11:57:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See later work \cite{Logan:1978:FDP}, and severe criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.", URL = "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf", abstract = "A rough qualitative explanation of this fact can easily be given. If we consider tables in which the entries become rarer the larger they are, we can draw the obvious conclusion that in any interval, say, between 10 and 99, or 10,000 and 99,999, there are more entries on the small side than on the large side.", acknowledgement = ack-nhfb, author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)", fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed the concept of electron spin, a critical step forward in the quantum mechanics of many-electron systems. Surprisingly, that work did not get them the Nobel Prize, but it did spur Wolfgang Pauli to present his Exclusion Principle in 1925, for which he received the 1945 Nobel Prize in Physics. After World War II, Goudsmit was the scientific head of the Alsos mission to capture German nuclear scientists. In the 1950s, he founded the journal Physical Review Letters. During the 1960s and 1970s, he was Editor-in-Chief of the main American physics journal, the Physical Review.", } @Article{Furry:1945:DND, author = "W. H. Furry and Henry Hurwitz", title = "Distribution of Numbers and Distribution of Significant Figures", journal = j-NATURE, volume = "155", number = "3924", pages = "52--53", day = "13", month = jan, year = "1945", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/155052a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Sun Sep 18 11:51:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Unpublished{Stigler:1945:DLD, author = "George J. Stigler", title = "The distribution of leading digits in statistical tables", year = "1945", bibdate = "Sat Nov 12 16:07:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Unpublished, but written about 1945--1946, and presented in an 1975 address at Haskell Hall, University of Chicago. Stigler's distribution is more complex than that of Newcomb and Benford. Stigler has $ F_d = (d \ln (d) - (d + 1) \ln (d + 1) + (1 + (10 / 9) \ln (10))) / 9 $, which gives leading-digit frequencies of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764, 0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for a comparison of the Benford and Stigler distributions, and their relations to Zipf and Pareto distributions. For derivations of Stigler's distribution, see \cite{Logan:1978:FDP,Raimi:1985:FDP}.", URL = "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/", acknowledgement = ack-nhfb, remark = "Stigler won the 1982 Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (often called the Nobel Prize in Economics, although that field was not among the original ones funded by Nobel's will).", } @Book{Furlan:1946:HSU, author = "Luigi Vladimir Furlan", title = "{Das Harmoniegesetz der Statistik: Eine Untersuchung {\"u}ber die metrische Interdependenz der sozialen Erscheinungen}. ({German}) [{The} {Law of Harmony} in statistics: an investigation of the metrical interdependence of social phenomena]", volume = "2", publisher = "Verlag f{\"u}r Recht und Gesellschaft A.-G.", address = "Basel, Switzerland", pages = "xii + 504", year = "1946", LCCN = "HA29 .F85", bibdate = "Mon Nov 14 09:40:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "{Beihefte zum Assekuranzjahrbuch}", acknowledgement = ack-nhfb, author-dates = "1886--", keywords = "Benford--Furlan Law", language = "German", } @Article{Geiringer:1948:RVF, author = "Hilda Geiringer", title = "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz der Statistik: Eine Untersuchung {\"u}ber die metrische Interdependenz der sozialen Erscheinungen}. ({German}) [{The} {Law of Harmony} in statistics: an investigation of the metrical interdependence of social phenomena]", journal = j-J-AM-STAT-ASSOC, volume = "43", number = "242", pages = "325--328", month = jun, year = "1948", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Nov 14 09:42:45 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See \cite{Furlan:1946:HSU}.", URL = "http://www.jstor.org/stable/2280379", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Hsu:1948:ESM, author = "E. H. Hs{\"u}", title = "An Experimental Study on ``Mental Numbers'' and a New Application", journal = j-J-GEN-PSYCH, volume = "38", number = "1", pages = "57--67", month = "????", year = "1948", CODEN = "JGPSAY", DOI = "https://doi.org/10.1080/00221309.1948.9711768", ISSN = "0022-1309 (print), 1940-0888 (electronic)", ISSN-L = "0022-1309", bibdate = "Sat Jan 07 09:29:53 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768", acknowledgement = ack-nhfb, fjournal = "The Journal of General Psychology", keywords = "Benford's Law", onlinedate = "06 Jul 2010", } @Book{Hardy:1949:DS, author = "G. H. (Godfrey Harold) Hardy", title = "Divergent series", publisher = pub-CLARENDON, address = pub-CLARENDON:adr, pages = "xvi + 396", year = "1949", LCCN = "QA295 .H29", bibdate = "Wed Nov 16 08:14:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1877--1947", } @Book{Zipf:1949:HBP, author = "George Kingsley Zipf", title = "Human behaviour and the principle of least effort", publisher = "Hafner Pub. Co.", address = "New York, NY, USA", pages = "xi + 573", year = "1949", LCCN = "H91 .Z5 1949a", bibdate = "Tue Nov 15 09:35:14 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1902--1950", remark = "Reprinted 1965.", subject = "Human ecology", } @Article{Anonymous:1950:BRZ, author = "Anonymous", title = "Book review: {Zipf, George K., \booktitle{Human behavior and the principle of least effort}. Cambridge, (Mass.): Addison-Wesley, 1949, pp. 573}", journal = j-J-CLIN-PSYCHOL, volume = "6", number = "3", pages = "306--306", year = "1950", CODEN = "JCPYAO", DOI = "https://doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO%3B2-7", ISSN = "0021-9762 (print), 1097-4679 (electronic)", ISSN-L = "0021-9762", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Clinical Psychology", } @Book{Feller:1950:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "????", year = "1950", LCCN = "QA273 .F37", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wiley series in probability and mathematical statistics. Probability and mathematical statistics", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", } @Article{Macon:1950:DFD, author = "N. Macon and L. Moser", title = "On the distribution of first digits of powers", journal = j-SCRIPTA-MATH, volume = "16", number = "??", pages = "290--291", month = "????", year = "1950", CODEN = "????", ISSN = "0036-9713", ISSN-L = "0036-9713", bibdate = "Sat Nov 12 16:28:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Scripta Math.", fjournal = "Scripta Mathematica", } @Article{Tsuji:1952:UDN, author = "M. Tsuji", title = "On the uniform distribution of numbers $ \bmod 1 $", journal = j-J-MATH-SOC-JPN, volume = "4", number = "3--4", pages = "313--322", month = "????", year = "1952", CODEN = "NISUBC", DOI = "https://doi.org/10.2969/jmsj/00430313", ISSN = "0025-5645", ISSN-L = "0025-5645", bibdate = "Sun Feb 17 06:33:32 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.jmsj/1261415780", acknowledgement = ack-nhfb, fjournal = "Journal of the {Mathematical Society of Japan}", } @InProceedings{Mandelbrot:1953:ITS, author = "Beno{\^\i}t B. Mandelbrot", editor = "Willis Jackson", booktitle = "{Communication theory: papers read at a Symposium on ``Applications of Communication Theory'' held at the Institution of Electrical Engineers, London, September 22nd--26th 1952}", title = "An Informational Theory of the Statistical Structure of Languages", publisher = pub-BUTTERWORTHS, address = pub-BUTTERWORTHS:adr, bookpages = "xii + 532", pages = "486--502", year = "1953", LCCN = "Q350 .S92 1952", bibdate = "Wed Nov 16 09:37:30 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://lccn.loc.gov/53004215; http://www.nytimes.com/2010/10/17/us/17mandelbrot.html", acknowledgement = ack-nhfb, remark = "The paper is incorrectly referenced as a book in \cite{Baek:2011:ZLU}. Mandelbrot got his Master of Science in Aeronautics at CalTech in 1948, and his Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in 1952 in Paris, so perhaps this is a translation of his thesis work.", } @Book{Blackwell:1954:TGS, author = "David Blackwell and Meyer A. Girshick", title = "Theory of Games and Statistical Decisions", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xi + 355", year = "1954", LCCN = "QA269 .B5", bibdate = "Mon Nov 14 10:04:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://catalog.hathitrust.org/Record/000577721", acknowledgement = ack-nhfb, author-dates = "David Blackwell (1919--2010)", keywords = "Benford's Law", remark = "Brief mention of Benford's Law on page 74, problem 2.7.2 (??).", } @Article{Simon:1955:CSD, author = "Herbert A. Simon", title = "On a Class of Skew Distribution Functions", journal = j-BIOMETRIKA, volume = "42", number = "3/4", pages = "425--440", month = dec, year = "1955", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2333389", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", MRclass = "62.0X", MRnumber = "0073085 (17,380e)", MRreviewer = "H. A. David", bibdate = "Sat Jun 21 14:32:48 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315425; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib", URL = "http://www.jstor.org/stable/2333389", acknowledgement = ack-nhfb, fjournal = "Biometrika", journal-URL = "http://biomet.oxfordjournals.org/content/by/year; http://www.jstor.org/journals/00063444.html", keywords = "distribution of income; distribution of species among genera; distributions of city populations; distributions of document word frequencies; distributions of scientific publication counts; Zipf's Law", remark = "This work is an extension of Yule's work \cite{Yule:1925:MTE}. See discussion \cite{Mandelbrot:1959:NCS} and comments \cite{Mitzenmacher:2003:BHG}.", } @Article{Devooght:1957:LZM, author = "J. Devooght", title = "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the {Zipf--Mandelbrot} law]", journal = "Acad. Roy. Belg. Bull. Cl. Sci. (5)", volume = "43", pages = "244--251", year = "1957", CODEN = "????", ISSN = "0001-4141", ISSN-L = "0001-4141", MRclass = "94.0X", MRnumber = "0088412 (19,516a)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe des Sciences. Koninklijke Belgische Academie. Mededelingen van de Klasse der Wetenschappen. 5e S{\'e}rie", language = "French", } @Book{Feller:1957:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "461 (vol. 1), 626 (vol. 2)", year = "1957", LCCN = "QA273 .F3712", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://catdir.loc.gov/catdir/toc/onix01/57010805.html", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", } @Article{Gini:1957:SFD, author = "Corrado Gini", title = "Sulla frequenza delle cifre iniziali dei numeri osservati. ({Italian}) [{On} the frequency of initial digits of observed numbers]", journal = "{Bulletin de l'Institut International de Statistique}", volume = "35", number = "2", pages = "57--76", year = "1957", CODEN = "BISQA3", ISSN = "????", MRclass = "62.00", MRnumber = "0117807 (22 \#8581)", bibdate = "Sun Sep 18 11:54:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "29th session, 2nd delivery, Rio de Janerio.", acknowledgement = ack-nhfb, ajournal = "Bull. Inst. Internat. Stat.", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", xxvolume = "34 (wrong!)", } @Article{Herzel:1957:SDD, author = "Amato Herzel", title = "Sulla distribuzione della cifre iniziali dei numeri statistici. ({Italian}) [{On} the frequency of initial digits of statistical numbers]", journal = "{Atti dell XV e XVII Riunione, Societa Italiana di Statistica}", volume = "??", number = "??", pages = "205--228", year = "1957", CODEN = "????", ISSN = "????", bibdate = "Sun Sep 18 12:00:07 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", language = "Italian", } @Article{Miller:1957:SEI, author = "George A. Miller", title = "Some Effects of Intermittent Silence", journal = j-AMER-J-PSYCHOLOGY, volume = "70", number = "2", pages = "311--314", month = jun, year = "1957", CODEN = "AJPCAA", ISSN = "0002-9556 (print), 1939-8298 (electronic)", ISSN-L = "0002-9556", bibdate = "Tue Nov 15 09:40:05 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/1419346", acknowledgement = ack-nhfb, fjournal = "The American Journal of Psychology", keywords = "Zipf's Law", } @Book{Zeller:1958:TLG, author = "Karl Zeller", title = "{Theorie der Limitierungsverfahren}. (German) [{Theory} of limiting processes]", volume = "15", publisher = pub-SV, address = pub-SV:adr, pages = "242", year = "1958", LCCN = "QA295 .Z4", bibdate = "Wed Nov 16 06:43:43 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "{Ergebnisse der Mathematik und ihrer Grenzgebiete}", acknowledgement = ack-nhfb, language = "German", subject = "series; convergence", } @Article{Mandelbrot:1959:NCS, author = "Beno{\^\i}t Mandelbrot", title = "A note on a class of skew distribution functions: analysis and critique of a paper by {H. A. Simon}", journal = j-INF-CONTROL, volume = "2", number = "??", pages = "90--99", month = apr, year = "1959", CODEN = "IFCNA4", DOI = "https://doi.org/10.1016/S0019-9958(59)90098-1", ISSN = "0019-9958 (print), 1878-2981 (electronic)", ISSN-L = "0019-9958", bibdate = "Wed Nov 16 09:45:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Simon:1955:CSD}.", abstract = "This note is a discussion of H. A. Simon's model (1955) concerning the class of frequency distributions generally associated with the name of G. K. Zipf. The main purpose is to show that Simon's model is analytically circular in the case of the linguistic laws of Estoup--Zipf and Willis--Yule. Insofar as the economic law of Pareto is concerned, Simon has himself noted that his model is a particular case of that of Champernowne; this is correct, with some reservation. A simplified version of Simon's model is included.", acknowledgement = ack-nhfb, fjournal = "Information and Control", journal-URL = "http://www.sciencedirect.com/science/journal/00199958", } @Article{Mandelbrot:1960:PLL, author = "Beno{\^\i}t Mandelbrot", title = "The {Pareto--Levy} law and the distribution of income", journal = j-INT-ECON-REV, volume = "1", number = "??", pages = "79--106", month = "????", year = "1960", CODEN = "INERAE", ISSN = "0020-6598 (print), 1468-2354 (electronic)", ISSN-L = "0020-6598", bibdate = "Wed Nov 23 11:07:01 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ingenta.com/journals/browse/bpl/iere", acknowledgement = ack-nhfb, fjournal = "International Economic Review", journal-URL = "http://www.jstor.org/journal/inteeconrevi", } @Article{Cigler:1961:NET, author = "J. Cigler and G. Helmberg", title = "{Neuere Entwicklungen der Theorie der Gleichverteilung}. ({German}) [{Recent} developments in the theory of uniform distribution]", journal = j-DEUTSCH-MATH-V, volume = "64", number = "??", pages = "1--50", month = "????", year = "1961", CODEN = "????", ISSN = "????", bibdate = "Sat Nov 12 16:33:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Jber. Deutsch. Math.--Verein", language = "German", } @Article{Pinkham:1961:DFS, author = "Roger S. Pinkham", title = "On the Distribution of First Significant Digits", journal = j-ANN-MATH-STAT, volume = "32", number = "4", pages = "1223--1230", month = dec, year = "1961", CODEN = "AASTAD", ISSN = "0003-4851 (print), 2168-8990 (electronic)", ISSN-L = "0003-4851", bibdate = "Sat Sep 17 10:19:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2237922", abstract = "It has been noticed by astute observers that well used tables of logarithms are invariably dirtier at the front than at the back. Upon reflection one is led to inquire whether there are more physical constants with low order first significant digits than high. Actual counts by Benford [2] show that not only is this the case but that it seems to be an empirical truth that whenever one has a large body of physical data, Farmer's Almanac, Census Reports, Chemical Rubber Handbook, etc., the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $. Any reader formerly unaware of this ``peculiarity'' will find an actual sampling experiment wondrously tantalizing. Thus, for example, approximately $ 0.7 $ of the physical constants in the Chemical Rubber Handbook begin with $4$ or less ($ \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted with the widespread intuitive evaluation $ 4 / 9 $ ths.", acknowledgement = ack-nhfb, fjournal = "Annals of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.aoms/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "From p. 1223: ``\ldots{} the proportion of these data with first significant digit $n$ or less is approximately $ \log_{10}(n + 1) $.''\par \ldots{} ``The only distribution for first significant digits which is invariant under scale change of the underlying distribution is $ \log_{10}(n + 1) $. Contrary to suspicion this is a non-trivial mathematical result, for the variable $n$ is discrete.''.\par From p. 1230: ``The foregoing results bear on questions of round-off in computing machines. Since $ d(u v) = u d v + v d u $, the error resulting from multiplying two rounded numbers will be governed primarily by the first significant digits of the two numbers being multiplied. Now the distribution of first significant digits, favoring as it does low order digits, tends to produce less error than would be the case if first significant digits were uniform as has sometimes been assumed.''\par Cited in \cite{Sterbenz:1974:FPC}.", } @Book{Hamming:1962:NMS, author = "R. W. (Richard Wesley) Hamming", title = "Numerical methods for scientists and engineers", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "xvii + 411", year = "1962", LCCN = "QA297 .H28", MRclass = "65.00", MRnumber = "0137279", MRreviewer = "G. E. Forsythe", bibdate = "Mon Aug 6 07:24:38 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; z3950.loc.gov:7090/Voyager", series = "International Series in Pure and Applied Mathematics", acknowledgement = ack-nhfb, HDnumber = "51", remark = "Cited in \cite{Sterbenz:1974:FPC}.", subject = "Numerical analysis; Electronic digital computers; random numbers", tableofcontents = "1. The difference calculus \\ 2. Roundoff noise \\ 3. The summation calculus \\ 4. Evaluation of infinite series \\ 5. Finite difference equations \\ 6. The finite Fourier series \\ 7--9. Polynomial approximation introduction \\ 10. A uniform method for finding formulas \\ 11. On finding the error term of a formula \\ 12. Formulas for definite integrals \\ 13. Indefinite integrals \\ 14. Introduction to differential equations \\ 15. A general theory of predictor-corrector methods \\ 16. Special methods of integrating ordinary differential equations \\ 17--18. Least squares theory and practice \\ 19. Chebyshev polynomials \\ 20. Rational functions \\ 21--22. Periodic functions --- Fourier series \\ 23. Nonperiodic functions --- the Fourier integral \\ 24. Linear filters --- smoothing and differentiating \\ 25. Integrals and differential equations \\ 26. Exponential approximation \\ 27. Singularities \\ 28. On finding zeros \\ 29. Simultaneous linear algebraic equations \\ 30. Inversion of matrices and eigenvalues \\ 31. Some examples of the simulation of situations and processes \\ 32. Random numbers and Monte Carlo methods \\ $N+1$: The art of computing for scientists and engineers", } @TechReport{Mandelbrot:1962:SNR, author = "Beno{\^\i}t Mandelbrot", title = "Statistics of natural resources and the law of {Pareto}", type = "Research Note", number = "NC-146", institution = "IBM", address = "Yorktown Heights, NY, USA", day = "29", month = jun, year = "1962", bibdate = "Mon Sep 10 17:35:59 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Weaver:1963:LLT, author = "Warren Weaver", title = "{Lady Luck}: The Theory of Probability", publisher = "Doubleday Anchor Series", address = "New York, NY, USA", pages = "392", year = "1963", LCCN = "QA273 .W4", bibdate = "Mon Nov 14 09:54:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Benford's Law is discussed on pp. 270--277.", acknowledgement = ack-nhfb, author-dates = "Warren, Weaver (1894--1978)", remark = "Reprinted in \cite{Weaver:1982:LLT}.", } @Article{Cigler:1964:MSU, author = "J. Cigler", title = "Methods of summability and uniform distribution $ \bmod 1 $", journal = j-COMPOS-MATH, volume = "16", number = "??", pages = "44--51", year = "1964", CODEN = "CMPMAF", ISSN = "0010-437X (print), 1570-5846 (electronic)", ISSN-L = "0010-437X", bibdate = "Mon Nov 14 10:15:31 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Compositio Mathematica", } @Article{Good:1965:LE, author = "I. J. Good", title = "Letter to the Editor", journal = j-AMER-STAT, volume = "19", number = "3", pages = "43--43", month = jun, year = "1965", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Nov 14 09:56:33 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2681423", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", keywords = "Benford's Law", remark = "Refers to \cite{Pinkham:1961:DFS}, and cites a review of that article published by Good in Mathematical Reviews (1962), page 214, which I have not yet been able to locate.", } @Article{Hamming:1965:NLB, author = "R. W. Hamming and W. L. Mammel", title = "A Note on the Location of the Binary Point in a Computing Machine", journal = j-IEEE-TRANS-ELEC-COMPUT, volume = "EC-14", number = "2", pages = "260--261", month = apr, year = "1965", CODEN = "IEECA8", DOI = "https://doi.org/10.1109/PGEC.1965.264258", ISSN = "0367-7508", ISSN-L = "0367-7508", bibdate = "Thu Jul 14 06:26:22 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electronic Computers", remark = "The authors consider the low-level multiplication circuit efficiency of placing the binary point before or after the first bit. If the leading bit is equally likely to be a 0 or a 1, then their analysis shows that it is better to place the point before the leading bit. However, they report that a more likely distribution is logarithmic (as predicted by Benford's Law, although the Newcomb / Benford work is neither mentioned nor cited), in which case there is no advantage for either choice of placement of the binary point. They conclude that it would be humane to place it after the leading digit, by analogy with how people learn decimal arithmetic.", } @Article{Konheim:1965:MDT, author = "Alan G. Konheim", title = "Mantissa Distributions (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "19", number = "89", pages = "143--144", month = apr, year = "1965", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2004111", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Book{Zipf:1965:PBL, author = "George Kingsley Zipf", title = "The psycho-biology of language: an introduction to dynamic philology", publisher = pub-MIT, address = pub-MIT:adr, pages = "xv + 336", year = "1965", LCCN = "P105 .Z5 1965", bibdate = "Wed Nov 16 09:07:09 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; prodorbis.library.yale.edu:7090/voyager", acknowledgement = ack-nhfb, author-dates = "1902--1950", remark = "Reprint of \cite{Zipf:1935:PBL}.", subject = "language; philology; semantics; psycholinguistics; comparative linguistics", } @Article{Ball:1966:BRB, author = "R. J. Ball", title = "Book Review: {{\booktitle{Random Processes and the Growth of Firms: A Study of the Pareto Law}}, by Josef Steindl}", journal = j-J-R-STAT-SOC-SER-A-GENERAL, volume = "129", number = "4", pages = "600--601", month = "????", year = "1966", CODEN = "JSSAEF", DOI = "https://doi.org/10.2307/2982275", ISSN = "0035-9238", ISSN-L = "0035-9238", bibdate = "Sat Jan 24 11:18:12 MST 2015", bibsource = "http://www.jstor.org/stable/i349635; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1960.bib", URL = "http://www.jstor.org/stable/2982275", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series A (General)", journal-URL = "http://www.jstor.org/journals/00359238.html", } @Book{Feller:1966:IPT, author = "William Feller", title = "Introduction to Probability Theory", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xviii + 626", year = "1966", ISSN = "0271-6232", LCCN = "QA273 .F3727 1966", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wiley series in probability and mathematical statistics. Probability and mathematical statistics", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", remark = "Benford's Law is discussed on p. 62.", } @Article{Flehinger:1966:PRI, author = "B. J. (Betty J.) Flehinger", title = "On the probability that a random integer has initial digit {$A$}", journal = j-AMER-MATH-MONTHLY, volume = "73", number = "10", pages = "1056--1061", month = dec, year = "1966", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2314636", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Sat Nov 12 15:33:14 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2314636", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Book{Petersen:1966:RMT, author = "Gordon Marshall Petersen", title = "Regular Matrix Transformations", publisher = pub-MCGRAW-HILL, address = pub-MCGRAW-HILL:adr, pages = "viii + 142", year = "1966", LCCN = "QA263 .P415 1966", bibdate = "Mon Nov 14 10:18:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Duncan:1967:AUD, author = "R. L. Duncan", title = "An Application of Uniform Distributions to the {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "5", number = "2", pages = "137--140", month = apr, year = "1967", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:04:52 MDT 2011", bibsource = "http://www.fq.math.ca/5-2.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/5-2/duncan.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Groos:1967:BCB, author = "Ole V. Groos", title = "Brief Communications: {Bradford's Law} and the {Keenan--Atherton} data", journal = j-AM-DOC, volume = "18", number = "1", pages = "46--46", month = jan, year = "1967", CODEN = "AMDOA7", DOI = "https://doi.org/10.1002/asi.5090180108", ISSN = "0096-946X (print), 1936-6108 (electronic)", ISSN-L = "0096-946X", bibdate = "Fri Sep 11 06:21:26 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/amdoc.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Documentation", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643/", onlinedate = "23 Apr 2007", } @Article{Mosteller:1967:DSR, author = "Frederick Mosteller and Cleo Youtz and Douglas Zahn", title = "The Distribution of Sums of Rounded Percentages", journal = j-DEMOGRAPHY, volume = "4", number = "2", pages = "850--858", month = jun, year = "1967", CODEN = "????", ISSN = "0070-3370 (print), 1533-7790 (electronic)", ISSN-L = "0070-3370", bibdate = "Thu Nov 24 08:03:16 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "See \cite{Diaconis:1979:RP} for further work.", URL = "http://muse.jhu.edu/journals/dem/; http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html; http://www.jstor.org/stable/2060324", abstract = "When percentages are computed for counts in several categories or for several positive measurements0 each taken as a fraction of their sum, the rounded percentages often fail to add to 100 percent. We investigate how frequently this failure occurs and what the distributions of sums of rounded percentages are for (1) an empirical set of data, (2) the multinomial distribution in small samples, (3) spacings between points dropped on an interval --- the broken-stick model; and (4) for simulation for several categories. The several methods produce similar distributions.We find that the probability that the sum of rounded percentages adds to exactly 100 percent is certain for two categories, about three-fourths for three categories, about two-thirds for four categories, and about [Formula: see text] for larger numbers of categories, c, on the average when categories are not improbable.", acknowledgement = ack-nhfb, fjournal = "Demography", pubmedid = "21318695", } @Article{Adhikari:1968:DMS, author = "A. K. Adhikari and B. P. Sarkar", title = "Distribution of most significant digit in certain functions whose arguments are random variables", journal = j-SANKHYA-B, volume = "30", number = "??", pages = "47--58", month = "????", year = "1968", CODEN = "SANBBV", ISSN = "0976-8386 (print), 0976-8394 (electronic)", ISSN-L = "0976-8394", bibdate = "Sat Nov 12 16:09:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Book{Feller:1968:IPT, author = "William Feller", title = "Introduction to Probability Theory and its Applications", volume = "2", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xviii + 509", year = "1968", ISBN = "0-471-25708-7", ISBN-13 = "978-0-471-25708-0", LCCN = "QA273 .F3713", bibdate = "Mon Nov 14 09:57:35 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a discussion of flaws in the derivation of Benford's Law in this book.", acknowledgement = ack-nhfb, author-dates = "William Feller (1906--1970)", remark = "Pages 63--64 (of xxiv + 669) in 1971 printing have only brief mention of two papers \cite{Benford:1938:LAN,Pinkham:1961:DFS}.", } @Article{Shenton:1968:PDM, author = "L. R. Shenton", title = "Periodicity and Density of Modified {Fibonacci} Sequences", journal = j-FIB-QUART, volume = "6", number = "2", pages = "109--116", month = apr, year = "1968", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:02 MDT 2011", bibsource = "http://www.fq.math.ca/6-2.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/6-2/shenton.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", keywords = "Benford's Law", } @Article{Wilk:1968:PPM, author = "M. B. Wilk and R. Gnanadesikan", title = "Probability Plotting Methods for the Analysis of Data", journal = j-BIOMETRIKA, volume = "55", number = "1", pages = "1--17", month = mar, year = "1968", CODEN = "BIOKAX", DOI = "https://doi.org/10.2307/2334448", ISSN = "0006-3444 (print), 1464-3510 (electronic)", ISSN-L = "0006-3444", bibdate = "Sat Jun 21 14:33:29 MDT 2014", bibsource = "http://www.jstor.org/journals/00063444.html; http://www.jstor.org/stable/i315458; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib", URL = "http://www.jstor.org/stable/2334448", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Biometrika", journal-URL = "http://www.jstor.org/journals/00063444.html", keywords = "empirical cumulative distribution function (ECDF); percent ($p$--$p$) plots; quantile ($q$--$q$) plots", remark = "This article does not mention Benford's Law, but MJN \cite{Nigrini:2012:BLA} lists this reference for analysis of data.", } @Article{Adhikari:1969:SRD, author = "A. K. Adhikari", title = "Some results on the distribution of the most significant digit", journal = j-SANKHYA-B, volume = "31", number = "??", pages = "413--420", month = "????", year = "1969", CODEN = "SANBBV", ISSN = "0976-8386 (print), 0976-8394 (electronic)", ISSN-L = "0976-8394", bibdate = "Sat Nov 12 16:12:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Article{Bumby:1969:FAM, author = "R. Bumby and E. Ellentuck", title = "Finitely additive measures and the first digit problem", journal = j-FUNDAM-MATH, volume = "65", number = "??", pages = "33--42", month = "????", year = "1969", CODEN = "????", ISSN = "0016-2736 (print), 1730-6329 (electronic)", ISSN-L = "0016-2736", bibdate = "Sat Nov 12 16:19:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fundamenta mathematicae", } @Article{Duncan:1969:NID, author = "R. L. Duncan", title = "Note on the Initial Digit Problem", journal = j-FIB-QUART, volume = "7", number = "5", pages = "474--475", month = dec, year = "1969", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:21 MDT 2011", bibsource = "http://www.fq.math.ca/7-5.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/7-5/duncan.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Fairthorne:1969:PDE, author = "Robert A. Fairthorne", title = "Progress in Documentation: Empirical Hyperbolic Distributions ({Bradford--Zipf--Mandelbrot}) for Bibliometric Description and Prediction", journal = j-J-DOC, volume = "25", number = "4", pages = "313--343", month = dec, year = "1969", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026481", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 06:27:27 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprinted in \cite{Fairthorne:2005:PDE}.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", remark = "According to \cite{Potter:1981:LLR}, this paper is the first to link the distributions of Bradford, Zipf, Mandelbrot, and Lotka.", } @Unpublished{Hafner:1969:CSR, author = "Everett M. Hafner", title = "Circular slide roulette", year = "1969", bibdate = "Mon Nov 14 10:00:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Unpublished but dated 1969. Presented in 1975 in an address at Hampshire College, Amherst, MA, USA", acknowledgement = ack-nhfb, } @Article{Haight:1969:TPD, author = "F. A. Haight", title = "Two probability distributions connected with {Zipf}'s rank-size conjecture", journal = j-ZASTOS-MAT, volume = "10", pages = "225--228", year = "1969", CODEN = "ZAMTAK", ISSN = "0044-1899", ISSN-L = "0044-1899", MRclass = "62.31", MRnumber = "0246425 (39 \#7729)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Polska Akademia Nauk. Instytut Matematyczny. Zastosowania Matematyki", } @Article{Holewijn:1969:UDS, author = "Dr. P. J. Holewijn", title = "On the uniform distribution of sequences of random variables", journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB, volume = "14", number = "2", pages = "89--92", month = "????", year = "1969", CODEN = "ZWVGAA", DOI = "https://doi.org/10.1007/BF00537514", ISSN = "0044-3719", ISSN-L = "0044-3719", bibdate = "Sat Apr 26 19:23:29 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib", URL = "http://link.springer.com/article/10.1007/BF00537514", acknowledgement = ack-nhfb, fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete", journal-URL = "http://link.springer.com/journal/440", } @Book{Knuth:1969:SA, author = "Donald E. Knuth", title = "Seminumerical Algorithms", volume = "2", publisher = pub-AW, address = pub-AW:adr, pages = "xi + 624", year = "1969", ISBN = "0-201-03802-1", ISBN-13 = "978-0-201-03802-6", LCCN = "QA76.5 .K57", MRclass = "68.00 (65.00)", MRnumber = "44 \#3531", MRreviewer = "M. Muller", bibdate = "Wed Dec 15 15:47:38 1993", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", price = "US\$19.75", series = "The Art of Computer Programming", acknowledgement = ack-nhfb, remark = "Benford's Law is discussed on pp. 219--229.", tableofcontents = "3: Random Numbers \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 9 \\ 3.2.1. The Linear Congruential Method / 9 \\ 3.2.1.1. Choice of modulus / 11 \\ 3.2.1.2. Choice of multiplier / 15 \\ 3.2.1.3. Potency / 21 \\ 3.2.2. Other Methods / 25 \\ 3.3. Statistical Tests / 34 \\ 3.3.1. General Test Procedures for Studying Random Data / 35 \\ 3.3.2. Empirical Tests / 54 \\ *3.3.3. Theoretical Tests / 69 \\ 3.3.4. The Spectral Test / 82 \\ 3.4. Other Types of Random Quantities / 100 \\ 3.4.1. Numerical Distributions / 101 \\ 3.4.2. Random Sampling and Shuffling / 121 \\ *3.5. What is a Random Sequence? / 127 \\ 3.6. Summary / 155 \\ 4: Arithmetic \\ 4.1. Positional Number Systems / 162 \\ 4.2. Floating-Point Arithmetic / 180 \\ 4.2.1. Single-Precision Calculations / 180 \\ 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\ *4.2.3. Double-Precision Calculations / 210 \\ 4.2.4. Statistical Distribution / 218 \\ 4.3. Multiple-Precision Arithmetic / 229 \\ 4.3.1. The Classical Algorithms / 229 \\ *4.3.2. Modular Arithmetic / 248 \\ *4.3.3. How Fast Can We Multiply? / 258 \\ 4.4. Radix Conversion / 280 \\ 4.5. Rational Arithmetic / 290 \\ 4.5.1. Fractions / 290 \\ 4.5.2. The Greatest Common Divisor / 293 \\ *4.5.3. Analysis of Euclid's Algorithm / 316 \\ 4.5.4. Factoring into Primes / 339 \\ 4.6. Polynomial Arithmetic / 360 \\ 4.6.1. Division of Polynomials / 363 \\ *4.6.2. Factorization of Polynomials / 381 \\ 4.6.3. Evaluation of Powers / 398 \\ 4.6.4. Evaluation of Polynomials / 422 \\ *4.7. Manipulation of Power Series / 444 \\ Answers to Exercises / 452 \\ Appendix A: MIX / 565 \\ 1. Description of MIX / 565 \\ 2. The MIX Assembly Language / 584 \\ Appendix B: Tables of Numerical Quantities / 596 \\ 1. Fundamental Constants (decimal) / 596 \\ 2. Fundamental Constants (octal) / 597 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 598 \\ Appendix C: Index to Notations / 600 \\ Index and Glossary / 605", xxyear = "{\noopsort{1968c}}1969", } @Article{Kuipers:1969:RPR, author = "L. Kuipers", title = "Remark on a Paper by {R. L. Duncan} Concerning the Uniform Distribution Mod $1$ of the Sequence of the Logarithms of the {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "7", number = "5", pages = "465--466", month = dec, year = "1969", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:21 MDT 2011", bibsource = "http://www.fq.math.ca/7-5.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Raimi:1969:DFS, author = "R. A. Raimi", title = "On the Distribution of First Significant Figures", journal = j-AMER-MATH-MONTHLY, volume = "76", number = "4", pages = "342--348", month = apr, year = "1969", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2316424", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:39:22 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Raimi:1969:PDF, author = "R. Raimi", title = "The peculiar distribution of first significant digits", journal = j-SCI-AMER, volume = "221", number = "6", pages = "109--120", month = dec, year = "1969", CODEN = "SCAMAC", DOI = "https://doi.org/10.1038/scientificamerican1269-109", ISSN = "0036-8733 (print), 1946-7087 (electronic)", ISSN-L = "0036-8733", bibdate = "Sat Nov 12 16:39:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Scientific American", journal-URL = "http://www.nature.com/scientificamerican", } @PhdThesis{Wong:1969:GDS, author = "James Teng Wong", title = "On the Generalization of the Distribution of the Significant Digits Under Computation", type = "{Ph.D.} thesis", school = "Department of Mathematics, Oregon State University", address = "Corvallis, OR, USA", pages = "52", year = "1969", bibdate = "Fri Nov 25 15:41:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://search.proquest.com/docview/302476508?accountid=14677", acknowledgement = ack-nhfb, } @Article{Aigner:1970:EPL, author = "Dennis J. Aigner and Arthur S. Goldberger", title = "Estimation of {Pareto's Law} from Grouped Observations", journal = j-J-AM-STAT-ASSOC, volume = "65", number = "330", pages = "712--723", month = jun, year = "1970", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:44 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314212; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib", URL = "http://www.jstor.org/stable/2284582", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Blum:1970:SID, author = "M. Blum", title = "On the Sums of Independently Distributed {Pareto} Variates", journal = j-SIAM-J-APPL-MATH, volume = "19", number = "1", pages = "191--198", month = jul, year = "1970", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", } @Article{Brown:1970:MOU, author = "J. L. {Brown, Jr.} and R. L. Duncan", title = "Modulo One Uniform Distribution of the Sequence of Logarithms of Certain Recursive Sequences", journal = j-FIB-QUART, volume = "8", number = "5", pages = "482--486", month = dec, year = "1970", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:31 MDT 2011", bibsource = "http://www.fq.math.ca/8-5.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", note = "See remark \cite{Kuipers:1973:RPD}.", URL = "http://www.fq.math.ca/Scanned/8-5/brown.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Hamming:1970:DN, author = "R. W. Hamming", title = "On the Distribution of Numbers", journal = j-BELL-SYST-TECH-J, volume = "49", number = "8", pages = "1609--1625", month = oct, year = "1970", CODEN = "BSTJAN", ISSN = "0005-8580", ISSN-L = "0005-8580", bibdate = "Tue Nov 9 11:15:55 MST 2010", bibsource = "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html; http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf; http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf", abstract = "This paper examines the distribution of the mantissas of floating-point numbers and shows how the arithmetic operations of a computer transform various distributions toward the limiting distribution $$ r(x) = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where $b$ is the base of the number system). The paper also gives a number of applications to hardware, software, and general computing which show that this distribution is not merely an amusing curiosity. A brief examination of the distribution of exponents is include.", acknowledgement = ack-nhfb, fjournal = "The Bell System Technical Journal", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/", } @Article{Hill:1970:ZLP, author = "Bruce M. Hill", title = "{Zipf}'s law and prior distributions for the composition of a population", journal = j-J-AM-STAT-ASSOC, volume = "65", number = "331", pages = "1220--1232", month = sep, year = "1970", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62.35", MRnumber = "0279936 (43 \#5657)", MRreviewer = "I. J. Good", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", URL = "http://www.jstor.org/stable/2284288", ZMnumber = "Zbl 0224.92011", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Orlov:1970:GZM, author = "Ju. K. Orlov", title = "A generalization of the {Zipf--Mandelbrot} law", journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe", volume = "57", pages = "37--40", year = "1970", CODEN = "????", ISSN = "????", MRclass = "94.50", MRnumber = "0274234 (42 \#9109)", MRreviewer = "T. Nemetz", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sakharth. SSR Mech. Akad. Moambe", } @Article{Taguchi:1970:ZLC, author = "Tokio Taguchi", title = "On {Zipf}'s law. {A} characterization of distributions in linguistics and demography", journal = j-PROC-INST-STATIST-MATH, volume = "17", pages = "83--90", year = "1970", CODEN = "????", ISSN = "0912-6112", ISSN-L = "0912-6112", bibdate = "Sat Nov 12 10:39:57 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0238.68026", acknowledgement = ack-nhfb, ajournal = "Proc. Inst. Statist. Math.", classmath = "68Q45 (Formal languages)", fjournal = "Proceedings of the Institute of Statistical Mathematics", language = "Japanese", } @Book{Zeller:1970:TLG, author = "Karl Zeller and Wolfgang Beekmann", title = "{Theorie der Limitierungsverfahren}. (German) [{Theory} of limiting processes]", volume = "15", publisher = pub-SV, address = pub-SV:adr, edition = "Second", pages = "xii + 314", year = "1970", LCCN = "QA295 .Z4 1970", bibdate = "Wed Nov 16 06:43:43 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Ergebnisse der Mathematik und ihrer Grenzgebiete", acknowledgement = ack-nhfb, language = "German", subject = "series; convergence", } @Article{Thorp:1971:PCD, author = "E. Thorp and R. Whitley", title = "{Poincar{\'e}}'s conjecture and the distribution of digits in logarithm tables", journal = j-COMPOS-MATH, volume = "21", number = "??", pages = "233--250", month = "????", year = "1971", CODEN = "CMPMAF", ISSN = "0010-437X (print), 1570-5846 (electronic)", ISSN-L = "0010-437X", bibdate = "Sat Nov 12 16:36:41 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Comp. Math.", fjournal = "Compositio Mathematica", } @Article{Wlodarski:1971:FLN, author = "J. Wlodarski", title = "{Fibonacci} and {Lucas} Numbers Tend to Obey {Benford's Law}", journal = j-FIB-QUART, volume = "9", number = "1", pages = "87--88", month = feb, year = "1971", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:05:33 MDT 2011", bibsource = "http://www.fq.math.ca/9-1.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Aigner:1972:CEP, author = "Dennis J. Aigner and Arthur S. Goldberger", title = "Corrigenda: Estimation of {Pareto's Law} from Grouped Observations", journal = j-J-AM-STAT-ASSOC, volume = "67", number = "337", pages = "252--252", month = mar, year = "1972", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:45 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314217; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib", URL = "http://www.jstor.org/stable/2284755", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Krevitt:1972:BCC, author = "Beth Krevitt and Belver C. Griffith", title = "Brief Communications: A comparison of several {Zipf}-type distributions in their goodness of fit to language data", journal = j-J-AM-SOC-INF-SCI, volume = "23", number = "3", pages = "220--221", month = may, year = "1972", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630230310", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:44 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Krevitt:1972:CSZ, author = "Beth Krevitt and Belver C. Griffith", title = "A comparison of several {Zipf}-type distributions in their goodness of fit to language data", journal = j-J-AM-SOC-INF-SCI, volume = "23", number = "3", pages = "220--221", year = "1972", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630230310", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Varian:1972:LEB, author = "Hal R. Varian", title = "Letter to the {Editor}: {Benford's Law}", journal = j-AMER-STAT, volume = "26", number = "3", pages = "65--66", month = jun, year = "1972", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Mar 30 11:34:37 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q", abstract = "Around 1938 the physicist Frank Benford observed a rather strange fact: tables of logarithms in libraries tend to be dirtier at the beginning than at the end. This indicated to Benford that people had more occasion to calculate with numbers beginning with 1 or 2 than with 8 or 9.\par Benford also found that the frequency of the digit $p$ being the first digit of a decimal number was very closely approximated by $ \log (p + 1) - \log p $ [i.e., $ \log (1 + 1 / p) $ ]. This has become known as Benford's law.", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Vlachy:1972:VFS, author = "Jan Vlach{\'y}", title = "Variable Factors in Scientific Communities (Observations on {Lotka's Law})", journal = "Teorie a Metoda", volume = "4", number = "??", pages = "91--120", month = "????", year = "1972", CODEN = "????", ISSN = "????", bibdate = "Fri Nov 25 07:53:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, xxvolume = "6", } @Article{Whitney:1972:MNI, author = "R. E. Whitney", title = "Mathematical Notes: Initial Digits for the Sequence of Primes", journal = j-AMER-MATH-MONTHLY, volume = "79", number = "2", pages = "150--152", month = feb, year = "1972", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2316536", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 28 12:36:38 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Wilkinson:1972:ABL, author = "Elizabeth A. Wilkinson", title = "The Ambiguity of {Bradford's Law}", journal = j-J-DOC, volume = "28", number = "2", pages = "122--130", month = "????", year = "1972", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026534", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:20:34 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @TechReport{Diaconis:1973:LMI, author = "Persi Diaconis", title = "Limits of measures of the integers with applications to random number generators and the distribution of leading digits", type = "Memorandum", number = "NS-211", institution = "Department of Statistics, Harvard University", address = "Cambridge, MA, USA", day = "22", month = mar, year = "1973", bibdate = "Sat Nov 12 16:23:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Kreifelts:1973:OBG, author = "Thomas Kreifelts", title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of Basis for a Floating-Point Arithmetic]", journal = j-COMPUTING, volume = "11", number = "4", pages = "353--363", month = dec, year = "1973", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Tue Jan 2 17:40:51 MST 2001", bibsource = "Compendex database; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; INSPEC Axiom database (1968--date)", note = "See correction \cite{Kreifelts:1975:OBF}.", acknowledgement = ack-nj # " and " # ack-nhfb, affiliation = "Inst. Numerische Datenverarbeitung, Bonn, West Germany", classification = "723; 921; C5230", description = "digital arithmetic", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", journalabr = "Comput (Vienna/NY)", keywords = "base; computer programming; floating point arithmetic; mathematical techniques; optimal choice; rounding errors", language = "German", } @Article{Kuipers:1973:RPD, author = "L. Kuipers and Jau-shyong Shiue", title = "Remark on a Paper by {Duncan} and {Brown} on the Sequence of Logarithms of Certain Recursive Sequences", journal = j-FIB-QUART, volume = "11", number = "3", pages = "292--293", month = oct, year = "1973", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:58:42 MDT 2011", bibsource = "http://www.fq.math.ca/11-3.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", note = "See \cite{Brown:1970:MOU}.", URL = "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Loynes:1973:SRP, author = "R. M. Loynes", title = "Some results in the probabilistic theory of asymptotic uniform distribution modulo 1", journal = j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB, volume = "26", number = "1", pages = "33--41", month = "????", year = "1973", CODEN = "ZWVGAA", DOI = "https://doi.org/10.1007/BF00533958", ISSN = "0044-3719", ISSN-L = "0044-3719", bibdate = "Sat Apr 26 19:24:39 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib", URL = "http://link.springer.com/article/10.1007/BF00533958", acknowledgement = ack-nhfb, fjournal = "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und verwandte Gebiete", journal-URL = "http://link.springer.com/journal/440", } @Article{Murphy:1973:BCL, author = "Larry J. Murphy", title = "Brief Communications: ``{Lotka's Law} in the humanities?''", journal = j-J-AM-SOC-INF-SCI, volume = "24", number = "6", pages = "461--462", month = nov, year = "1973", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630240607", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:48 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Murphy:1973:LLH, author = "Larry J. Murphy", title = "{Lotka's Law} in the Humanities?", journal = j-J-AM-SOC-INF-SCI, volume = "24", number = "6", pages = "461--462", month = nov # "\slash " # dec, year = "1973", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630240607", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:09:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Petruszewycz:1973:LLE, author = "M. Petruszewycz", title = "{L'histoire} de la loi d'{Estoup--Zipf}: documents. ({French}) [{The} history of the {Estoup--Zipf} law]", journal = "Math. Sci. Humaines", volume = "??", number = "44", pages = "41--56", year = "1973", CODEN = "????", ISSN = "0025-5815", ISSN-L = "0025-5815", MRclass = "92A25", MRnumber = "0354071 (50 \#6553)", MRreviewer = "J. S. Joel", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Centre de Math{\'e}matique Sociale. \'Ecole Pratique des Hautes \'Etudes. Math{\'e}matiques et Sciences Humaines", language = "French", } @Article{Sarkar:1973:OSD, author = "B. P. Sarkar", title = "An observation on the significant digits of the binomial coefficients and factorials", journal = j-SANKHYA-B, volume = "35", number = "??", pages = "363--364", month = "????", year = "1973", CODEN = "SANBBV", ISSN = "0976-8386 (print), 0976-8394 (electronic)", ISSN-L = "0976-8394", bibdate = "Sat Nov 12 16:29:39 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sankhya Ser. B (Indian J. of Statist.)", fjournal = "Sankhy{\=a} (Indian Journal of Statistics), Series B. Methodological", } @Article{Schatte:1973:VMG, author = "Peter Schatte", title = "{Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}. ({German}) [Distribution of the mantissa in the floating-point representation of a random variable]", journal = j-Z-ANGE-MATH-MECH, volume = "53", number = "??", pages = "553--565", month = "????", year = "1973", CODEN = "ZAMMAX", ISSN = "0044-2267 (print), 1521-4001 (electronic)", ISSN-L = "0044-2267", bibdate = "Mon Nov 14 16:35:28 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", language = "German", } @Article{Sentance:1973:FAB, author = "W. A. Sentance", title = "A Further Analysis of {Benford's Law}", journal = j-FIB-QUART, volume = "11", number = "5", pages = "490--494", month = dec, year = "1973", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:58:46 MDT 2011", bibsource = "http://www.fq.math.ca/11-5.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/11-5/sentance.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Banks:1974:AMN, author = "William P. Banks and David K. Hill", title = "The apparent magnitude of number scaled by random production", journal = j-J-EXP-PSYCH-GEN, volume = "102", number = "2", pages = "353--376", month = feb, year = "1974", CODEN = "JPGEDD", DOI = "https://doi.org/10.1037/h0035850", ISSN = "0096-3445 (print), 1939-2222 (electronic)", ISSN-L = "0096-3445", bibdate = "Fri Feb 15 06:32:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://psycnet.apa.org/journals/xge/102/2/353/; http://psycnet.apa.org/psycinfo/1974-24305-001", acknowledgement = ack-nhfb, fjournal = "Journal of Experimental Psychology: General", } @PhdThesis{Diaconis:1974:WSA, author = "Persi Diaconis", title = "Weak and Strong Averages in probability and the theory numbers", type = "{Ph.D.} thesis", school = "Department of Statistics, Harvard University", address = "Cambridge, MA, USA", pages = "xvii + 117", year = "1974", bibdate = "Mon Nov 14 10:26:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Duran:1974:ACS, author = "J. Peter Duran", title = "Almost convergence, summability and ergodicity", journal = j-CAN-J-MATH, volume = "26", number = "??", pages = "372--387", month = "????", year = "1974", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-1974-039-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:38:45 MDT 2011", bibsource = "http://cms.math.ca/cjm/v26/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", remark = "In relation to Benford's Law, see theorem 6.2.", } @Article{Hill:1974:RFF, author = "Bruce M. Hill", title = "The rank-frequency form of {Zipf}'s law", journal = j-J-AM-STAT-ASSOC, volume = "69", number = "348", pages = "1017--1026", month = dec, year = "1974", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62E15", MRnumber = "0426242 (54 \#14188)", MRreviewer = "S. M. Samuels", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", ZMnumber = "Zbl 0301.60011", acknowledgement = ack-nhfb, classification = "B0240 (Probability and statistics); C1140 (Probability and statistics)", corpsource = "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI, USA", fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "Bose--Einstein allocation; distribution; random processes; rank frequency form; statistics; Zipf's law", treatment = "T Theoretical or Mathematical", } @Book{Kuipers:1974:UDS, author = "Lauwerens Kuipers and Harald Niederreiter", title = "Uniform distribution of sequences", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 390", year = "1974", ISBN = "0-471-51045-9", ISBN-13 = "978-0-471-51045-1", LCCN = "QA292 .K84", bibdate = "Sat Nov 12 15:42:53 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Pure and applied mathematics", acknowledgement = ack-nhfb, remark = "``A Wiley-Interscience publication.''.", subject = "Sequences (Mathematics); Uniform distribution (Probability theory)", } @Article{Schorr:1974:LLL, author = "Alan E. Schorr", title = "{Lotka's Law} and Library Science", journal = "RQ", volume = "14", number = "1", pages = "32--33", month = "Fall", year = "1974", CODEN = "????", ISSN = "0033-7072", ISSN-L = "0033-7072", bibdate = "Fri Nov 25 08:12:46 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "RQ", fjournal = "Reference Quarterly", } @Unpublished{Singmaster:1974:RSB, author = "D. Singmaster", title = "Recurrent sequences and {Benford}'s law", year = "1974", bibdate = "Sat Nov 12 16:25:29 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Preprint submitted to Fibonacci Quarterly in 1974, but never published there.", acknowledgement = ack-nhfb, } @Book{Sterbenz:1974:FPC, author = "Pat H. Sterbenz", title = "Floating Point Computation", publisher = pub-PH, address = pub-PH:adr, pages = "xiv + 316", year = "1974", ISBN = "0-13-322495-3", ISBN-13 = "978-0-13-322495-5", LCCN = "QA76.8.I12 S771 1974", MRclass = "68A05 (65G05)", MRnumber = "50 1556", bibdate = "Sat May 29 08:01:36 1999", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib", series = "Prentice-Hall Series in Automatic Computation.", acknowledgement = ack-nj # " and " # ack-nhfb, keywords = "Compiling (Electronic computers); Computation by computer systems --- Floating point representation; Floating-point arithmetic; IBM 360 (Computer) --- Programming", remark = "From p. 116: ``There is general agreement that the mantissas of floating-point numbers are not uniformly distributed. [See Hamming (1962) [\cite{Hamming:1962:NMS}], Pinkham (1961) [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].] Instead, it is customary to assume that they are distributed logarithmically, that is, that the probability density function is $$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1} \leq m \leq 1. $$ This assumption is based on the following observations: First, this distribution reproduces itself under multiplication, but a uniform distribution does not. [See Hamming (1962) [\cite{Hamming:1962:NMS}] and Exercise 20.] A second justification is based on the fact that many of the numbers that arise in computation represent measurable quantities such as lengths, forces, etc., and it is reasonable to believe that the distribution of the mantissas of such quantities is independent of the units in which they are measured. Pinkham (1961) shows that this leads to the conclusion that the distribution of mantissas must be logarithmic.''", reviewer = "F. J. Murray", tableofcontents = "Preface / ix \\ 1. Floating-Point Number Systems / 1 \\ 1.1 Fixed-Point Calculation / 1 \\ 1.2 Floating-Decimal Representation of Numbers / 4 \\ 1.3 Floating-Decimal Arithmetic / 6 \\ 1.4 Floating-Point Number Systems / 9 \\ 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\ 1.6 Laws of Algebra / 14 \\ 1.7 Inequalities in FP(r,p, c) / 21 \\ 1.8 FP(r, p, clq) / 22 \\ 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\ 1.10 Division / 33 \\ Exercises / 35 \\ 2. Floating-Point Overflow and Underflow / 39 \\ 2.1 Bounds for Exponents / 39 \\ 2.2 $\Omega$-Zero Fixup / 41 \\ 2.3 Interrupt / 44 \\ 2.4 Messages and Tests / 46 \\ 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\ 2.6 Example / 50 \\ 2.7 Counting Mode / 57 \\ 2.8 Gradual Underflow / 59 \\ 2.9 Imprecise Interrupt / 61 \\ 2.10 Changing the Treatment of Spill / 62 \\ 2.11 Virtual Overflow and Underflow / 64 \\ 2.12 Division by Zero and Indeterminant Forms / 66 \\ Exercises / 67 \\ 3. Error Analysis / 71 \\ 3.1 Significant Digits / 71 \\ 3.2 Relative Error / 73 \\ 3.3 Relative Error in FP(r,p, clq) / 75 \\ 3.4 Approximate Laws of Algebra / 80 \\ 3.5 Propagation of Rounding Error / 87 \\ 3.6 X**N / 92 \\ 3.7 Condition / 98 \\ 3.8 Error Analysis of a Program / 103 \\ 3.9 Backward Error Analysis / 105 \\ 3.10 Examples / 107 \\ 3.11 Changing the Problem / 109 \\ 3.12 Statistical Error Analysis / 113 \\ Exercises / 117 \\ 4. Example / 123 \\ 4.1 Quadrature / 123 \\ 4.2 Power Series / 130 \\ 4.3 Exact Sums and Differences in FP(r, p, clq) / 137 \\ 4.4 Dismantling Floating-Point Numbers / 143 \\ Exercises / 146 \\ 5. Double-Precision Calculation / 154 \\ 5.1 Programs Using Double-Precision Arithmetic / 155 \\ 5.2 Implicit Typing of Names / 162 \\ 5.3 Routines to Perform Double-Precision Arithmetic / 163 \\ 5.4 Double-Precision Multiplication / 165 \\ 5.5 Double-Precision Addition and Subtraction / 168 \\ 5.6 Double-Precision Division / 171 \\ 5.7 Writing Double-Precision Programs Without Language Support / 178 \\ 5.8 Uses of Double-Precision / 180 \\ 5.9 Higher-Precision Arithmetic / 185 \\ Exercises / 186 \\ 6. Rounding / 189 \\ 6.1 General Considerations / 189 \\ 6.2 Uses of Rounding / 191 \\ 6.3 Implementation of Rounding / 192 \\ 6.4 Bias Removal / 194 \\ 6.5 Other ``Rounding'' Procedures / 197 \\ Exercises / 198 \\ 7. Automatic Analysis of Error / 201 \\ 7.1 Introduction / 201 \\ 7.2 Significance Arithmetic / 202 \\ 7.3 Noisy Mode / 205 \\ 7.4 Interval Arithmetic / 207 \\ 7.5 Rerunning the Program in Higher-Precision / 213 \\ Exercises / 222 \\ 8. Radix Conversion / 224 \\ 8.1 Equivalent Number of Digits / 224 \\ 8.2 Properties of Conversion Transformations / 228 \\ 8.3 Conversion Techniques / 232 \\ Exercises / 238 \\ 9/ Carefully Written Programs / 240 \\ 9.1 Introduction / 240 \\ 9.2 Average Problem / 240 \\ 9.3 Quadratic Equation / 246 \\ Exercises / 252 \\ 10. Checking and Testing / 255 \\ 10.1 Range Checking / 255 \\ 10.2 Mathematical Checks / 256 \\ 10.3 Testing / 259 \\ Exercises / 261 \\ 11. Language Features for Floating-Point Computation / 263 \\ 11.1 Introduction / 263 \\ 11.2 Predictability, Controllability, Observability / 264 \\ 11.3 Ease of Programming / 265 \\ 11.4 Machine Independence / 267 \\ Exercises / 269 \\ 12. Floating-Point Hardware / 271 \\ 12.1 Choice of Radix / 271 \\ 12.2 The Representation of Floating-Point Numbers / 273 \\ 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\ 12.4 Unnormalized Numbers and Unnormalized Arithmetic / 278 \\ Exercises / 282 \\ 13. Complex Numbers / 285 \\ 13.1 Programs Using Complex Numbers / 285 \\ 13.2 Relative Error / 286 \\ 13.3 Complex Arithmetic / 287 \\ Exercises / 297 \\ Bibliography / 301 \\ Glossary of Symbols / 309 \\ Index / 311", } @Article{Tsao:1974:DSD, author = "Nai Kuan Tsao", title = "On the Distributions of Significant Digits and Roundoff Errors", journal = j-CACM, volume = "17", number = "5", pages = "269--271", month = may, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65G05", MRnumber = "49 6595", MRreviewer = "N. N. Abdelmalek", bibdate = "Mon Jan 22 07:26:38 MST 2001", bibsource = "Compendex database; ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Generalized logarithmic law is derived for the distribution of the first $t$ significant digits of a random digital integer. This result is then used to determine the distribution of the roundoff errors in floating-point operations, which is a mixture of uniform and reciprocal distributions.", acknowledgement = ack-nhfb, classcodes = "C5230 (Digital arithmetic methods)", classification = "921", corpsource = "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "Benford's Law; digital arithmetic; digital integer; distributions; error analysis; floating point operations; Law of Anomalous Numbers; logarithmic law; mathematical techniques; mean value; random; reciprocal; roundoff errors; significant digits; uniform distribution; variance; Zipf's Law", oldlabel = "Tsao74", treatment = "T Theoretical or Mathematical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74", } @Article{Voos:1974:BCL, author = "Henry Voos", title = "Brief Communications: {Lotka} and information science", journal = j-J-AM-SOC-INF-SCI, volume = "25", number = "4", pages = "270--272", month = jul, year = "1974", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630250410", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:50 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Voos:1974:LIS, author = "Henry Voos", title = "{Lotka} and Information Science", journal = j-J-AM-SOC-INF-SCI, volume = "25", number = "4", pages = "270--272", month = jul # "\slash " # aug, year = "1974", CODEN = "AISJB6", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:14:01 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", keywords = "Lotka's Law", } @Article{Yavuz:1974:ZLE, author = "Davras Yavuz", title = "{Zipf}'s law and entropy", journal = j-IEEE-TRANS-INF-THEORY, volume = "20", number = "5", pages = "650--650", year = "1974", CODEN = "IETTAW", DOI = "https://doi.org/10.1109/TIT.1974.1055269", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", bibdate = "Sat Nov 12 10:43:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0295.94048", acknowledgement = ack-nhfb, classmath = "94A15 (General topics of information theory)", fjournal = "IEEE Transactions on Information Theory", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18", } @InProceedings{Bennett:1975:SDI, author = "John M. Bennett", booktitle = "Int. Comput. Symp. 1975, Proc., Antibes, (1975)", title = "Storage design for information retrieval: {Scarrott}'s conjecture and {Zipf}'s law", publisher = "????", address = "????", pages = "233--237", year = "1975", bibdate = "Sat Nov 12 10:49:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0322.68068", acknowledgement = ack-nhfb, classmath = "68P20 (Information storage and retrieval) 68N01 (General)", } @Book{Hardy:1975:ITN, author = "Godfrey H. Hardy and Edward M. Wright", title = "An Introduction to the Theory of Numbers", publisher = pub-CLARENDON, address = pub-CLARENDON:adr, edition = "Fourth", pages = "421", year = "1975", ISBN = "0-19-853310-1", ISBN-13 = "978-0-19-853310-8", LCCN = "????", bibdate = "Fri Jun 24 12:32:14 2005", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hill:1975:SFZ, author = "Bruce M. Hill and Michael Woodroofe", title = "Stronger forms of {Zipf}'s law", journal = j-J-AM-STAT-ASSOC, volume = "70", number = "349", pages = "212--219", month = mar, year = "1975", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62E15 (62D05)", MRnumber = "0440763 (55 \#13633)", MRreviewer = "I. J. Good", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", ZMnumber = "Zbl 0326.92014", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Kemperman:1975:BDM, author = "J. H. B. Kemperman", title = "Bounds on the discrepancy modulo $1$ of a real random variable", journal = j-BULL-INST-MATH-STAT, volume = "4", number = "1", pages = "138--138", month = "????", year = "1975", CODEN = "SMBCVA", ISSN = "0146-3942", ISSN-L = "0146-3942", bibdate = "Sat Nov 12 16:26:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Abstract no. 75t-47.", acknowledgement = ack-nhfb, fjournal = "Bulletin --- Institute of Mathematical Statistics", keywords = "Benford's Law", } @Article{Kreifelts:1975:OBF, author = "T. Kreifelts", title = "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik (Berichtigung)} ({German}) {Optimal Basis Choice for a Floating-Point Arithmetic (Correction)}", journal = j-COMPUTING, volume = "14", number = "3", pages = "313--314", month = sep, year = "1975", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", bibdate = "Fri Sep 16 16:30:39 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "See \cite{Kreifelts:1973:OBG}.", acknowledgement = ack-nj, fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", language = "German", } @Article{Partridge:1975:DDW, author = "D. Partridge", title = "A dynamic database which automatically removes unwanted generalisation for the efficient analysis of language features that exhibit a disparate frequency distribution", journal = j-COMP-J, volume = "18", number = "1", pages = "43--48", month = feb, year = "1975", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Tue Mar 25 13:51:56 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif", abstract = "A self-organising database was developed as part of a general language analysis system. The periodic, automatic reorganisation of the database was aimed at increasing the efficiency of analysis of a language in which the constituent features exhibit a Zipfian type rank-frequency relationship. Such a distribution means that only a small number of features account for a large proportion of the information, while a large number of possible features are seldom encountered and thus seldom accessed within the database. The mechanism described aims at reconciling two conflicting procedures: condensation by generalisation of language features to minimise the total size of the database, and the particularisation of the few commonly occurring features to minimise the average analysis time. Results are presented for the application of this mechanism to the analysis of batches of FORTRAN programs that constituted part of the `normal' workload for computers within five different environments.", acknowledgement = ack-nhfb, classcodes = "C6120 (File organisation); C7820 (Humanities computing)", classification = "723", corpsource = "Univ. Nairobi, Kenya", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "analysis; data bases; data processing; disparate frequency distribution; dynamic database; file organisation; language; language translation and linguistics; self organising; unwanted generalisation", treatment = "P Practical", } @Article{Pope:1975:BLP, author = "Andrew Pope", title = "{Bradford's Law} and the periodical literature of information science", journal = j-J-AM-SOC-INF-SCI, volume = "26", number = "4", pages = "207--213", month = jul, year = "1975", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630260403", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:54 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Schorr:1975:BCL, author = "Alan Edward Schorr", title = "Brief Communications: {Lotka's Law} and {Map Librarianship}", journal = j-J-AM-SOC-INF-SCI, volume = "26", number = "3", pages = "189--190", month = may, year = "1975", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630260308", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:53 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Schorr:1975:LLH, author = "Alan E. Schorr", title = "{Lotka's Law} and the History of Legal Medicine", journal = "Research in Librarianship", volume = "30", number = "??", pages = "205--209", month = sep, year = "1975", CODEN = "????", ISSN = "0034-5245", ISSN-L = "0034-5245", bibdate = "Fri Nov 25 08:17:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Res. Librarianship", } @Article{Schorr:1975:LLM, author = "Alan E. Schorr", title = "{Lotka's Law} and Map Librarianship", journal = j-J-AM-SOC-INF-SCI, volume = "26", number = "3", pages = "189--190", month = may # "\slash " # jun, year = "1975", CODEN = "AISJB6", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:11:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Webb:1975:DFD, author = "William Webb", title = "Distribution of the First Digits of {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "13", number = "4", pages = "334--336", month = dec, year = "1975", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:59:03 MDT 2011", bibsource = "http://www.fq.math.ca/13-4.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/13-4/webb.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", keywords = "Benford's Law", } @Article{Woodroofe:1975:ZL, author = "Michael Woodroofe and Bruce Hill", title = "On {Zipf}'s law", journal = j-J-APPL-PROBAB, volume = "12", number = "3", pages = "425--434", month = sep, year = "1975", CODEN = "JPRBAM", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "62E20 (62P10)", MRnumber = "0440764 (55 \#13634)", MRreviewer = "I. J. Good", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3212857", ZMnumber = "Zbl 0343.60012", abstract = "A Zipf's law is a probability distribution on the positive integers which decays algebraically. Such laws describe (approximately) a large class of phenomena. We formulate a model for such phenomena and, in terms of our model, give necessary and sufficient conditions for a Zipf's law to hold.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", journal-URL = "http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/", keywords = "classical occupancy problem; laws of large numbers: weak convergence; regularly varying functions", } @Article{Worthen:1975:ABL, author = "Dennis B. Worthen", title = "The Application of {Bradford's Law} to Monographs", journal = j-J-DOC, volume = "31", number = "1", pages = "19--25", month = "????", year = "1975", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026590", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:18:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{Allison:1976:LLP, author = "Paul D. Allison and Derek de Solla Price and Belver C. Griffith and Michael J. Moravcsik and John A. Stewart", title = "{Lotka's Law}: a Problem in Its Interpretation and Application", journal = j-SOC-STUD-SCI, volume = "6", number = "2", pages = "269--276", day = "1", month = may, year = "1976", CODEN = "SSSCDH", DOI = "https://doi.org/10.1177/030631277600600205", ISSN = "0306-3127 (print), 1460-3659 (electronic)", ISSN-L = "0306-3127", bibdate = "Mon Dec 3 09:12:29 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib", URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631277600600205", acknowledgement = ack-nhfb, fjournal = "Social Studies of Science", journal-URL = "http://sss.sagepub.com/content/by/year", keywords = "Lotka's Law of scientific authorship for the relative contributions of the most prolific authors", } @Article{Billera:1976:PSC, author = "Louis J. Billera and Robert E. Bixby", title = "{Pareto} Surfaces of Complexity $1$", journal = j-SIAM-J-APPL-MATH, volume = "30", number = "1", pages = "81--89", month = jan, year = "1976", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, classification = "B0250 (Combinatorial mathematics); C1160 (Combinatorial mathematics)", corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA", fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", keywords = "1-commodity representation; attainable sets; complexity 1; game theory; graph theory; Pareto surfaces; set theory", treatment = "T Theoretical or Mathematical", } @Article{Brambilla:1976:DDA, author = "Francisco Brambilla", title = "La distribuzione delle aziende secondo le dimensioni. {Verifica} empirica della legge logonormale e di quella di {Zipf} e nuovi modelli interpretativi. ({Italian}) [{The} distribution of firms by size. {Empirical} test of the log-normal law and {Zipf}'s law and new models of interpretation]", journal = "Giornale degli Economisti e Annali de Economia (Nuova Serie)", volume = "35", number = "3--4", pages = "131--153, 235", month = mar # "\slash " # apr, year = "1976", CODEN = "????", ISSN = "0017-0097", ISSN-L = "0017-0097", MRclass = "90A15", MRnumber = "0452510 (56 \#10789)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/23242834", acknowledgement = ack-nhfb, ajournal = "Giorn. Econom. Ann. Econom. (N.S.)", fjournal = "Giornale degli Economisti e Annali de Economia", language = "Italian", } @Article{Cohen:1976:EFD, author = "Daniel I. A. Cohen", title = "An explanation of the first digit phenomenon", journal = j-J-COMB-THEORY-A, volume = "20", number = "3", pages = "367--370", month = may, year = "1976", CODEN = "JCBTA7", ISSN = "0097-3165 (print), 1096-0899 (electronic)", ISSN-L = "0097-3165", bibdate = "Thu Feb 15 16:29:51 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Combinatorial Theory (Series A)", journal-URL = "http://www.sciencedirect.com/science/journal/00973165", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Davis:1976:SRI, author = "Basil Davis", title = "Some Remarks on Initial Digits", journal = j-FIB-QUART, volume = "14", number = "1", pages = "13--14", month = feb, year = "1976", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:59:05 MDT 2011", bibsource = "http://www.fq.math.ca/14-1.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/14-1/davis.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Feldstein:1976:CED, author = "Alan Feldstein and Richard Goodman", title = "Convergence Estimates for the Distribution of Trailing Digits", journal = j-J-ACM, volume = "23", number = "2", pages = "287--297", month = apr, year = "1976", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/321941.321948", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Wed Jan 15 18:12:53 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "An analysis is made of the distribution of trailing digits (tail end digits) of positive real floating-point numbers represented in arbitrary base $ \beta $ and randomly chosen from a logarithmic distribution. The analysis shows that the $n$ th digit for $ n \geq 2 $ is actually approximately uniformly distributed. The approximation depends upon both $n$ and the base beta. It becomes better as $n$ increases, and it is exact in the limit as $ n \rightarrow \infty $. A table of this distribution is presented for various $ \beta $ and $n$, along with a table of the maximum digit by digit deviation $ \Delta $ of the logarithmic distribution from the uniform distribution. Various asymptotic results for $ \Delta $ are included.", acknowledgement = ack-nhfb, classification = "723", fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", journalabr = "J Assoc Comput Mach", keywords = "Benford's Law; computer arithmetic; computer programming; Law of Anomalous Numbers; Zipf's Law", } @Article{Haspers:1976:YFB, author = "Jan H. Haspers", title = "The yield formula and {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "27", number = "5", pages = "281--287", month = sep, year = "1976", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630270503", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:57 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Hubert:1976:NIB, author = "John J. Hubert", title = "On the {Naranan} interpretation of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "27", number = "5", pages = "339--341", month = sep, year = "1976", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630270510", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:57 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Orlov:1976:CBP, author = "Ju. K. Orlov", title = "The connection between the {Pareto} distribution and the generalized {Zipf--Mandelbrot} law", journal = "Sakharthvelos SSR Mecnierebatha Akademiis Moambe", volume = "83", number = "1", pages = "57--60", year = "1976", CODEN = "????", ISSN = "????", MRclass = "90A15", MRnumber = "0434355 (55 \#7321)", MRreviewer = "S. Krcevinac", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Sakharth. SSR Mech. Akad. Moambe", } @Article{Raimi:1976:FDP, author = "Ralph A. Raimi", title = "The first digit problem", journal = j-AMER-MATH-MONTHLY, volume = "83", number = "7", pages = "521--538", month = aug # "\slash " # sep, year = "1976", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2319349", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Sat Nov 12 15:49:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2319349", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", remark = "This article surveys the literature up to 1976, reports defects in several earlier mathematical `explanations' of Benford's Law, and gives a 52-entry bibliography of prior work. All of those entries are incorporated in this bibliography. It criticizes parts of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the author reiterates that view in \cite{Raimi:1985:FDP}). See also later work \cite{Logan:1978:FDP}. On page 529, Raimi writes ``If the first digits of all the tables in the universe obey some fixed distribution law, Stigler's or Benford's or some other, that law must surely be independent of the system of units chosen, since God is not known to favor either the metric system or the English system. In other words, a universal first digit law, if it exists, must be scale-invariant.''", remark-2 = "This is so far the second earliest reference that I have found to \cite{Newcomb:1881:NFU}; the earliest is \cite{Boring:1920:LNL}, which has only brief mention of the question of digit frequencies. Raimi comments on p. 522: ``This assertion, whatever it may mean, will be called Benford's Law because it has been thought by many writers to have originated with the General Electric Company physicist Frank Benford [2]. Certainly Benford popularized the problem, and he may well have been unaware that the polymathic Simon Newcomb, primarily an astronomer but also sometime editor of The American Journal of Mathematics, had also formulated the same law 57 years earlier [1]. There is ample precedent for naming laws and theorems for persons other than their discoverers, else half of analysis would be named after Euler. Besides, even Newcomb implied that the observation giving rise to the Benford law was an old one in his day. One would hate to change the name of the law now only to find later that another change was called for.''", } @Article{Rouault:1976:PAE, author = "Alain Rouault", title = "Propri{\'e}t{\'e}s asymptotiques d'un {$n$}-{\'e}chantillon d'une variable al{\'e}atoire d{\'e}nombrable connues sous le nom de lois de {Zipf}. ({French}) [Asymptotic properties of an $n$-sample of a denumerable random variable known under the name of {Zipf}'s law]", journal = j-C-R-ACAD-SCI-PARIS-SER-AB, volume = "283", number = "6", pages = "Aiv, A379--A380", year = "1976", CODEN = "CHASAP", ISSN = "0151-0509", ISSN-L = "0151-0509", MRclass = "62E20", MRnumber = "0423644 (54 \#11619)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de l'Acad{\'e}mie des Sciences. S{\'e}ries A et B", language = "French", } @Article{Rouault:1976:SML, author = "Alain Rouault", title = "Sources markoviennes et lois de {Zipf}. ({French}) [{Markovian} source and {Zipf} laws]", journal = j-C-R-ACAD-SCI-PARIS-SER-AB, volume = "283", number = "10", pages = "Aiii, A789--A790", year = "1976", CODEN = "CHASAP", ISSN = "0151-0509", ISSN-L = "0151-0509", MRclass = "62E20", MRnumber = "0423645 (54 \#11620)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Comptes Rendus Hebdomadaires des S{\'e}ances de l'Acad{\'e}mie des Sciences. S{\'e}ries A et B", language = "French", } @Article{Vlachy:1976:TFL, author = "Jan Vlach{\'y}", title = "Time Factor in {Lotka's Law}", journal = "Probleme de Informare si Documentare", volume = "10", number = "2", pages = "44--87", month = "????", year = "1976", CODEN = "PIDCA6", ISSN = "0032-924X", ISSN-L = "0032-924X", bibdate = "Fri Nov 25 07:56:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Prob. inf. \& doc.", } @Article{Brookes:1977:TBL, author = "Bertram C. Brookes", title = "Theory of the {Bradford Law}", journal = j-J-DOC, volume = "33", number = "3", pages = "180--209", month = "????", year = "1977", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026641", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:16:18 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{Clark:1977:ESL, author = "Douglas W. Clark and C. Cordell Green", title = "An Empirical Study of List Structure in {Lisp}", journal = j-CACM, volume = "20", number = "2", pages = "78--87", month = feb, year = "1977", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Mon Jan 22 06:31:28 MST 2001", bibsource = "Compendex database; ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib; http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Static measurements of the list structure of five large Lisp programs are reported and analyzed. These measurements reveal substantial regularity, or predictability, among pointers to atoms and especially among pointers to lists. Pointers to atoms are found to obey, roughly, Zipf's law, which governs word frequencies in natural languages; pointers to lists usually point to a location physically nearby in memory. The use of such regularities in the space-efficient representation of list structure is discussed.", acknowledgement = ack-nhfb, classcodes = "C6130 (Data handling techniques); C6140D (High level languages)", classification = "723", comment = "Great paper; evidence pro CDR-coding, con fancy CONS", corpsource = "Carnegie-Mellon Univ., Pittsburgh, PA, USA", fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", journalabr = "Commun ACM", keywords = "computer programming languages; data processing --- Data Structures; empirical study; LISP; list structure; measurements; regularity", oldlabel = "ClarkG77", treatment = "P Practical", XMLdata = "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77", } @Article{Coile:1977:LFD, author = "Russell C. Coile", title = "{Lotka}'s Frequency Distribution of Scientific Productivity", journal = j-J-AM-SOC-INF-SCI, volume = "28", number = "6", pages = "366--370", month = nov, year = "1977", CODEN = "AISJB6", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 08:08:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", keywords = "Lotka's Law", } @Article{Diaconis:1977:DLD, author = "Persi Diaconis", title = "The distribution of leading digits and uniform distribution $ \bmod 1 $", journal = j-ANN-PROBAB, volume = "5", number = "1", pages = "72--81", month = feb, year = "1977", CODEN = "APBYAE", DOI = "https://doi.org/10.1214/aop/1176995891", ISSN = "0091-1798 (print), 2168-894X (electronic)", ISSN-L = "0091-1798", bibdate = "Sun Apr 20 10:44:17 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.aop/1176995891", acknowledgement = ack-nhfb, fjournal = "Annals of Probability", journal-URL = "http://projecteuclid.org/all/euclid.aop", keywords = "Benford's Law", } @Article{Goudsmit:1977:PEP, author = "Samuel Goudsmit", title = "Pitfalls in Elementary Probability", journal = j-PROC-AMER-PHIL-SOC, volume = "121", number = "2", pages = "188--189", day = "29", month = apr, year = "1977", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Fri Mar 22 08:50:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Based on a lecture presented November 11, 1976.", URL = "http://www.jstor.org/stable/986527", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", keywords = "Benford's Law; biased coin flips; biased dice throws; roulette wheels", } @Article{Hubert:1977:LEL, author = "John J. Hubert", title = "Letters to the {Editor}: {Lotka's Law} in the humanities", journal = j-J-AM-SOC-INF-SCI, volume = "28", number = "1", pages = "66--66", month = jan, year = "1977", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630280115", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Krisciunas:1977:LEL, author = "Kevin Krisciunas", title = "Letters to the {Editor}: {Lotka's Law} --- year by year", journal = j-J-AM-SOC-INF-SCI, volume = "28", number = "1", pages = "65--66", month = jan, year = "1977", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630280114", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:02:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Kubovy:1977:RAA, author = "M. Kubovy", title = "Response Availability and the Apparent Spontaneity of Numerical Choices", journal = "Journal of Experimental Psychology: Human Performance and Performance", volume = "3", number = "2", pages = "359--364", month = may, year = "1977", DOI = "https://doi.org/10.1037/0096-1523.3.2.359", ISSN = "0096-1523 (print), 1939-1277 (electronic)", ISSN-L = "0096-1523", bibdate = "Sat Sep 10 12:51:40 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://psycnet.apa.org/index.cfm?fa=search.displayrecord&uid=1977-30946-001", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Ylvisaker:1977:TR, author = "Donald Ylvisaker", title = "Test Resistance", journal = j-J-AM-STAT-ASSOC, volume = "72", number = "359", pages = "551--556", month = sep, year = "1977", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Jan 25 08:05:48 MST 2012", bibsource = "http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314242; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib", URL = "http://www.jstor.org/stable/2286216", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Brady:1978:MBL, author = "W. G. Brady", title = "More on {Benford}'s Law", journal = j-FIB-QUART, volume = "16", number = "1", pages = "51--52", month = feb, year = "1978", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 17:59:24 MDT 2011", bibsource = "http://www.fq.math.ca/16-1.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/16-1/brady.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly", journal-URL = "http://www.fq.math.ca/", } @Article{Brookes:1978:FRD, author = "Bertram C. Brookes and Jos{\'e} M. Griffiths", title = "Frequency-rank distributions", journal = j-J-AM-SOC-INF-SCI, volume = "29", number = "1", pages = "5--13", month = jan, year = "1978", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630290104", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 10:40:13 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", keywords = "Anomalous Law of Numbers; Benford's Law", } @PhdThesis{Chen:1978:ZL, author = "Wen-Chen Chen", title = "On {Zipf}'s law", type = "Thesis ({Ph.D.})", school = "University of Michigan", address = "Ann Arbor, MI, USA", pages = "114", year = "1978", MRclass = "Thesis", MRnumber = "2627928", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871", acknowledgement = ack-nhfb, remark = "Available from ProQuest LLC, Ann Arbor, MI, USA. Author given name appears as Wen-Cheng in MathSciNet database.", } @Article{Drott:1978:EEB, author = "M. Carl Drott and Belver C. Griffith", title = "An empirical examination of {Bradford's Law} and the scattering of scientific literature", journal = j-J-AM-SOC-INF-SCI, volume = "29", number = "5", pages = "238--246", month = sep, year = "1978", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630290506", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:02 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Elshoff:1978:SSC, author = "James L. Elshoff", title = "A study of the structural composition of {PL/I} programs", journal = j-SIGPLAN, volume = "13", number = "6", pages = "29--37", month = jun, year = "1978", CODEN = "SINODQ", DOI = "https://doi.org/10.1145/987515.987518", ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic)", ISSN-L = "0362-1340", bibdate = "Wed Jun 18 16:08:52 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Some research on a theory of the structural composition of an algorithm has recently been reported. The theory embodies models of operator and operand distributions that have been proposed by Bayer, Zipf, and Zweben. This paper reports a study in which the three models of operator distributions are compared with the measured distributions found in 34 PL/I programs. Two of three models, one by Zipf and one by Zweben, are shown to correlate highly with the measured distributions. Two variations of the Zipf model are then formulated and tested with good results. Also, the relationship between the method of counting operators and the models is investigated.", acknowledgement = ack-nhfb, classification = "C4240 (Programming and algorithm theory); C6140D (High level languages)", corpsource = "Computer Sci. Dept., General Motors Res. Labs., Warren, MI, USA", fjournal = "ACM SIG{\-}PLAN Notices", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706", keywords = "counting operators; operator distributions; PL/1; PL/1 programs; programming theory; structural composition", treatment = "T Theoretical or Mathematical", } @Book{Heaps:1978:IRC, author = "Harold Stanley Heaps", title = "Information retrieval, computational and theoretical aspects", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xii + 344", year = "1978", ISBN = "0-12-335750-0", ISBN-13 = "978-0-12-335750-2", LCCN = "Z699 .H38", bibdate = "Sat Nov 12 11:36:39 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Library and information science", acknowledgement = ack-nhfb, remark = "Heaps's Law is given on pp. 206--208.", subject = "Information storage and retrieval systems", } @Article{Hubert:1978:BCR, author = "John J. Hubert", title = "Brief Communications: A relationship between two forms of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "29", number = "3", pages = "159--161", month = may, year = "1978", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630290311", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:01 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "23 Mar 2007", } @Article{Logan:1978:FDP, author = "Jonothan L. Logan and Samuel A. Goudsmit", title = "The First Digit Phenomenon", journal = j-PROC-AMER-PHIL-SOC, volume = "122", number = "4", pages = "193--197", day = "18", month = aug, year = "1978", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Fri Mar 30 11:20:35 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "This paper contains derivations of both Stigler's Law and Benford's Law, and receives strong criticism in \cite{Raimi:1985:FDP}. This paper contains an important historical note that is recorded in entry \cite{Benford:1938:LAN}.", URL = "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C; http://www.jstor.org/stable/986530", abstract = "Forty years ago an article appeared in these Proceedings, which has since then attracted much attention of mathematicians and some physicists. It was written by Frank Benford, a physicist from the General Electric Company at Schenectady. He had examined a large number of numerical tables, the kind that are printed in almanacs, and in scientific and technical handbooks. He noticed a most unusual and unexpected property of many of these tables. Consider, for example, the numbers representing the populations of states or all the countries in the world, or their areas, their budgets, their numbers of hospital beds, etc. One would expect that on the average just as many of these entries would begin with the digit $1$ as with $2$ or $3$ or $4$, and so on. But Benford noticed that small values of the first digits occur far more often.", acknowledgement = ack-nhfb, author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)", fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", remark = "In 1925, Samuel Goudsmit and George Uhlenbeck proposed the concept of electron spin, a critical step forward in the quantum mechanics of many-electron systems. Surprisingly, that work did not get them the Nobel Prize, but it did spur Wolfgang Pauli to present his Exclusion Principle in 1925, for which he received the 1945 Nobel Prize in Physics. After World War II, Goudsmit was the scientific head of the Alsos mission to capture German nuclear scientists. In the 1950s, he founded the journal Physical Review Letters. During the 1960s and 1970s, he was Editor-in-Chief of the main American physics journal, the Physical Review.", } @Article{Praunlich:1978:BDN, author = "Peter Praunlich and Michael Kroll", title = "{Bradford}'s distribution: a new formulation", journal = j-J-AM-SOC-INF-SCI, volume = "29", number = "2", pages = "51--55", month = mar, year = "1978", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630290203", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:01 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Rouault:1978:LZS, author = "Alain Rouault", title = "Lois de {Zipf} et sources markoviennes. ({French}) [{Zipf}'s law and {Markovian} sources]", journal = "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)", volume = "14", number = "2", pages = "169--188", year = "1978", CODEN = "AHPBAR", ISSN = "0020-2347", ISSN-L = "0020-2347", MRclass = "62E99 (60J20 62P99)", MRnumber = "507732 (80c:62026a)", MRreviewer = "Bruce M. Hill", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annales de l'Institut Henri Poincar{\'e}. Section B. Calcul des Probabilit{\'e}s et Statistique. Nouvelle S{\'e}rie", language = "French", } @Article{Samson:1978:STU, author = "W. B. Samson and R. H. Davis", title = "Search Times Using Hash Tables for Records with Non-Unique Keys", journal = j-COMP-J, volume = "21", number = "3", pages = "210--214", month = aug, year = "1978", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Tue Mar 25 13:51:56 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/hash.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif", abstract = "Recent research in hash coding has concentrated on unique keys, or uniform distributions of keys. This paper is intended to clarify the effect of non-unique keys with various distributions on search times in the hash table thus enabling recommendations to be made to those who must deal with hash tables of this type. It is found that extreme rank-order frequency distribution of keys, such as the Zipf distribution, result in much higher access times than more uniform distributions, but it is possible to reduce these to some extent by loading records with common keys on to the hash table first.", acknowledgement = ack-nhfb, classcodes = "C6120 (File organisation); C6130 (Data handling techniques)", classification = "723", corpsource = "Dept. of Math. and Computer Studies, Dundee Coll. of Technol., Dundee, UK", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", journalabr = "Comput J", keywords = "common keys; compiler symbol; computer programming; data handling; data processing --- Data Structures; direct access files; distribution; extreme; file organisation; hash tables; higher access times; non unique keys; overflow method; rank order frequency distribution of keys; records; search times; simulation; tables; uniform distributions; Zipf", treatment = "T Theoretical or Mathematical", } @Article{Brookes:1979:LEB, author = "B. C. Brookes", title = "Letters to the {Editor}: The {Bradford Law}: a new calculus for the social sciences?", journal = j-J-AM-SOC-INF-SCI, volume = "30", number = "4", pages = "233--234", month = jul, year = "1979", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630300412", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:05 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Diaconis:1979:RP, author = "Persi Diaconis and David Freedman", title = "On Rounding Percentages", journal = j-J-AM-STAT-ASSOC, volume = "74", number = "366", pages = "359--364", month = jun, year = "1979", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Nov 23 11:24:59 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", note = "The authors extend prior work on correctness of sums of rounded percentages \cite{Mosteller:1967:DSR}, and criticize biased rounding practices in \cite{Benford:1938:LAN}.", URL = "http://www.jstor.org/stable/2284288", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", keywords = "Benford's Law", remark = "When percentage-column entries are rounded, their sum may differ from 100\%. The authors use a prior proof \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded values, the probability of a correct sum is $ \sqrt {6 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that rounding may produce large changes in computed chi-squared values, and they conclude their article with this recommendation: ``it is important to calculate with many-digit accuracy when computing $ \chi^2 $ for large sample sizes.''", } @Article{Marulli:1979:BCB, author = "Luciana Marulli and Michael E. D. Koenig", title = "Brief Communications: {Bradford} distribution of data elements", journal = j-J-AM-SOC-INF-SCI, volume = "30", number = "2", pages = "107--108", month = mar, year = "1979", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630300209", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:04 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Mohanty:1979:MMQ, author = "Siba N. Mohanty", title = "Models and Measurements for Quality Assessment of Software", journal = j-COMP-SURV, volume = "11", number = "3", pages = "251--275", month = sep, year = "1979", CODEN = "CMSVAN", DOI = "https://doi.org/10.1145/356778.356783", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:25:12 MDT 2008", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib; http://www.acm.org/pubs/contents/journals/surveys/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.", acknowledgement = ack-nhfb, annote = "Several software quality assessment methods which span the software life cycle are discussed. The quality of a system design can be estimated by measuring the system entropy function or the system work function. The quality improvement due to reconfiguration can be determined by calculating system entropy loading measures. Software science and Zipf's law are shown to be useful for estimating program length and implementation time.", country = "USA", date = "11/10/79", descriptors = "Software; design; software engineering; reliability; measurement; model; fundamentals in statistics; performance evaluation", enum = "2189", fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", references = "65", } @Article{Radhakrishnan:1979:LLC, author = "T. Radhakrishnan and R. Kernizan", title = "{Lotka's Law} and Computer Science Literature", journal = j-J-AM-SOC-INF-SCI, volume = "30", number = "1", pages = "51--54", month = jan, year = "1979", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630300109", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Nov 25 07:45:09 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "6 September 2007", remark = "This paper analyzes publication statistics from Communications of the Association for Computing Machinery (CACM) and in the Journal of the ACM (JACM).", } @Article{Vlachy:1979:FDS, author = "Jan Vlach{\'y}", title = "Frequency Distribution of Scientific Performance: a Bibliography of {Lotka's Law} and Related Phenomena", journal = j-SCIENTOMETRICS, volume = "1", number = "1", pages = "107--130", month = sep, year = "1979", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02016844", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Fri Nov 25 07:59:34 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/BF02016844; http://www.springerlink.com/content/0138-9130/", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", xxjournal = "Scientometrics, Bibliography Section", } @Article{Brookes:1980:FISa, author = "Bertram C. Brookes", title = "The foundations of information science. {Part I}. {Philosophical} aspects", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "3--4", pages = "125--133", month = jun, year = "1980", CODEN = "JISCDI", DOI = "https://doi.org/10.1177/016555158000200302", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/3-4/125.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", journal-URL = "http://jis.sagepub.com/", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1980:FISb, author = "Bertram C. Brookes", title = "The foundations of information science. {Part II}. {Quantitative} aspects: classes of things and the challenge of human individuality", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "5", pages = "209--221", month = oct, year = "1980", CODEN = "JISCDI", DOI = "https://doi.org/10.1177/016555158000200502", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 11:01:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/5/209.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", journal-URL = "http://jis.sagepub.com/", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Brookes:1980:FISc, author = "Bertram C. Brookes", title = "The foundations of information science. {Part III}. {Quantitative} aspects: Objective maps and subjective landscapes", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "2", number = "6", pages = "269--275", month = dec, year = "1980", CODEN = "JISCDI", DOI = "https://doi.org/10.1177/016555158000200602", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/2/6/269.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", journal-URL = "http://jis.sagepub.com/", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Chen:1980:WFZ, author = "Wen Chen Chen", title = "On the weak form of {Zipf}'s law", journal = j-J-APPL-PROBAB, volume = "17", number = "3", pages = "611--622", year = "1980", CODEN = "JPRBAM", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "62E10 (62F10)", MRnumber = "580021 (81m:62021)", MRreviewer = "Patrick L. Brockett", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3212955", ZMnumber = "Zbl 0435.60017", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", journal-URL = "http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/", } @Article{Dunn:1980:SFW, author = "Stanley Dunn", title = "Surveyor's Forum: {Working} on Interpretations", journal = j-COMP-SURV, volume = "12", number = "2", pages = "255--255", month = jun, year = "1980", CODEN = "CMSVAN", DOI = "https://doi.org/10.1145/356810.356817", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:27:10 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/surveys/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.", acknowledgement = ack-nhfb, fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", } @Article{Leimkuhler:1980:EFB, author = "Ferdinand F. Leimkuhler", title = "An Exact Formulation of {Bradford's Law}", journal = j-J-DOC, volume = "36", number = "4", pages = "285--292", month = "????", year = "1980", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026699", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:14:04 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "An exact, discrete formulation of Bradford's law describing the distribution of articles in journals is derived by showing that Bradford's law is a special case of the Zipf--Mandelbrot `rank frequency' law. A relatively simple method is presented for fitting the model to empirical data and estimating the number of journals and articles in a subject collection. This method is demonstrated with an example application.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{McKee:1980:POR, author = "Arnold F. McKee", title = "The {Pareto} Optimum: Reconcilable with Social Thought?", journal = "International Journal of Social Economics", volume = "7", number = "7", pages = "366--375", month = "????", year = "1980", CODEN = "ISLEBC", DOI = "https://doi.org/10.1108/eb013878", ISSN = "0306-8293 (print), 1758-6712 (electronic)", ISSN-L = "0306-8293", bibdate = "Fri Nov 25 07:01:57 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Mohanty:1980:SFW, author = "Siba Mohanty", title = "Surveyor's Forum: {Working} on Interpretations", journal = j-COMP-SURV, volume = "12", number = "2", pages = "256--256", month = jun, year = "1980", CODEN = "CMSVAN", DOI = "https://doi.org/10.1145/356810.356818", ISSN = "0010-4892", ISSN-L = "0360-0300", bibdate = "Thu Jun 19 09:27:10 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/surveys/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.", acknowledgement = ack-nhfb, fjournal = "ACM Computing Surveys", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J204", } @Article{Asai:1981:GFB, author = "Isao Asai", title = "A general formulation of {Bradford}'s distribution: the graph-oriented approach", journal = j-J-AM-SOC-INF-SCI, volume = "32", number = "2", pages = "113--119", month = mar, year = "1981", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630320206", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:10 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Brookes:1981:FIS, author = "Bertram C. Brookes", title = "The foundations of information science. {Part IV}. {Information} science: the changing paradigm", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "3", number = "1", pages = "3--12", month = feb, year = "1981", CODEN = "JISCDI", DOI = "https://doi.org/10.1177/016555158100300102", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Mon Feb 25 10:36:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jis.sagepub.com/content/3/1/3", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", journal-URL = "http://jis.sagepub.com/", keywords = "Anomalous Law of Numbers; Benford's Law", } @Book{Fleiss:1981:SMR, author = "Joseph L. Fleiss", title = "Statistical Methods for Rates and Proportions", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xviii + 321", year = "1981", ISBN = "0-471-06428-9", ISBN-13 = "978-0-471-06428-2", LCCN = "QA279 .F58 1981", bibdate = "Fri Mar 22 08:46:57 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley series in probability and mathematical statistics", URL = "http://www.loc.gov/catdir/description/wiley032/80026382.html; http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html; http://www.loc.gov/catdir/toc/onix02/80026382.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Analysis of variance; Sampling (Statistics); Biometry", } @Article{Kennard:1981:MDF, author = "Robert W. Kennard and John E. Reith", title = "{M32}. {On} the distribution of first digits", journal = j-COMMUN-STAT-SIMUL-COMPUT, volume = "10", number = "1", pages = "97--98", year = "1981", CODEN = "CSSCDB", DOI = "https://doi.org/10.1080/03610918108812195", ISSN = "0361-0918", ISSN-L = "0361-0918", bibdate = "Sat Jan 30 06:32:15 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics: Simulation and Computation", journal-URL = "http://www.tandfonline.com/loi/lssp20", keywords = "Benford's Law", onlinedate = "27 Jun 2007", } @Article{Morse:1981:IEB, author = "Philip M. Morse", title = "Implications of the exact {Bradford} distribution", journal = j-J-AM-SOC-INF-SCI, volume = "32", number = "1", pages = "43--50", month = jan, year = "1981", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630320106", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:10 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "22 Mar 2007", } @Article{Pavlov:1981:DFF, author = "A. I. Pavlov", title = "On the distribution of fractions and {F. Benford}'s law", journal = j-IZV-AKAD-NAUK-SSSR-MAT, volume = "45", number = "4", pages = "760--774, 927", year = "1981", CODEN = "IZAMAT", ISSN = "0373-2436", ISSN-L = "0373-2436", MRclass = "10K10", MRnumber = "631437 (83m:10093)", MRreviewer = "Michael Keane", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia (Moscow)", xxtitle = "On the distribution mod one and {Benford}'s law", } @Article{Peters:1981:EFB, author = "James V. Peters", title = "An Equivalent Form of {Benford's Law}", journal = j-FIB-QUART, volume = "19", number = "1", pages = "74--76", month = feb, year = "1981", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", MRclass = "60C05 (10K10 60-01)", MRnumber = "606117 (82k:60024)", MRreviewer = "L. E. Clarke", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.fq.math.ca/19-1.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/19-1/peters.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Peters:1981:SCC, author = "James V. Peters", title = "Short Communications: a combinatoric proof of {Benford}'s law", journal = j-AEQUATIONES-MATHEMATICAE, volume = "23", number = "1", pages = "122--123", year = "1981", CODEN = "AEMABN", DOI = "https://doi.org/10.1007/BF02188018", ISSN = "0001-9054 (print), 1420-8903 (electronic)", ISSN-L = "0001-9054", MRclass = "Contributed Item", MRnumber = "1553878", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/accesspage/article/10.1007/BF02188018", acknowledgement = ack-nhfb, fjournal = "Aequationes Mathematicae", journal-URL = "http://link.springer.com/journal/10", } @Article{Potter:1981:LLR, author = "William Gray Potter", title = "{Lotka's Law} revisited", journal = j-LIBR-TRENDS, volume = "31", number = "2", pages = "21--39", month = "Summer", year = "1981", CODEN = "LIBTA3", ISSN = "0024-2594 (print), 1559-0682 (electronic)", ISSN-L = "0024-2594", bibdate = "Thu Nov 24 14:41:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842", acknowledgement = ack-nhfb, fjournal = "Library Trends", } @Article{Preece:1981:DFD, author = "D. A. Preece", title = "Distributions of Final Digits in Data", journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN, volume = "30", number = "1", pages = "31--60", month = mar, year = "1981", ISSN = "0039-0526 (print), 1467-9884 (electronic)", ISSN-L = "0039-0526", bibdate = "Wed Nov 23 12:19:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2987702", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series D (The Statistician)", journal-URL = "http://www.jstor.org/journals/00390526.html", remark = "This paper extends previous work \cite{Yule:1927:RS} on human bias in the recording of last digits in measurements, or from roundings, or from later scale conversions, and how such bias can be detected.", } @Article{Schatte:1981:RVL, author = "Peter Schatte", title = "On random variables with logarithmic mantissa distribution relative to several bases", journal = j-ELEK-INFO-KYBER, volume = "17", number = "??", pages = "293--295", month = "????", year = "1981", CODEN = "EIVKAX", ISSN = "0013-5712", ISSN-L = "0013-5712", bibdate = "Sat Nov 12 15:53:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elektronische Informationsverarbeitung und Kybernetik (EIK)", } @Article{Washington:1981:BLF, author = "Lawrence C. Washington", title = "{Benford's Law} for {Fibonacci} and {Lucas} Numbers", journal = j-FIB-QUART, volume = "19", number = "2", pages = "175--177", month = apr, year = "1981", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", MRclass = "10A30 (10A35)", MRnumber = "614056 (82f:10009)", MRreviewer = "S. P. Mohanty", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.fq.math.ca/19-2.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/19-2/washington.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Fedorowicz:1982:TFZ, author = "Jane Fedorowicz", title = "The Theoretical Foundation of {Zipf's Law} and Its Application to the Bibliographic Database Environment", journal = j-J-AM-SOC-INF-SCI, volume = "33", number = "5", pages = "285--293", year = "1982", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630330507", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Fedorowicz:1982:ZMA, author = "Jane Fedorowicz", title = "A {Zipfian} Model of an Automatic Bibliographic System: An Application to {MEDLINE}", journal = j-J-AM-SOC-INF-SCI, volume = "33", number = "4", pages = "223--232", month = jul, year = "1982", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630330406", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:14 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "6 Sep 2007", } @Article{Lefort:1982:LOA, author = "B. Lefort", title = "{L}'Emploi des Outils au Cours de Taches d'Entretien et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of Tools in Maintenance Tasks and the {Zipf--Mandelbrot Law}]", journal = j-TRAV-HUM, volume = "45", number = "2", pages = "307--316", month = "????", year = "1982", CODEN = "TRHUAH", ISSN = "0041-1868 (print), 2104-3663 (electronic)", ISSN-L = "0041-1868", bibdate = "Mon Sep 10 07:17:32 MDT 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/40657805", acknowledgement = ack-nhfb, fjournal = "Le Travail Humain", language = "French", } @Article{MacRoberts:1982:REL, author = "Michael H. MacRoberts and Barbara R. MacRoberts", title = "A Re-evaluation of {Lotka}'s {Law of Scientific Productivity}", journal = j-SOC-STUD-SCI, volume = "12", number = "3", pages = "443--450", day = "1", month = aug, year = "1982", CODEN = "SSSCDH", DOI = "https://doi.org/10.1177/030631282012003005", ISSN = "0306-3127 (print), 1460-3659 (electronic)", ISSN-L = "0306-3127", bibdate = "Mon Dec 3 09:12:38 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib", URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631282012003005", acknowledgement = ack-nhfb, fjournal = "Social Studies of Science", journal-URL = "http://sss.sagepub.com/content/by/year", keywords = "Lotka's Law of scientific authorship for the relative contributions of the most prolific authors", } @Article{Pavlov:1982:DFP, author = "A. I. Pavlov", title = "On the Distribution of Fractional Parts and {Benford's Law}", journal = j-MATH-USSR-IZV, volume = "19", number = "1", pages = "65--77", month = "????", year = "1982", CODEN = "MUSIAE", DOI = "https://doi.org/10.1070/IM1982v019n01ABEH001411", ISSN = "0025-5726 (print), 2169-5075 (electronic)", ISSN-L = "0025-5726", bibdate = "Sun Nov 13 10:46:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://stacks.iop.org/0025-5726/19/i=1/a=A05", abstract = "This article investigates the distribution of the first digits (from the left) in the $q$-nary expansions of numerical sequences and functions ($q$ an integer $ \geq 2 $ )", acknowledgement = ack-nhfb, fjournal = "Mathematics of the {USSR} --- Izvestiya", journal-URL = "http://iopscience.iop.org/0025-5726", } @PhdThesis{Perline:1982:EVM, author = "Richard K. Perline", title = "An extreme value model of weakly harmonic ({Pareto--Zipf} type) laws", type = "Thesis ({Ph.D.})", school = "Department of Behavioral Sciences, The University of Chicago", address = "Chicago, IL, USA", pages = "129", month = dec, year = "1982", MRnumber = "2611828", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://search.proquest.com/docview/251796701", acknowledgement = ack-nhfb, remark = "Available from ProQuest LLC, Ann Arbor, MI, USA.", } @Article{Regazzini:1982:BFL, author = "Eugenio Regazzini", title = "The {Benford--Furlan} law as a statistical law", journal = j-STATISTICA-BOLOGNA, volume = "42", number = "3", pages = "351--370", year = "1982", CODEN = "STATDJ", ISSN = "0390-590X (print), 1973-2201 (electronic)", ISSN-L = "0390-590X", MRclass = "62E99 (10K05 62A15)", MRnumber = "695467 (84h:62032)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistica (Bologna)", } @Article{Turner:1982:DLS, author = "Peter R. Turner", title = "The distribution of leading significant digits", journal = j-IMA-J-NUMER-ANAL, volume = "2", number = "4", pages = "407--412", month = oct, year = "1982", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/2.4.407", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65G99 (60E05)", MRnumber = "84f:65038", MRreviewer = "Seppo Linnainmaa", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Book{Weaver:1982:LLT, author = "Warren Weaver", title = "{Lady Luck}: the theory of probability", publisher = pub-DOVER, address = pub-DOVER:adr, pages = "392", year = "1982", ISBN = "0-486-24342-7", ISBN-13 = "978-0-486-24342-9", LCCN = "QA273 .W4 1982", bibdate = "Mon Nov 14 11:35:17 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/description/dover031/82007396.html", acknowledgement = ack-nhfb, author-dates = "1894--1978", remark = "Reprint of \cite{Weaver:1963:LLT}.", subject = "Probabilities", } @Article{White:1982:FSS, author = "Warren H. White", title = "On the form of steady-state solutions to the coagulation equations", journal = j-J-COLLOID-INTERFACE-SCI, volume = "87", number = "1", pages = "204--208", month = may, year = "1982", CODEN = "JCISA5", DOI = "https://doi.org/10.1016/0021-9797(82)90382-4", ISSN = "0021-9797 (print), 1095-7103 (electronic)", ISSN-L = "0021-9797", bibdate = "Thu Feb 28 10:46:13 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0021979782903824", acknowledgement = ack-nhfb, fjournal = "Journal of Colloid and Interface Science", keywords = "power law; scale invariance; Zipf's law", } @Article{Iyengar:1983:SPL, author = "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R. Uppuluri", title = "String patterns of leading digits", journal = j-APPL-MATH-COMP, volume = "12", number = "4", pages = "321--337", month = jul, year = "1983", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/0096-3003(83)90045-0", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Feb 16 18:02:26 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", URL = "http://www.sciencedirect.com/science/article/pii/0096300383900450", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Montroll:1983:NOD, author = "Elliott W. Montroll and Michael F. Shlesinger", title = "On $ 1 / f $ noise and other distributions with long tails", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "79", number = "10", pages = "3380--3383", day = "15", month = may, year = "1983", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.79.10.3380", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Thu Feb 28 11:03:24 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.pnas.org/content/79/10/3380.abstract", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/search", keywords = "power law; scale invariance; Zipf's law", } @Article{Orlov:1983:SSZ, author = "Yu. K. Orlov and R. Ya. Chitashvili", title = "The statistical significance of {Zipf}'s distribution", journal = "Soobshch. Akad. Nauk Gruzin. SSR", volume = "109", number = "3", pages = "505--508", year = "1983", CODEN = "????", ISSN = "0132-1447", ISSN-L = "0132-1447", MRclass = "62E99 (62P99)", MRnumber = "723296", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR", } @Article{Schatte:1983:AUD, author = "Peter Schatte", title = "On the asymptotic uniform distribution of sums reduced $ \bmod 1 $", journal = j-MATH-NACHR, volume = "115", number = "1", pages = "257--281", month = "????", year = "1983", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19841150121", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Sat Feb 16 19:12:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", } @Article{Schatte:1983:SUD, author = "Peter Schatte", title = "On {$ H_\infty $}-summability and the uniform distribution of sequences", journal = j-MATH-NACHR, volume = "113", number = "1", pages = "237--243", month = "????", year = "1983", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19831130122", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Sat Feb 16 19:13:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", } @Article{Whittaker:1983:SID, author = "James V. Whittaker", title = "On Scale-Invariant Distributions", journal = j-SIAM-J-APPL-MATH, volume = "43", number = "2", pages = "257--267", month = apr, year = "1983", CODEN = "SMJMAP", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "60E05 (10K10 62E10)", MRnumber = "84h:60035", MRreviewer = "K. C. Chanda", bibdate = "Thu Oct 15 18:16:06 MDT 1998", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib; JSTOR database", acknowledgement = ack-nhfb, affiliation = "Univ of British Columbia, Dep of Mathematics, Vancouver, BC, Can", classification = "922", fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", journalabr = "SIAM J Appl Math", keywords = "probability", } @Article{Bennett:1984:ZLS, author = "J. M. Bennett", title = "{Zipf's Law}, Structured Programming and Creativity", journal = j-AUSTRALIAN-COMP-J, volume = "16", number = "4", pages = "122--129", year = "1984", CODEN = "ACMJB2", ISSN = "0004-8917", ISSN-L = "0004-8917", bibdate = "Fri Mar 9 17:59:26 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "As software projects increase in size, the effort required to implement them increases at a greater rate. The use of higher level languages and adherence to various rules of ``good programming practice'' appear to help only marginally in reducing the impact of this non-linear effect, and progress can only be made by calling on techniques for managing complexity which have emerged in other fields. Hierarchical structures are discussed with particular reference to software as is the effect which appears to be common to a wide range of human activities, and which is known as Zipf's law. The effects of variation in individual programming skills, the roles of creativity, invention and innovation and lessons to be learned from case studies of past failure are also examined.", acknowledgement = ack-nhfb, fjournal = "Australian Computer Journal", keywords = "creativity; innovation; invention; large software projects; project failures; structured programming; Zipf's law", } @Article{Boroda:1984:ZML, author = "M. G. Boroda and A. A. Polikarpov", title = "The {Zipf--Mandelbrot} law and units of different levels of text organization", journal = "Tartu Riikl. {\"U}l. Toimetised", volume = "??", number = "689", pages = "35--60", year = "1984", CODEN = "????", ISSN = "????", MRclass = "92A25", MRnumber = "781731 (86c:92030)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta et Commentationes Universitatis Tartuensis", } @Article{Brookes:1984:RTE, author = "Bertram C. Brookes", title = "Ranking techniques and the empirical log law", journal = j-INFO-PROC-MAN, volume = "20", number = "1--2", pages = "37--46", month = "????", year = "1984", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/0306-4573(84)90038-4", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Mon Feb 25 10:38:32 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0306457384900384", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", keywords = "Anomalous Law of Numbers; Benford's Law", } @Article{Bunt:1984:MPL, author = "Richard B. Bunt and Jennifer M. Murphy and Shikharesh Majumdar", title = "A measure of program locality and its application", journal = j-SIGMETRICS, volume = "12", number = "3", pages = "28--40", month = aug, year = "1984", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/1031382.809311", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Thu Jun 26 11:00:50 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Although the phenomenon of locality has long been recognized as the single most important characteristic of program behaviour, relatively little work has been done in attempting to measure it. Recent work has led to the development of an intrinsic measure of program locality based on the Bradford--Zipf distribution. Potential applications for such a measure are many, and include the evaluation of program restructuring methods (manual and automatic), the prediction of system performance, the validation of program behaviour models, and the enhanced understanding of the phenomena that characterize program behaviour. A consideration of each of these areas is given in connection with the proposed measure, both to increase confidence in the validity of the measure and to illustrate a methodology for dealing with such problems.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", } @Article{Cohen:1984:PNF, author = "D. I. A. Cohen and T. M. Katz", title = "Prime numbers and the first digit phenomenon", journal = j-J-NUMBER-THEORY, volume = "18", number = "3", pages = "261--268", month = jun, year = "1984", CODEN = "JNUTA9", DOI = "https://doi.org/10.1016/0022-314X(84)90061-1", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Fri Nov 25 13:58:58 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", } @Article{Fedorowicz:1984:DEU, author = "Jane Fedorowicz", title = "Database evaluation using multiple regression techniques", journal = j-SIGMOD, volume = "14", number = "2", pages = "70--76", year = "1984", CODEN = "SRECD8", ISBN = "0-89791-128-8", ISBN-13 = "978-0-89791-128-3", ISSN = "0163-5808 (print), 1943-5835 (electronic)", ISSN-L = "0163-5808", bibdate = "Mon Dec 9 07:58:51 MST 1996", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "A model of the inverted file of an automated bibliographic system is constructed using the Zipf distribution of word frequency. By ascertaining the parameters of the Zipfian model of the inverted file system, one can estimate the minimum data storage requirements of the database. In addition, given a few additional system parameters, access time for a specified query can be estimated. The estimation procedures are accomplished using logarithmic transformations and multiple regression techniques. This paper introduces the Zipfian models, their regression formulation, and their results and interpretation for application to database evaluation.", acknowledgement = ack-nhfb, affiliation = "Northwestern Univ, Kellogg Graduate Sch of Management, Evanston, IL, USA", affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of Management, Evanston, IL, USA", classification = "723; 901; 922", conference = "SIGMOD '84, Proceedings of Annual Meeting (ACM Special Interest Group on Management of Data).", fjournal = "SIGMOD Record (ACM Special Interest Group on Management of Data)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J689", keywords = "access time model; bibliographic techniques; database systems; evaluation; information storage systems; mathematical models; multiple regression techniques; Zipfian model", meetingaddress = "Boston, MA, USA", sponsor = "ACM, Special Interest Group on Management of Data, New York, NY, USA", } @Article{Friedberg:1984:DFD, author = "Stephen H. Friedberg", title = "The Distribution of First Digits", journal = j-COLLEGE-MATH-J, volume = "15", number = "2", pages = "120--125", month = mar, year = "1984", CODEN = "????", DOI = "https://doi.org/10.1080/00494925.1984.11972760", ISSN = "0746-8342 (print), 1931-1346 (electronic)", ISSN-L = "0746-8342", bibdate = "Thu Feb 14 09:49:53 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collegemathj.bib", URL = "http://www.jstor.org/stable/2686516; http://www.tandfonline.com/doi/abs/10.1080/00494925.1984.11972760", acknowledgement = ack-nhfb, fjournal = "College Mathematics Journal", journal-URL = "https://maa.tandfonline.com/loi/ucmj20; https://www.jstor.org/journal/collmathj", keywords = "Benford's Law", onlinedate = "30 Jan 2018", } @Article{Fuchs:1984:PDP, author = "A. Fuchs and G. Letta", title = "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}. ({French}) [{On} the problem of the first decimal digit]", journal = "{Bollettino della Unione Matem{\`a}tica Italiana. Serie VI. B}", volume = "3", pages = "451--461", year = "1984", ISSN = "0392-4041", ISSN-L = "0392-4041", bibdate = "Wed Aug 12 10:09:50 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0557.60011", acknowledgement = ack-nhfb, ajournal = "Boll. Unione Mat. Ital., VI. Ser., B", keywords = "analytical density; asymptotic density; first-digit problem", language = "French", ZMclass = "60B99 (Probability theory on general structures)", ZMreviewer = "R. Scozzafava", } @Article{Karmeshu:1984:RBL, author = "Karmeshu and N. C. Lind and V. Cano", title = "Rationales for {Bradford's Law}", journal = j-SCIENTOMETRICS, volume = "6", number = "4", pages = "233--241", month = jul, year = "1984", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02279358", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:02:53 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib", URL = "http://link.springer.com/article/10.1007/BF02279358", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Kohyama:1984:TIC, author = "Tamotsu Kohyama and Y{\=o}ji Aizawa", title = "Theory of the intermittent chaos. {$ 1 / f $} spectrum and the {Pareto--Zipf} law", journal = j-PROG-THEOR-PHYS, volume = "71", number = "5", pages = "917--929", year = "1984", CODEN = "PTPKAV", DOI = "https://doi.org/10.1143/PTP.71.917", ISSN = "0033-068X (print), 1347-4081 (electronic)", ISSN-L = "0033-068X", MRclass = "58F13 (76F99)", MRnumber = "756214 (86a:58063)", MRreviewer = "Joseph Ford", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Progress of Theoretical Physics", journal-URL = "http://ptp.oxfordjournals.org/content/by/year", } @Article{Maia:1984:UBL, author = "M. J. F. Maia and M. D. Maia", title = "On the Unity of {Bradford's Law}", journal = j-J-DOC, volume = "40", number = "3", pages = "206--216", month = "????", year = "1984", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026765", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:11:46 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{McLaughlin:1984:DFI, author = "William I. McLaughlin and Sylvia A. Lundy", title = "Digit Functions of Integer Sequences", journal = j-FIB-QUART, volume = "22", number = "2", pages = "105--115", month = may, year = "1984", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:00:30 MDT 2011", bibsource = "http://www.fq.math.ca/22-2.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Nagasaka:1984:BL, author = "Kenji Nagasaka", title = "On {Benford}'s law", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "36", number = "1", pages = "337--352", month = "????", year = "1984", CODEN = "AISXAD", DOI = "https://doi.org/10.1007/BF02481974", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRclass = "60F99 (11K06 11K36 62E99)", MRnumber = "758506 (86a:60052)", MRreviewer = "L. Kuipers", bibdate = "Sat Jan 31 18:19:56 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/BF02481974", acknowledgement = ack-nhfb, ajournal = "Ann. Inst. Statist. Math.", fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", journal-URL = "http://link.springer.com/journal/10463", } @Article{Schatte:1984:AUD, author = "Peter Schatte", title = "On the asymptotic uniform distribution of sums reduced $ \bmod 1 $", journal = j-MATH-NACHR, volume = "115", number = "1", pages = "275--281", month = "????", year = "1984", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19841150121", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Sat Nov 12 15:54:14 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", } @Article{Turner:1984:FRD, author = "Peter R. Turner", title = "Further revelations on l.s.d", journal = j-IMA-J-NUMER-ANAL, volume = "4", number = "2", pages = "225--231", month = apr, year = "1984", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/4.2.225", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65G10 (11K99)", MRnumber = "85m:65039", MRreviewer = "Calvin T. Long", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database", abstract = "In a recent paper the author showed that the distribution of leading significant digits, l.s.d., resulting from successive multiplications is logarithmic. In this paper these results are extended by establishing, still without any assumptions of invariance to scaling, that this distribution remains invariant under all further arithmetic operations --- both multiplicative and additive. The fact that 30\% of decimal numbers have l.s.d. 1 persists.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "l. s. d. (leading significant digits)", } @Article{Yuan:1984:LOC, author = "Y. Yuan", title = "On the least {$Q$}-order of convergence of variable metric algorithms", journal = j-IMA-J-NUMER-ANAL, volume = "4", number = "2", pages = "233--239", month = apr, year = "1984", CODEN = "IJNADH", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65K05", MRnumber = "85h:65133", MRreviewer = "A. I. \c Schiop", bibdate = "Sat Dec 23 17:06:35 MST 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", } @Article{Barlow:1985:RED, author = "J. L. Barlow and E. H. Bareiss", title = "On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic", journal = j-COMPUTING, volume = "34", number = "4", pages = "325--347", month = dec, year = "1985", CODEN = "CMPTA2", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "65G05", MRnumber = "87c:65045", MRreviewer = "N. N. Abdelmalek", bibdate = "Tue Oct 12 16:33:42 MDT 1999", bibsource = "Compendex database; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database", acknowledgement = ack-nhfb, affiliation = "Pennsylvania State Univ, Computer Science Dep, University Park, PA, USA", affiliationaddress = "USA", classification = "723", fjournal = "Computing", journal-URL = "http://link.springer.com/journal/607", journalabr = "Computing (Vienna/New York)", keywords = "computer arithmetic; computer metatheory; floating point arithmetic; logarithmic arithmetic; roundoff error distributions", } @Article{Bradford:1985:SIS, author = "Samuel C. Bradford", title = "Sources of Information on Specific Subjects", journal = j-J-INFO-SCI-PRINCIPLES-PRACTICE, volume = "10", number = "4", pages = "173--180", month = oct, year = "1985", CODEN = "JISCDI", ISSN = "0165-5515 (print), 1741-6485 (electronic)", ISSN-L = "0165-5515", bibdate = "Fri Nov 25 11:49:58 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprint of \cite{Bradford:1934:SIS}, the source of Bradford's Law.", acknowledgement = ack-nhfb, fjournal = "Journal of Information Science, Principles and Practice", journal-URL = "http://jis.sagepub.com/", } @Article{Egghe:1985:CLL, author = "L. Egghe", title = "Consequences of {Lotka's Law} for the {Law of Bradford}", journal = j-J-DOC, volume = "41", number = "3", pages = "173--189", month = "????", year = "1985", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026780", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:23:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", keywords = "Bradford's Law", } @Article{Faber:1985:AML, author = "Vance Faber and Andrew B. {White, Jr.} and G. Milton Wing", title = "Analysis of a model that leads to the {Pareto} law of wealth distribution", journal = j-J-MATH-ANAL-APPL, volume = "112", number = "2", pages = "579--594", year = "1985", CODEN = "JMANAK", DOI = "https://doi.org/10.1016/0022-247X(85)90264-1", ISSN = "0022-247X (print), 1096-0813 (electronic)", ISSN-L = "0022-247X", MRclass = "90A14", MRnumber = "813621 (87b:90027)", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Analysis and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/0022247X", } @Article{Lagarias:1985:PG, author = "Jeffrey C. Lagarias", title = "The $ 3 x + 1 $ Problem and Its Generalizations", journal = j-AMER-MATH-MONTHLY, volume = "92", number = "1", pages = "3--23", month = jan, year = "1985", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11K55 (11K31)", MRnumber = "86i:11043", MRreviewer = "A. D. Pollington", bibdate = "Mon Jun 28 12:37:47 MDT 1999", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", keywords = "Benford's Law", } @Article{Pao:1985:LLT, author = "Miranda Lee Pao", title = "{Lotka}'s law: a testing procedure", journal = j-INFO-PROC-MAN, volume = "21", number = "4", pages = "305--320", month = "????", year = "1985", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/0306-4573(85)90055-X", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Fri Nov 25 08:41:41 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", } @Article{Raimi:1985:FDP, author = "Ralph A. Raimi", title = "The First Digit Phenomenon Again", journal = j-PROC-AMER-PHIL-SOC, volume = "129", number = "2", pages = "211--219", month = jun, year = "1985", CODEN = "PAPCAA", ISSN = "0003-049X (print), 2326-9243 (electronic)", ISSN-L = "0003-049X", bibdate = "Sat Nov 12 16:56:54 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", note = "This paper contains strong criticism of a derivation of Benford's Law \cite{Logan:1978:FDP}.", URL = "http://www.jstor.org/stable/986989", acknowledgement = ack-nhfb, fjournal = "Proceedings of the {American Philosophical Society} held at {Philadelphia} for promoting useful knowledge", journal-URL = "http://www.jstor.org/journal/procamerphilsoci", remark = "This paper contains mathematical derivations of both Stigler's Law and Benford's Law. Raimi comments on p. 217: ``the Benford law itself as a conclusion to be derived is by no means as firm as Kepler's planetary curves. Indeed, it has been pointed out by Diaconis and Freedman [D-F] [\cite{Diaconis:1979:RP}] that a statistical analysis of Benford's announced data gives a high probability to the conjecture that he did a bit of rounding-off here and there, always in the direction of his law. The license that a physicist often takes on the path from his hypotheses to verified, observable, and repeatable conclusion is not justified here.''.", } @Article{Tichy:1985:UDD, author = "Robert F. Tichy", title = "Uniform distribution and diophantine inequalities", journal = j-MONAT-MATH, volume = "99", number = "2", pages = "147--152", month = jun, year = "1985", CODEN = "MNMTA2", DOI = "https://doi.org/10.1007/BF01304194", ISSN = "0026-9255 (print), 1436-5081 (electronic)", ISSN-L = "0026-9255", bibdate = "Sun Feb 17 06:26:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/BF01304194", ZMnumber = "0538.10039", acknowledgement = ack-nhfb, fjournal = "Monatshefte f{\"u}r Mathematik", journal-URL = "http://link.springer.com/journal/605", keywords = "diophantine inequalities; discrepancy; Uniformly distributed sequences", ZMclass = "11K06 (General theory of distribution modulo 1); 11D75 (Diophantine inequalities)", } @Article{Tuldava:1985:FST, author = "Yu. A. Tuldava", title = "The frequency structure of a text and {Zipf}'s law", journal = "Tartu Riikl. {\"U}l. Toimetised", volume = "??", number = "711", pages = "93--116", year = "1985", CODEN = "????", ISSN = "????", MRclass = "92A25 (94A15)", MRnumber = "836129 (87c:92063)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Tartu Riikliku {\"U}likooli Toimetised. Uchenye Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta et Commentationes Universitatis Tartuensis", } @Article{Uppuluri:1985:DFD, author = "V. R. R. Uppuluri and S. A. Patil", title = "The distribution of the first $j$ digits of beta related random variables", journal = j-COMMUN-STAT-SIMUL-COMPUT, volume = "14", number = "2", pages = "467--472", year = "1985", CODEN = "CSSCDB", DOI = "https://doi.org/10.1080/03610918508812450", ISSN = "0361-0918", ISSN-L = "0361-0918", bibdate = "Sat Jan 30 06:32:23 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics: Simulation and Computation", journal-URL = "http://www.tandfonline.com/loi/lssp20", keywords = "Benford's Law", } @Article{Chen:1986:RBL, author = "Ye-Sho Chen and Ferdinand F. Leimkuhler", title = "A relationship between {Lotka's Law}, {Bradford's Law}, and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "5", pages = "307--314", year = "1986", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Chen:1986:RRB, author = "Ye-Sho Chen and Ferdinand F. Leimkuhler", title = "Research: A relationship between {Lotka's Law}, {Bradford's Law}, and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "5", pages = "307--314", month = sep, year = "1986", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:27 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Jan 1999", } @Article{Egghe:1986:RDB, author = "L. Egghe", title = "Research: The dual of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "4", pages = "246--255", month = jul, year = "1986", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198607)37:4<246::AID-ASI10>3.0.CO%3B2-D", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:27 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Jan 1999", } @Article{Feldstein:1986:OUS, author = "Alan Feldstein and Peter Turner", title = "Overflow, underflow, and severe loss of significance in floating-point addition and subtraction", journal = j-IMA-J-NUMER-ANAL, volume = "6", number = "2", pages = "241--251", month = apr, year = "1986", CODEN = "IJNADH", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65G05", MRnumber = "89h:65065", bibdate = "Sat Dec 23 14:52:49 2000", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this paper it is shown that, under the assumption of the logarithmic distribution of numbers, floating-point addition and subtraction can result in overflow or underflow with alarming frequency --- a frequency that increases rapidly with machine speed unless the range of the exponent is also increased. If numbers are assumed to be distributed in accordance with Sweeney's (1965) experiments, then severe loss of significance occurs with large probability in floating point subtraction. These results have implications for computer design and lead to the suggestion of a long word format which will reduce the risks to acceptable levels.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law", } @Article{Green:1986:BRP, author = "M. W. Green", title = "Book Reviews: {{\em Pareto Distributions}}, by {B. C. Arnold}", journal = j-APPL-STAT, volume = "35", number = "2", pages = "215--215", year = "1986", CODEN = "APSTAG", ISSN = "0035-9254 (print), 1467-9876 (electronic)", ISSN-L = "0035-9254", bibdate = "Sat Apr 21 10:24:36 MDT 2001", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; JSTOR database", acknowledgement = ack-nhfb, fjournal = "Applied Statistics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues", } @Article{Hoare:1986:DFS, author = "G. T. Q. Hoare and E. Wright", title = "The distribution of first significant digits", journal = j-MATH-GAZ, volume = "70", number = "451", pages = "34--37", month = mar, year = "1986", CODEN = "MAGAAS", ISSN = "0025-5572 (print), 2056-6328 (electronic)", ISSN-L = "0025-5572", bibdate = "Sat Feb 16 17:57:52 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3615826", acknowledgement = ack-nhfb, fjournal = "Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", } @Article{Katz:1986:FDP, author = "Talbot M. Katz and Daniel I. A. Cohen", title = "The First Digit Property for Exponential Sequences is Independent of the Underlying Distribution", journal = j-FIB-QUART, volume = "24", number = "1", pages = "2--7", month = feb, year = "1986", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:00:45 MDT 2011", bibsource = "http://www.fq.math.ca/24-1.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/24-1/katz.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Lemons:1986:NTD, author = "Don S. Lemons", title = "On the number of things and the distribution of first digits", journal = j-AMER-J-PHYSICS, volume = "54", number = "9", pages = "816--817", month = sep, year = "1986", CODEN = "AJPIAS", DOI = "https://doi.org/10.1119/1.14453", ISSN = "0002-9505 (print), 1943-2909 (electronic)", ISSN-L = "0002-9505", bibdate = "Wed Nov 23 12:03:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ajp.aapt.org/", acknowledgement = ack-nhfb, fjournal = "American Journal of Physics", journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp", keywords = "Benford's Law", remark = "Lemons gives a derivation of Benford's Law that does not assume scale invariance, unlike other widely-cited derivations \cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.", } @Book{Lines:1986:NYT, author = "Malcolm E. Lines", title = "A number for your thoughts: facts and speculations about numbers from {Euclid} to the latest computers", publisher = pub-ADAM-HILGER, address = pub-ADAM-HILGER:adr, pages = "vi + 214", year = "1986", ISBN = "0-85274-495-1 (paperback)", ISBN-13 = "978-0-85274-495-6 (paperback)", LCCN = "QA241 .L617 1986", bibdate = "Wed Nov 23 11:34:02 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.gbv.de:20011/gvk", URL = "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html", acknowledgement = ack-nhfb, remark = "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law of Benford''.", subject = "number theory", } @Article{MacRoberts:1986:QMC, author = "Michael H. MacRoberts and Barbara R. MacRoberts", title = "Quantitative Measures of Communication in Science: a Study of the Formal Level", journal = j-SOC-STUD-SCI, volume = "16", number = "1", pages = "151--172", day = "1", month = feb, year = "1986", CODEN = "SSSCDH", DOI = "https://doi.org/10.1177/030631286016001008", ISSN = "0306-3127 (print), 1460-3659 (electronic)", ISSN-L = "0306-3127", bibdate = "Mon Dec 3 09:12:44 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib", note = "See \cite{Stigler:1987:PMF} and reply \cite{MacRoberts:1987:MFU}.", URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631286016001008", acknowledgement = ack-nhfb, fjournal = "Social Studies of Science", journal-URL = "http://sss.sagepub.com/content/by/year", } @Article{Pao:1986:EEL, author = "Miranda Lee Pao", title = "An empirical examination of {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "1", pages = "26--33", month = jan, year = "1986", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/asi.4630370105", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:25 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "24 May 2007", } @Article{Pao:1986:REE, author = "Miranda Lee Pao", title = "Research: An empirical examination of {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "37", number = "1", pages = "26--33", month = jan, year = "1986", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198601)37:1<26::AID-ASI4>3.0.CO%3B2-Z", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:25 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Jan 1999", } @Article{Patil:1986:DFD, author = "S. A. Patil and V. R. R. Uppuluri", title = "The Distribution of First $j$ Digits", journal = j-COLLEGE-MATH-J, volume = "17", number = "3", pages = "240--243", month = may, year = "1986", CODEN = "????", DOI = "https://doi.org/10.1080/07468342.1986.11972963", ISSN = "0746-8342 (print), 1931-1346 (electronic)", ISSN-L = "0746-8342", bibdate = "Thu Feb 14 09:50:20 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collegemathj.bib", URL = "http://www.jstor.org/stable/2686982; http://www.tandfonline.com/doi/abs/10.1080/07468342.1986.11972963", acknowledgement = ack-nhfb, fjournal = "College Mathematics Journal", journal-URL = "https://maa.tandfonline.com/loi/ucmj20; https://www.jstor.org/journal/collmathj", keywords = "Benford's Law", onlinedate = "30 Jan 2018", } @Article{Pontigo:1986:QAB, author = "J. Pontigo and F. W. Lancaster", title = "Qualitative aspects of the {Bradford} distribution", journal = j-SCIENTOMETRICS, volume = "9", number = "1--2", pages = "59--70", month = jan, year = "1986", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02016608", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:02:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib", URL = "http://link.springer.com/article/10.1007/BF02016608", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Schatte:1986:ALD, author = "Peter Schatte", title = "On the asymptotic logarithmic distribution of the floating-point mantissas of sums", journal = j-MATH-NACHR, volume = "127", number = "1", pages = "7--20", month = "????", year = "1986", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19861270102", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Sun Feb 17 06:04:23 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", } @Article{Tichy:1986:GZU, author = "Robert F. Tichy", title = "{Gleichverteilung und zahlentheoretische Ungleichungen II}. ({German}) [{Uniform} distribution and number-theoretic inequalities {II}]", journal = "Anzeiger der {\"O}sterreichischen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse", volume = "122(1985)", number = "??", pages = "95--99", month = "????", year = "1986", CODEN = "OSAWA8", DOI = "????", ISSN = "0065-535X", ISSN-L = "0065-535X", bibdate = "Sun Feb 17 06:24:23 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", acknowledgement = ack-nhfb, ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.", classmath = "11K06 (General theory of distribution modulo 1); 11J25 (Diophantine inequalities)", keywords = "diophantine inequalities; discrepancy; H infinity; logarithmic mean; summation method; uniform distribution", language = "German", xxnote = "Despite repeated searches, I have not found this journal online, not even from links at the Austrian Academy of Sciences, \path=http://www.oeaw.ac.at=.", } @Article{Bak:1987:SOC, author = "Per Bak and Chao Tang and Kurt Wiesenfeld", title = "Self-organized criticality: An explanation of the $ 1 / f $ noise", journal = j-PHYS-REV-LET, volume = "59", number = "4", pages = "381--384", month = jul, year = "1987", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.59.381", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Thu Feb 28 10:54:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.59.381", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Chen:1987:AZL, author = "Ye-Sho Chen and Ferdinand F. Leimkuhler", title = "Analysis of {Zipf}'s law: An index approach", journal = j-INFO-PROC-MAN, volume = "23", number = "3", pages = "171--182", day = "1", month = apr, year = "1987", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/0306-4573(87)90002-1", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0306457387900021", ZMnumber = "0614.62150", abstract = "A rigorous analysis of Zipf's law is made using an index for the sequence of observed values of the variables in a Zipf-type relationship. Three important properties relating rank, count, and frequency are identified. Using this approach, the shape of Zipf-type curves can be described in terms of three distinct regions and two parameters of the Mandelbrot--Zipf law. This result has considerable practical significance, since it provides rigorous foundations for the application of Zipf's law.", acknowledgement = ack-nhfb, classmath = "62P99 (Appl. of statistics)", fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", keywords = "index approach; Mandelbrot-Zipf law; Zipf's law", } @Article{Chen:1987:BLI, author = "Ye-Sho Chen and F. F. Leimkuhler", title = "{Bradford's Law}: An index approach", journal = j-SCIENTOMETRICS, volume = "11", number = "3--4", pages = "183--198", month = mar, year = "1987", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02016591", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:03:03 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib", URL = "http://link.springer.com/article/10.1007/BF02016591", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Fedorowicz:1987:DPE, author = "Jane Fedorowicz", title = "Database Performance Evaluation in an Indexed File Environment", journal = j-TODS, volume = "12", number = "1", pages = "85--110", month = mar, year = "1987", CODEN = "ATDSD3", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Sat Apr 14 10:34:48 MDT 2001", bibsource = "Compendex database; Database/Graefe.bib; Database/Wiederhold.bib; http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf; http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/; http://www.acm.org/pubs/toc/Abstracts/tods/13675.html", abstract = "The use of database systems for managerial decision making often incorporates information-retrieval capabilities with numeric report generation. Of great concern to the user of such a system is the response time associated with issuing a query to the database. This study presents a procedure for estimating response time for one of the most frequently encountered physical storage mechanisms, the indexed file. The model provides a fairly high degree of accuracy, but is simple enough so that the cost of applying the model is not exorbitant. The model incorporates the knowledge that the distribution of access key occurrences is known to follow Zipf's law. It first estimates the access time required to complete the query, which includes the time needed for all input and output transactions, and CPU time used in performing the search. The effects of multiple users on an individual's response time are then assessed using a simple regression estimation technique. The two-step procedure allows for the separation of access time from multiuser influences.", acknowledgement = ack-nhfb, affiliation = "Boston Univ, Boston, MA, USA", affiliationaddress = "Boston Univ, Boston, MA, USA", annote = "a procedure for estimating response time; distribution of access key occurrences follow Zipf's law. Early version with Kellogg, J. L. Model provides a fairly high degree of accuracy but is simple. The effects of multiple users are assessed using simple regression estimation.", classification = "723; 912; 922", fjournal = "ACM Transactions on Database Systems", generalterms = "Design; Performance", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "data processing --- File organization; database performance; database systems; indexed file environment; MANAGEMENT --- Information Systems; multiple users, design; Performance; performance; response time; statistical methods --- regression analysis; Zipf's law", subject = "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems Management, File organization. {\bf H.2.2}: Information Systems, DATABASE MANAGEMENT, Physical Design, Access methods. {\bf H.3.2}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Storage, File organization. {\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Retrieval models.", } @Article{Hosking:1987:PQE, author = "J. R. M. Hosking and J. R. Wallis", title = "Parameter and Quantile Estimation for the Generalized {Pareto} Distribution", journal = j-TECHNOMETRICS, volume = "29", number = "3", pages = "339--349", month = "????", year = "1987", CODEN = "TCMTA2", ISSN = "0040-1706 (print), 1537-2723 (electronic)", ISSN-L = "0040-1706", bibdate = "Fri Nov 25 16:39:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Technometrics", journal-URL = "http://www.jstor.org/journals/00401706.html; http://www.tandfonline.com/loi/utch20", } @Article{Kunoff:1987:FDP, author = "Sharon Kunoff", title = "{$ N! $} has the First Digit Property", journal = j-FIB-QUART, volume = "25", number = "4", pages = "365--367", month = nov, year = "1987", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:01:00 MDT 2011", bibsource = "http://www.fq.math.ca/25-4.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{MacRoberts:1987:MFU, author = "Michael H. MacRoberts and Barbara R. MacRoberts", title = "Measurement in the Face of Universal Uncertainty: a Reply to {Stigler}", journal = j-SOC-STUD-SCI, volume = "17", number = "2", pages = "334--336", day = "1", month = may, year = "1987", CODEN = "SSSCDH", DOI = "https://doi.org/10.1177/030631287017002008", ISSN = "0306-3127 (print), 1460-3659 (electronic)", ISSN-L = "0306-3127", bibdate = "Mon Dec 3 09:12:46 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib", note = "See \cite{MacRoberts:1986:QMC}.", URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002008", acknowledgement = ack-nhfb, fjournal = "Social Studies of Science", journal-URL = "http://sss.sagepub.com/content/by/year", } @Article{Nagasaka:1987:BLL, author = "Kenji Nagasaka and Jau-Shyong Shiue", title = "{Benford}'s law for linear recurrence sequences", journal = "Tsukuba J. Math.", volume = "11", number = "2", pages = "341--351", year = "1987", CODEN = "????", ISSN = "0387-4982", ISSN-L = "0387-4982", MRclass = "60E99 (11B37)", MRnumber = "926460 (88m:60047)", MRreviewer = "L. Kuipers", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Tsukuba Journal of Mathematics", } @Article{Nicholls:1987:BCE, author = "Paul Travis Nicholls", title = "Brief Communications: Estimation of {Zipf} parameters", journal = j-J-AM-SOC-INF-SCI, volume = "38", number = "6", pages = "443--445", month = nov, year = "1987", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:31 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "24 May 2007", } @Article{Nicholls:1987:EZP, author = "Paul Travis Nicholls", title = "Estimation of {Zipf} parameters", journal = j-J-AM-SOC-INF-SCI, volume = "38", number = "6", pages = "443--445", year = "1987", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", } @Article{Sanders:1987:PPUa, author = "Robert Sanders", title = "The {Pareto Principle}: Its Use and Abuse", journal = "Journal of Consumer Marketing", volume = "4", number = "1", pages = "47--50", month = "????", year = "1987", CODEN = "????", DOI = "https://doi.org/10.1108/eb008188", ISSN = "0736-3761", ISSN-L = "0736-3761", bibdate = "Fri Nov 25 06:56:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Sanders:1987:PPUb, author = "Robert Sanders", title = "The {Pareto Principle}: Its Use and Abuse", journal = "Journal of Services Marketing", volume = "1", number = "2", pages = "37--40", month = "????", year = "1987", CODEN = "????", DOI = "https://doi.org/10.1108/eb024706", ISSN = "0887-6045", ISSN-L = "0887-6045", bibdate = "Fri Nov 25 06:56:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Schatte:1987:ABM, author = "Peter Schatte", title = "On the asymptotic behaviour of the mantissa distribution of sums", journal = j-J-INFO-PROC-CYBERNETICS-EIK, volume = "23", number = "??", pages = "353--360", month = "????", year = "1987", CODEN = "JICYE5", ISSN = "0863-0593", ISSN-L = "0863-0593", bibdate = "Sat Nov 12 15:58:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "J. Inform. Process. Cybern. EIK", fjournal = "Journal of Information Processing and Cybernetics: EIK", } @Article{Schatte:1987:SEU, author = "Peter Schatte", title = "Some estimates of the {$ \mathcal {H}_\infty $}-uniform distribution", journal = j-MONAT-MATH, volume = "103", number = "3", pages = "233--249", month = sep, year = "1987", CODEN = "MNMTA2", DOI = "https://doi.org/10.1007/BF01364342", ISSN = "0026-9255 (print), 1436-5081 (electronic)", ISSN-L = "0026-9255", bibdate = "Sat Nov 12 15:57:05 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/BF01364342", acknowledgement = ack-nhfb, fjournal = "Monatshefte f{\"u}r Mathematik", journal-URL = "http://link.springer.com/journal/605", } @Article{Stigler:1987:PMF, author = "Stephen M. Stigler", title = "Precise Measurement in the Face of Error: a Comment on {MacRoberts} and {MacRoberts}", journal = j-SOC-STUD-SCI, volume = "17", number = "2", pages = "332--334", day = "1", month = may, year = "1987", CODEN = "SSSCDH", DOI = "https://doi.org/10.1177/030631287017002007", ISSN = "0306-3127 (print), 1460-3659 (electronic)", ISSN-L = "0306-3127", bibdate = "Mon Dec 3 09:12:46 MST 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/socstudsci.bib", note = "See \cite{MacRoberts:1986:QMC} and reply \cite{MacRoberts:1987:MFU}.", URL = "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002007", acknowledgement = ack-nhfb, fjournal = "Social Studies of Science", journal-URL = "http://sss.sagepub.com/content/by/year", } @Article{Tague:1987:MVZ, author = "Jean Tague and Paul Nicholls", title = "The maximal value of a {Zipf} size variable: Sampling properties and relationship to other parameters", journal = j-INFO-PROC-MAN, volume = "23", number = "3", pages = "155--170", day = "7", month = jun, year = "1987", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/0306-4573(87)90001-X", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/030645738790001X", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", keywords = "Zipf's Law", } @Article{Tichy:1987:GS, author = "Robert F. Tichy", title = "{Gleichverteilung zum Summierungsverfahren {$ H_\infty $}}. ({German}) [{Uniform} distribution to the {$ H_\infty $} summation method]", journal = j-MATH-NACHR, volume = "131", number = "??", pages = "119--125", month = "????", year = "1987", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19871310112", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Mon Feb 18 06:44:11 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", ZMnumber = "0626.10044", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", keywords = "$H_\infty$-discrepancy; difference sequences; real sequences; uniform distribution", language = "German", ZMclass = "11K06 (General theory of distribution modulo 1); 40J05 (Summability in abstract structures)", ZMreviewer = "D. Leitmann", } @Article{Turner:1987:DDI, author = "Peter R. Turner", title = "The Distribution of l.s.d. and Its Implications for Computer Design", journal = j-MATH-GAZ, volume = "71", number = "455", pages = "26--31", month = mar, year = "1987", CODEN = "MAGAAS", DOI = "https://doi.org/10.2307/3616283", ISSN = "0025-5572 (print), 2056-6328 (electronic)", ISSN-L = "0025-5572", bibdate = "Tue Oct 30 23:36:58 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "[l.s.d. = least significant digits]. The topic is variously known as Benford's Law, the Law of Anomalous Numbers, and Zipf's Law.", acknowledgement = ack-nhfb, fjournal = "Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", keywords = "Benford's Law; Law of Anomalous Numbers; logarithmic distribution; overflow; underflow; Zipf's Law", } @Article{Belevitch:1988:PQD, author = "Vitold Belevitch", title = "{{\`A}} propos de la queue de la distribution de {Zipf}. ({French}) [{On} the tail of the {Zipf} distribution]", journal = "Ann. Soc. Sci. Bruxelles S{\'e}r. I", volume = "102", number = "3", pages = "73--85 (1989)", year = "1988", CODEN = "ASSBAH", ISSN = "0037-959X", ISSN-L = "0037-959X", MRclass = "92A90", MRnumber = "1016850 (90g:92114)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annales de la Societ{\'e} Scientifique de Bruxelles. S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques et Physiques", language = "French", } @Article{Carslaw:1988:AIN, author = "C. A. Carslaw", title = "Anomalies in Income Numbers: Evidence of Goal-Oriented Behavior", journal = j-ACCOUNT-REV, volume = "63", number = "2", pages = "321--327", month = apr, year = "1988", CODEN = "ACRVAS", ISSN = "0001-4826 (print), 1558-7967 (electronic)", ISSN-L = "0001-4826", bibdate = "Sat Sep 10 11:00:09 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/248109", acknowledgement = ack-nhfb, fjournal = "The Accounting Review", journal-URL = "https://www.jstor.org/journal/accountingreview", keywords = "Benford's Law; New Zealand firms; second-digit frequency", remark-1 = "This paper references neither Newcomb nor Benford, but it uses their digit-frequency formula from \cite{Feller:1966:IPT} to compare with data on revenues of New Zealand companies.", remark-2 = "According to \cite{Kossovsky:2015:BLT}, this may be the first published serious use of Benford's Law for fraud detection in accounting, although the possibility had been mentioned 16 years earlier \cite{Varian:1972:LEB}, and that earlier paper is not cited in this 1988 paper.", } @Article{Hill:1988:RNG, author = "Theodore Hill", title = "Random number guessing and the first digit phenomenon", journal = j-PSYCHOL-REP, volume = "62", number = "3", pages = "967--971", month = jun, year = "1988", CODEN = "PYRTAZ", DOI = "https://doi.org/10.2466/pr0.1988.62.3.967", ISSN = "0033-2941 (print), 1558-691X (electronic)", ISSN-L = "0033-2941", bibdate = "Fri Feb 15 06:41:31 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967", acknowledgement = ack-nhfb, ajournal = "Psychol. rep.", fjournal = "Psychological Reports", } @InCollection{Kanemitsu:1988:BLF, author = "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard Rauzy and Jau-Shyong Shiue", booktitle = "Probability theory and mathematical statistics ({Kyoto}, 1986)", title = "On {Benford}'s law: the first digit problem", volume = "1299", publisher = pub-SV, address = pub-SV:adr, pages = "158--169", year = "1988", DOI = "https://doi.org/10.1007/BFb0078471", MRclass = "11K06 (60E99)", MRnumber = "935987 (89d:11059)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Math.", acknowledgement = ack-nhfb, } @InCollection{Nicolis:1988:PBZ, author = "John S. Nicolis", booktitle = "Synergetics, order and chaos ({Madrid}, 1987)", title = "On the parallel between {Zipf}'s law and {$ 1 / f $} processes in chaotic systems possessing coexisting attractors", publisher = "World Sci. Publ.", address = "Teaneck, NJ, USA", pages = "723--734", year = "1988", MRclass = "58F13 (00A69)", MRnumber = "1115922 (92g:58087)", MRreviewer = "Dieter H. Mayer", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Prather:1988:CET, author = "R. E. Prather", title = "Comparison and Extension of Theories of {Zipf} and {Halstead}", journal = j-COMP-J, volume = "31", number = "3", pages = "248--252", month = jun, year = "1988", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Tue Mar 25 13:51:56 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/", URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif; http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif", acknowledgement = ack-nhfb, affiliation = "Trinity Univ, San Antonio, TX, USA", affiliationaddress = "Trinity Univ, San Antonio, TX, USA", classcodes = "C6110B (Software engineering techniques)", classification = "723", corpsource = "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX, USA", fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", keywords = "behavioural psychology; computer programming; computer software; empirical law; Halstead metrics; Halstead's hypothesis; length estimates; Measurements; probabilistic hypothesis; process; programming; software engineering; software metrication; software science; Zipf metrics; Zipf's law", treatment = "T Theoretical or Mathematical", } @Article{Sanders:1988:PPU, author = "Robert Sanders", title = "The {Pareto Principle}: Its Use and Abuse", journal = "Journal of Business \& Industrial Marketing", volume = "3", number = "2", pages = "37--40", month = "????", year = "1988", CODEN = "????", DOI = "https://doi.org/10.1108/eb006057", ISSN = "0885-8624", ISSN-L = "0885-8624", bibdate = "Fri Nov 25 07:04:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Schatte:1988:ASC, author = "Peter Schatte", title = "On the Almost Sure Convergence of Floating-Point Mantissas and {Benford's Law}", journal = j-MATH-NACHR, volume = "135", number = "1", pages = "79--83", month = "????", year = "1988", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19881350108", ISSN = "0025-584X", ISSN-L = "0025-584X", MRclass = "60F15 (11K31)", MRnumber = "944219 (89g:60114)", MRreviewer = "S. A. Book", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", onlinedate = "12 Nov 2006", reviewer = "S. A. Book", } @Article{Schatte:1988:LIL, author = "Peter Schatte", title = "On a law of the iterated logarithm for sums {$ \bmod 1 $} with application to {Benford}'s law", journal = j-PROBAB-THEORY-RELAT-FIELDS, volume = "77", number = "2", pages = "167--178", month = feb, year = "1988", CODEN = "PTRFEU", DOI = "https://doi.org/10.1007/BF00334035", ISSN = "0178-8051 (print), 1432-2064 (electronic)", ISSN-L = "0178-8051", MRclass = "60F15 (11K31)", MRnumber = "927235 (89b:60081)", MRreviewer = "L. Kuipers", bibdate = "Sun Apr 27 11:18:06 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/probab-theory-relat-fields.bib", URL = "http://link.springer.com/article/10.1007/BF00334035", acknowledgement = ack-nhfb, fjournal = "Probability Theory and Related Fields", journal-URL = "http://link.springer.com/journal/440", } @Article{Schatte:1988:MDC, author = "Peter Schatte", title = "On Mantissa Distribution in Computing and {Benford's Law}", journal = j-J-INFO-PROC-CYBERNETICS-EIK, volume = "24", number = "9", pages = "443--455", month = "????", year = "1988", CODEN = "JICYE5", ISSN = "0863-0593", ISSN-L = "0863-0593", MRclass = "60E05 (11K06 11K31 65G99)", MRnumber = "984516 (90g:60016)", MRreviewer = "F. Schweiger", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/eik/eik24.html#Schatte88", acknowledgement = ack-nhfb # "\slash " # ack-nj, dblp-key = "journals/eik/Schatte88", dblp-mdate = "2020-03-06", fjournal = "Journal of Information Processing and Cybernetics: EIK", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Schatte:1988:UDC, author = "Peter Schatte", title = "On the uniform distribution of certain sequences and {Benford}'s law", journal = j-MATH-NACHR, volume = "136", number = "1", pages = "271--273", year = "1988", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.19881360119", ISSN = "0025-584X", ISSN-L = "0025-584X", MRclass = "11K06 (11K31)", MRnumber = "952478 (89j:11075)", MRreviewer = "O. P. Stackelberg", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", onlinedate = "11 Nov 2006", } @Article{Tichy:1988:SRC, author = "Robert F. Tichy", title = "{Statistische Resultate {\"u}ber computergerechte Darstellungen von Zahlen}. ({German}) [Statistical results on computer-oriented representations of numbers]", journal = "Anzeiger der {\"O}sterreichischen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Klasse", volume = "1987", number = "??", pages = "1--8", month = "????", year = "1988", CODEN = "OSAWA8", DOI = "????", ISSN = "0065-535X", ISSN-L = "0065-535X", bibdate = "Mon Feb 18 06:45:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", ZMnumber = "0625.10041", acknowledgement = ack-nhfb, ajournal = "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.", language = "German", xxnote = "Despite repeated searches, I have not found this journal online, not even from links at the Austrian Academy of Sciences, \path=http://www.oeaw.ac.at=.", ZMclass = "11K16 (Normal numbers, etc.); 11J71 (Distribution modulo one); 11K38 (Irregularities of distribution)", } @Article{Arnold:1989:BEP, author = "Barry C. Arnold and S. James Press", title = "{Bayesian} estimation and prediction for {Pareto} data", journal = j-J-AM-STAT-ASSOC, volume = "84", number = "408", pages = "1079--1084", month = "????", year = "1989", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", MRclass = "62F15 (62F10)", MRnumber = "92f:62034", bibdate = "Mon May 5 12:36:01 MDT 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Chen:1989:ZLT, author = "Ye-Sho Chen", title = "{Zipf}'s laws in text modeling", journal = "International Journal of General Systems. Methodology, Applications, Education", volume = "15", number = "3", pages = "233--252", year = "1989", CODEN = "IJGSAX", DOI = "https://doi.org/10.1080/03081078908935048", ISSN = "0308-1079, 1026-7492, 1563-5104", ISSN-L = "0308-1079", MRclass = "92A90", MRnumber = "1015844", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Internat. J. Gen. Systems", fjournal = "International Journal of General Systems. Methodology, Applications, Education", } @Article{Family:1989:KDG, author = "Fereydoon Family and Paul Meakin", title = "Kinetics of droplet growth processes: Simulations, theory, and experiments", journal = j-PHYS-REV-A, volume = "40", number = "7", pages = "3836--3854", month = oct, year = "1989", CODEN = "PLRAAN", DOI = "https://doi.org/10.1103/PhysRevA.40.3836", ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519", ISSN-L = "1050-2947", bibdate = "Thu Feb 28 10:49:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevA.40.3836", acknowledgement = ack-nhfb, fjournal = "Physical Review A (Atomic, Molecular, and Optical Physics)", journal-URL = "http://pra.aps.org/browse", } @InProceedings{Kitsuregawa:1989:EBS, author = "Masaru Kitsuregawa and Masaya Nakayama and Mikio Takagi", title = "The Effect of Bucket Size Tuning in the Dynamic Hybrid {GRACE} Hash Join Method", crossref = "Apers:1989:VLD", pages = "257--266", month = aug, year = "1989", CODEN = "VLDBDP", bibdate = "Sat Jan 25 17:38:12 MST 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/hash.bib", abstract = "In this paper, we show detailed analysis and performance evaluation of the Dynamic Hybrid GRACE Hash Join Method (DHGH Method) when the tuple distribution in buckets is unbalanced. The conventional Hash Join Methods specify the tuple distribution in buckets statically. However it may differ from estimation since join operations are applied with selection operations. When the tuple distribution in buckets is unbalanced, the processing cost of join operation becomes more costly than the ideal case when you use Hybrid Hash Join Method (HH Method). On the other hand, when you use the DHGH Method, the destaging buckets are selected dynamically, gives the same performance as the ideal case even if the tuple distribution in buckets is unbalanced such as Zipf-like distributions.", acknowledgement = ack-nhfb, affiliation = "Univ of Tokyo", affiliationaddress = "Tokyo, Jpn", classification = "723", journalabr = "Very Large Data Bases Int Conf Very Large Data Bases", keywords = "Computer Metatheory --- Programming Theory; Computer Programming --- Algorithms; Database Systems; Query Processing; Relational; Relational Algebra; VLDB", } @Article{Lang:1989:UAB, author = "Sheau-Dong Lang and James R. Driscoll and Jiann H. Jou", title = "A Unified Analysis of Batched Searching of Sequential and Tree-Structured Files", journal = j-TODS, volume = "14", number = "4", pages = "604--618", month = dec, year = "1989", CODEN = "ATDSD3", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", MRclass = "68P10 (68P20)", MRnumber = "1 073 204", bibdate = "Sat Apr 14 10:34:48 MDT 2001", bibsource = "Database/Graefe.bib; Database/Wiederhold.bib; http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf; http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/; http://www.acm.org/pubs/toc/Abstracts/tods/76908.html", abstract = "A direct and unified approach is used to analyze the efficiency of batched searching of sequential and tree-structured files. The analysis is applicable to arbitrary search distributions, and closed-form expressions are obtained for the expected batched searching cost and savings. In particular, we consider a search distribution satisfying Zipf's law for sequential files and four types of uniform (random) search distribution for sequential and tree-structured files. These results unify and extend earlier research on batched searching and estimating block accesses for database systems.", acknowledgement = ack-nhfb, affiliation = "Central Florida Univ., Orlando, FL, USA", annote = "closed-form expressions for the number of accesses needed given arbitrary search distributions.", fjournal = "ACM Transactions on Database Systems", generalterms = "Algorithms; Design; Performance; Theory", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "algorithms; design; performance; theory", subject = "{\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Search process. {\bf H.3.2}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Storage, File organization. {\bf H.2.2}: Information Systems, DATABASE MANAGEMENT, Physical Design, Access methods.", } @Article{Nicholls:1989:RBM, author = "Paul Travis Nicholls", title = "Research: Bibliometric modeling processes and the empirical validity of {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "40", number = "6", pages = "379--385", month = nov, year = "1989", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(198911)40:6<379::AID-ASI1>3.0.CO%3B2-Q", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:37 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "27 May 2007", } @Article{Nicolis:1989:CDM, author = "G. Nicolis and C. Nicolis and John S. Nicolis", title = "Chaotic dynamics, {Markov} partitions, and {Zipf}'s law", journal = j-J-STAT-PHYS, volume = "54", number = "3--4", pages = "915--924", month = feb, year = "1989", CODEN = "JSTPSB", DOI = "https://doi.org/10.1007/BF01019781", ISSN = "0022-4715 (print), 1572-9613 (electronic)", ISSN-L = "0022-4715", MRclass = "58F13 (58F14 58F20)", MRnumber = "988565 (90b:58184)", MRreviewer = "Shi Hai Li", bibdate = "Thu Aug 28 18:40:55 MDT 2014", bibsource = "http://link.springer.com/journal/10955; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=54&issue=3; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib", URL = "http://link.springer.com/article/10.1007/BF01019781", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Physics", journal-URL = "http://link.springer.com/journal/10955", } @Article{Nicolis:1989:PBZ, author = "John S. Nicolis and Ichiro Tsuda", title = "On the parallel between {Zipf}'s law and {$ 1 / f $} processes in chaotic systems possessing coexisting attractors", journal = j-PROG-THEOR-PHYS, volume = "82", number = "2", pages = "254--274", year = "1989", CODEN = "PTPKAV", ISSN = "0033-068X (print), 1347-4081 (electronic)", ISSN-L = "0033-068X", MRclass = "58F13 (92K20)", MRnumber = "1023357 (91d:58165)", MRreviewer = "Nima Geffen", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Progress of Theoretical Physics", journal-URL = "http://ptp.oxfordjournals.org/content/by/year", } @Article{Schatte:1989:MUD, author = "Peter Schatte", title = "On measures of uniformly distributed sequences and {Benford}'s law", journal = j-MONAT-MATH, volume = "107", number = "3", pages = "245--256", year = "1989", CODEN = "MNMTA2", DOI = "https://doi.org/10.1007/BF01300347", ISSN = "0026-9255 (print), 1436-5081 (electronic)", ISSN-L = "0026-9255", MRclass = "11K36 (60F99)", MRnumber = "1008683 (90k:11097)", MRreviewer = "Kazuo Goto", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Monatshefte f{\"u}r Mathematik", journal-URL = "http://link.springer.com/journal/605", } @Article{Shanbhag:1989:BRBa, author = "D. N. Shanbhag", title = "Book Review: {{\booktitle{Pareto Distributions}}, by B. C. Arnold}", journal = j-J-R-STAT-SOC-SER-A-STAT-SOC, volume = "152", number = "2", pages = "253--254", month = "????", year = "1989", CODEN = "JSSAEF", DOI = "https://doi.org/10.2307/2982920", ISSN = "0964-1998 (print), 1467-985X (electronic)", ISSN-L = "0964-1998", bibdate = "Sat Jan 24 15:13:38 MST 2015", bibsource = "http://www.jstor.org/stable/i349642; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-a-1980.bib", URL = "http://www.jstor.org/stable/2982920", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series A (Statistics in Society)", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-985X; http://www.jstor.org/journals/09641998.html", } @Article{Shieh:1989:BZE, author = "Yeung-Nan Shieh", title = "The {Beckmann--Zipf} effect and plant location under uniform pricing", journal = j-ECONOM-LETT, volume = "30", number = "1", pages = "89--92", day = "1", month = jan, year = "1989", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/0165-1765(89)90162-6", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "90A12 (90B05)", MRnumber = "1010312", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0165176589901626", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Thomas:1989:UPR, author = "Jacob K. Thomas", title = "Unusual patterns in reported earnings", journal = j-ACCOUNT-REV, volume = "59", number = "4", pages = "773--787", month = oct, year = "1989", CODEN = "ACRVAS", ISSN = "0001-4826 (print), 1558-7967 (electronic)", ISSN-L = "0001-4826", bibdate = "Fri Feb 15 06:49:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/247861", acknowledgement = ack-nhfb, fjournal = "The Accounting Review", keywords = "Benford's Law; distribution of first digits; distribution of second digits", } @Article{Xekalaki:1989:APY, author = "E. Xekalaki and J. Panaretos", title = "On the Association of the {Pareto} and the {Yule} Distribution", journal = j-THEORY-PROBAB-APPL, volume = "33", number = "1", pages = "191--195", month = "????", year = "1989", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/1133028", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Tue Apr 1 10:40:04 MDT 2014", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/33/1; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib", acknowledgement = ack-nhfb, fjournal = "Theory of Probability and its Applications", journal-URL = "http://epubs.siam.org/tvp", onlinedate = "January 1989", } @Article{Egghe:1990:RAT, author = "L. Egghe", title = "Research: Applications of the theory of {Bradford}'s {Law} to the calculation of {Leimkuhler's Law} and to the completion of bibliographies", journal = j-J-AM-SOC-INF-SCI, volume = "41", number = "7", pages = "469--492", month = oct, year = "1990", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199010)41:7<469::AID-ASI1>3.0.CO%3B2-P", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:41 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Jan 1999", } @Article{Egghe:1990:RND, author = "L. Egghe", title = "Research: A note on different {Bradford} multipliers", journal = j-J-AM-SOC-INF-SCI, volume = "41", number = "3", pages = "204--209", month = apr, year = "1990", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199004)41:3<204::AID-ASI7>3.0.CO%3B2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:39 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Jan 1999", } @Article{Katsikas:1990:CDG, author = "A. A. Katsikas and J. S. Nicolis", title = "Chaotic dynamics of generating {Markov} partitions and linguistic sequences mimicking {Zipf}'s law", journal = "Nuovo Cimento D (1)", volume = "12", number = "2", pages = "177--195", year = "1990", CODEN = "NCSDDN", DOI = "https://doi.org/10.1007/BF02450454", ISSN = "0392-6737 (print), 1826-9893 (electronic)", ISSN-L = "0392-6737", MRclass = "92A90 (58F13 92A08 94A15)", MRnumber = "1049338 (90m:92114)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D. Serie 1", } @InCollection{Nagasaka:1990:BLL, author = "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong Shiue", booktitle = "Number theory, {Vol}.\ {I} ({Budapest}, 1987)", title = "{Benford}'s law: the logarithmic law of first digit", volume = "51", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "361--391", year = "1990", MRclass = "11K06", MRnumber = "1058225 (92b:11048)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Colloq. Math. Soc. J{\'a}nos Bolyai", acknowledgement = ack-nhfb, } @Article{Peritz:1990:BDB, author = "Bluma C. Peritz", title = "A {Bradford} distribution for bibliometrics", journal = j-SCIENTOMETRICS, volume = "18", number = "5--6", pages = "323--329", month = may, year = "1990", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02020148", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:03:16 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib", URL = "http://link.springer.com/article/10.1007/BF02020148", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Schatte:1990:BLC, author = "Peter Schatte", title = "On {Benford}'s law for continued fractions", journal = j-MATH-NACHR, volume = "148", pages = "137--144", year = "1990", CODEN = "MTMNAQ", ISSN = "0025-584X", ISSN-L = "0025-584X", MRclass = "11K50 (11K06)", MRnumber = "1127337 (92m:11077)", MRreviewer = "Harald Niederreiter", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", } @Book{Szekely:1990:PKN, author = "G{\'a}bor J. Sz{\'e}kely", title = "{Paradoxa: klassische und neue {\"U}berraschungen aus Wahrscheinlichkeitsrechnung und mathematischer Statistik}. (German) [{Paradoxes}: traditional and new surprises in probability and mathematical statistics]", publisher = "Deutsch", address = "Thun, Switzerland", pages = "239", year = "1990", ISBN = "3-87144-850-8", ISBN-13 = "978-3-87144-850-8", LCCN = "????", bibdate = "Thu Nov 17 19:26:05 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.gbv.de:20011/gvk", note = "Translation by Ulrike Leitner from the Hungarian original.", URL = "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf; http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004", acknowledgement = ack-nhfb, language = "German", } @Article{VandenBroeck:1990:LFB, author = "C. {Van den Broeck} and R. Kawai", title = "Learning in feedforward {Boolean} networks", journal = j-PHYS-REV-A, volume = "42", number = "??", pages = "6210--??", day = "15", month = nov, year = "1990", CODEN = "PLRAAN", DOI = "https://doi.org/10.1103/PhysRevA.42.6210", ISSN = "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519", ISSN-L = "1050-2947", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevA.42.6210", acknowledgement = ack-nhfb, fjournal = "Physical Review A (Atomic, Molecular, and Optical Physics)", journal-URL = "http://pra.aps.org/browse", keywords = "Zipf's Law", } @Article{Yeh:1990:ODT, author = "Hsiaw-Chan Yeh", title = "One discrete time series model for fat-tailed integer random variables: {Zipf} process", journal = "Bulletin of the Institute of Mathematics. Academia Sinica", volume = "18", number = "1", pages = "19--33", year = "1990", CODEN = "BIMSDG", ISSN = "0304-9825", ISSN-L = "0304-9825", MRclass = "60J10 (62M10)", MRnumber = "1072827 (91i:60175)", MRreviewer = "Ed McKenzie", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Bull. Inst. Math. Acad. Sinica", fjournal = "Bulletin of the Institute of Mathematics. Academia Sinica", } @Article{Antonini:1991:NUD, author = "Rita Giuliano Antonini", title = "On the Notion of Uniform Distribution Mod $1$", journal = j-FIB-QUART, volume = "29", number = "3", pages = "230--234", month = aug, year = "1991", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:01:34 MDT 2011", bibsource = "http://www.fq.math.ca/29-3.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/29-3/antonini.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", keywords = "Benford's Law", } @Article{Burke:1991:BLP, author = "John Burke and Eric Kincanon", title = "{Benford}'s law and physical constants: The distribution of initial digits", journal = j-AMER-J-PHYSICS, volume = "59", number = "10", pages = "952--952", month = oct, year = "1991", CODEN = "AJPIAS", DOI = "https://doi.org/10.1119/1.16838", ISSN = "0002-9505 (print), 1943-2909 (electronic)", ISSN-L = "0002-9505", bibdate = "Mon Nov 14 17:31:11 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B; http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1", acknowledgement = ack-nhfb, fjournal = "American Journal of Physics", journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp", } @Article{Burrell:1991:BDG, author = "Q. L. Burrell", title = "The {Bradford} distribution and the {Gini} index", journal = j-SCIENTOMETRICS, volume = "21", number = "2", pages = "181--194", month = jun, year = "1991", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02017568", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:03:22 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib", URL = "http://link.springer.com/article/10.1007/BF02017568", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Chen:1991:ZLN, author = "Ye-Sho Chen", title = "{Zipf}'s law in natural languages, programming languages, and command languages: the {Simon--Yule} approach", journal = j-INT-J-SYST-SCI, volume = "22", number = "11", pages = "2299--2312", year = "1991", CODEN = "IJSYA9", DOI = "https://doi.org/10.1080/00207729108910791", ISSN = "0020-7721 (print), 1464-5319 (electronic)", ISSN-L = "0020-7721", bibdate = "Sat Nov 12 10:50:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0793.68020", abstract = "Zipf's law and issues in natural languages, programming languages and command languages related to it, are reviewed. We point out the need for a unified theory to resolve the issues. Based on Herbert Simon's creative process for scientific discovery, we evaluate four leading theories of language generation. As a result, the Simon--Yule model of text generation is selected as a promising theory. The implications of the theory related to the issues in natural languages, programming languages and command languages are discussed.", acknowledgement = ack-nhfb, classmath = "68N15 (Programming languages) 68T50 (Natural language processing)", fjournal = "International Journal of Systems Science", journal-URL = "http://www.tandfonline.com/loi/tsys20", keywords = "command languages; natural languages; programming languages; Simon-Yule model; text generation; Zipf's law", } @Book{Durrett:1991:PTE, author = "Richard Durrett", title = "Probability: theory and examples", publisher = "Wadsworth and Brooks\slash Cole Advanced Books and Software", address = "Pacific Grove, CA, USA", pages = "ix + 453", year = "1991", ISBN = "0-534-13206-5", ISBN-13 = "978-0-534-13206-4", LCCN = "QA273 .D865 1991", bibdate = "Mon Nov 21 10:06:18 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", price = "US\$49.95", series = "The Wadsworth and Brooks\slash Cole statistics\slash probability series", acknowledgement = ack-nhfb, remark = "Benford's Law is treated on pp. 300ff. Hill \cite[page 893]{Hill:1995:BII} reports that Durrett has a proof that the $k$-th digit of powers of integers follows Benford's Law.", subject = "Probabilities", } @Book{Hardy:1991:DS, author = "G. H. (Godfrey Harold) Hardy", title = "Divergent series", publisher = "Chelsea Pub. Co.", address = "New York, NY, USA", edition = "Second", pages = "xvi + 396", year = "1991", ISBN = "0-8284-0334-1", ISBN-13 = "978-0-8284-0334-4", LCCN = "QA295 .H29 1991", bibdate = "Wed Nov 16 08:17:27 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1877--1947", remark = "Unaltered reprint of \cite{Hardy:1949:DS}, despite label of second edition.", subject = "Divergent series", } @Article{Katsikas:1991:CDG, author = "A. A. Katsikas and J. S. Nicolis", title = "Chaotic Dynamics of Generating {Markov} Partitions, and Linguistic Sequences Mimicking {Zipf}'s Law", journal = j-LECT-NOTES-COMP-SCI, volume = "565", pages = "335--??", year = "1991", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon May 13 08:51:55 MDT 1996", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Schatte:1991:NBL, author = "P. Schatte and K. Nagasaka", title = "A note on {Benford}'s law for second order linear recurrences with periodical coefficients", journal = j-Z-ANAL-ANWEND, volume = "10", number = "2", pages = "251--254", year = "1991", CODEN = "????", ISSN = "0232-2064 (print), 1661-4534 (electronic)", ISSN-L = "0232-2064", MRclass = "11K31", MRnumber = "1155374 (93b:11101)", MRreviewer = "F. Schweiger", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}", } @Article{Schatte:1991:ULI, author = "P. Schatte", title = "On a uniform law of the iterated logarithm for sums mod {$1$} and {Benford}'s law", journal = "Litovsk. Mat. Sb.", volume = "31", number = "1", pages = "205--217", year = "1991", CODEN = "????", DOI = "https://doi.org/10.1007/BF00972327", ISSN = "0132-2818", ISSN-L = "0132-2818", MRclass = "60F15 (11K99)", MRnumber = "1161363 (93g:60067)", MRreviewer = "O. P. Stackelberg", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys. Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\ Matematicheski{\u\i} Sbornik", xxnote = "Check pages: reprinted in two version of this journal??", } @Book{Schroeder:1991:FCP, author = "Manfred Schroeder", title = "Fractals, Chaos, Power Laws", publisher = pub-W-H-FREEMAN, address = pub-W-H-FREEMAN:adr, pages = "xviii + 429", year = "1991", ISBN = "0-671-74217-5, 0-7167-2136-8, 0-7167-2357-3", ISBN-13 = "978-0-671-74217-1, 978-0-7167-2136-9, 978-0-7167-2357-8", LCCN = "QD921 .S3 1990", bibdate = "Wed Dec 15 10:41:35 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/bibnet/authors/s/shannon-claude-elwood.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib", abstract = "Reveals the extraordinary dimensions of new mathematical insights about the nature of physical reality; explores the powerful applications of these symmetry concepts in physics, chemistry, music, and the visual arts. Includes such areas as deterministic chaos and strange attractors, iterated mappings, nonlinear dynamics, Cayley trees, cellular automata, random fractals and related topics.", acknowledgement = ack-nhfb, shorttableofcontents = "Introduction \\ Similarity and dissimilarity \\ Self-similarity --- discrete, continuous, strict, and otherwise \\ Power laws: endless sources of self-similarity \\ Noises: white, pink, brown, and black \\ Brownian motion, gambling losses, and intergalactic voids: random fractals par excellence \\ Cantor sets: self-similarity and arithmetic dust \\ Fractals in higher dimensions and a digital sundial \\ Multifractals: intimately intertwined fractals \\ Some practical fractals and their measurement \\ Iteration, strange mappings, and a billion digits for $\pi$ \\ A self-similar sequence, the logistic parabola, and symbolic dynamics \\ A forbidden symmetry, Fibonacci's rabbits, and a new state of matter \\ Periodic and quasiperiodic structures in space --- the route to spatial chaos \\ Percolation: from forest fires to epidemics \\ Phase transitions and renormalization \\ Cellular automata", tableofcontents = "Preface / xiii \\ 1: Introduction / 1 \\ Einstein, Pythagoras, and Simple Similarity / 3 \\ A Self-Similar Array of Self-Preserving Queens / 4 \\ A Self-Similar Snowflake / 7 \\ A New Dimension for Fractals / 9 \\ A Self-Similar Tiling and a ``Non-Euclidean'' Paradox / 13 \\ At the Gates of Cantor's Paradise / 15 \\ The Sierpinski Gasket / 17 \\ Sir Pinski's Game and Deterministic Chaos / 20 \\ Three Bodies Cause Chaos / 25 \\ Strange Attractors, Their Basins, and a Chaos Game 2 / 7 \\ Percolating Random Fractals / 30 \\ Power Laws: from Alvarez to Zipf / 33 \\ Newton's Iteration and How to Abolish Two-Nation Boundaries / 38 \\ Could Minkowski Hear the Shape of a Drum? / 40 \\ Discrete Self-Similarity: Creases and Center Folds / 45 \\ Golden and Silver Means and Hyperbolic Chaos / 49 \\ Winning at Fibonacci Nim / 53 \\ Self-Similar Sequences from Square Lattices / 55 \\ John Horton Conway's ``Death Bet'' / 57 \\ 2: Similarity and Dissimilarity / 61 \\ More Than One Scale / 61 \\ To Scale or Not to Scale: A Bit of Biology and Astrophysics / 63 \\ Similarity in Physics: Some Astounding Consequences / 66 \\ Similarity in Concert Halls, Microwaves, and Hydrodynamics / 68 \\ Scaling in Psychology / 70 \\ Acousticians, Alchemy, and Concert Halls / 72 \\ Preference and Dissimilarity: Concert Halls Revisited / 74 \\ 3: Self-Similarity --- Discrete, Continuous, Strict, and Otherwise / 81 \\ The Logarithmic Spiral, Cutting Knives, and Wideband Antennas / 89 \\ Some Simple Cases of Self-Similarity / 93 \\ Weierstrass Functions and a Musical Paradox / 96 \\ More Self-Similarity in Music: The Tempered Scales of Bach / 99 \\ The Excellent Relations between the Primes 3, 5, and 7 / 102 \\ 4: Power Laws: Endless Sources of Self-Similarity / 103 \\ The Sizes of Cities and Meteorites / 103 \\ A Fifth Force of Attraction / 105 \\ Free of Natural Scales / 107 \\ Bach Composing on All Scales / 107 \\ Birkhoff's Aesthetic Theory / 109 \\ Heisenberg's Hyperbolic Uncertainty Principle / 112 \\ Fractional Exponents / 115 \\ The Peculiar Distribution of the First Digit / 116 \\ The Diameter Exponents of Trees, Rivers, Arteries, and Lungs / 117 \\ 5: Noises: White, Pink, Brown, and Black / 121 \\ Pink Noise / 122 \\ Self-Similar Trends on the Stock Market / 126 \\ Black Noises and Nile Floods / 129 \\ Warning: World Warming / 131 \\ Fractional Integration: A Modem Tool / 131 \\ Brownian Mountains / 133 \\ Radon Transform and Computer Tomography / 134 \\ Fresh and Tired Mountains / 135 \\ 6: Brownian Motion, Gambling Losses, and Intergalactic Voids: Random Fractals Par Excellence / 139 \\ The Brownian Beast Tamed / 140 \\ Brownian Motion as a Fractal / 141 \\ How Many Molecules? / 143 \\ The Spectrum of Brownian Motion / 144 \\ The Gambler's Ruin, Random Walks, and Information Theory / 145 \\ Counterintuition Runs Rampant in Random Runs / 146 \\ More Food for Fair Thought / 147 \\ The St. Petersburg Paradox / 148 \\ Shannon's Outguessing Machine / 149 \\ The Classical Mechanics of Roulette and Shannon's Channel Capacity / 150 \\ The Clustering of Poverty and Galaxies / 152 \\ Levy Flights through the Universe / 155 \\ Paradoxes from Probabilistic Power Laws / 155 \\ Invariant Distributions: Gauss, Cauchy, and Beyond / 157 \\ 7: Cantor Sets: Self-Similarity and Arithmetic Dust / 161 \\ A Comer of Cantor's Paradise / 161 \\ Cantor Sets as Invariant Sets / 165 \\ Symbolic Dynamics and Deterministic Chaos / 166 \\ Devil's Staircases and a Pinball Machine / 167 \\ Mode Locking in Swings and Clocks / 171 \\ The Frustrated Manhattan Pedestrian / 172 \\ Arnold Tongues 17 / 4 \\ 8: Fractals in Higher Dimensions and a Digital Sundial / 177 \\ Cartesian Products of Cantor Sets / 177 \\ A Leaky Gasket, Soft Sponges, and Swiss Cheeses / 178 \\ A Cantor-Set Sundial / 181 \\ Fat Fractals / 183 \\ 9: Multifractals: Intimately Intertwined Fractals / 187 \\ The Distributions of People and Ore / 187 \\ Self-Affine Fractals without Holes / 190 \\ The Multifractal Spectrum: Turbulence and Diffusion-Limited Aggregation / 193 \\ Viscous Fingering / 199 \\ Multifractals on Fractals / 200 \\ Fractal Dimensions from Generalized Entropies / 203 \\ The Relation between the Multifractal Spectrum $f(\alpha)$ and the Mass Exponents $(q)$ / 205 \\ Strange Attractors as Multifractals / 206 \\ A Greedy Algorithm for Unfavorable Odds / 207 \\ 10: Some Practical Fractals and Their Measurement / 211 \\ Dimensions from Box Counting / 213 \\ The Mass Dimension / 215 \\ The Correlation Dimension / 220 \\ Infinitely Many Dimensions / 220 \\ The Determination of Fractal Dimensions from Time Series / 223 \\ Abstract Concrete / 224 \\ Fractal Interfaces Enforce Fractional Frequency Exponents / 225 \\ The Fractal Dimensions of Fracture Surfaces / 230 \\ The Fractal Shapes of Clouds and Rain Areas / 231 \\ Cluster Agglomeration / 232 \\ Diffraction from Fractals / 233 \\ 11: Iteration, Strange Mappings, and a Billion Digits for Pi / 237 \\ Looking for Zeros and Encountering Chaos / 239 \\ The Strange Sets of Julia / 243 \\ A Multifractal Julia Set / 245 \\ The Beauty of Broken Linear Relationships / 249 \\ The Baker's Transformation and Digital Musical Chairs / 251 \\ Arnol'd's Cat Map / 253 \\ A Billion Digits for $\pi$ / 257 \\ Bushes and Flowers from Iterations / 259 \\ 12: A Self-Similar Sequence, the Logistic Parabola, and Symbolic Dynamics / 263 \\ Self-Similarity from the Integers / 264 \\ The Logistic Parabola and Period Doubling / 268 \\ Self-Similarity in the Logistic Parabola / 272 \\ The Scaling of the Growth Parameter / 274 \\ Self-Similar Symbolic Dynamics / 277 \\ Periodic Windows Embedded in Chaos / 279 \\ The Parenting of New Orbits / 282 \\ The Calculation of the Growth Parameters for Different Orbits / 286 \\ Tangent Bifurcations, Intermittency, and I/f Noise / 289 \\ A Case of Complete Chaos / 291 \\ The Mandelbrot Set / 295 \\ The Julia Sets of the Complex Quadratic Map / 297 \\ 13: A Forbidden Symmetry, Fibonacci's Rabbits, and a New State of Matter / 301 \\ The Forbidden Fivefold Symmetry / 301 \\ Long-Range Order from Neighborly Interactions / 304 \\ Generation of the Rabbit Sequence from the Fibonacci Number System / 307 \\ The Self-Similar Spectrum of the Rabbit Sequence / 308 \\ Self-Similarity in the Rabbit Sequence / 310 \\ A One-Dimensional Quasiperiodic Lattice / 310 \\ Self-Similarity from Projections / 311 \\ More Forbidden Symmetries / 315 \\ 14: Periodic and Quasiperiodic Structures in Space --- The route to Spatial Chaos / 319 \\ Periodicity and Quasiperiodicity in Space / 320 \\ The Devil's Staircase for Ising Spins / 321 \\ Quasiperiodic Spatial Distributions / 322 \\ Beatty Sequence Spins / 325 \\ The Scaling Laws for Quasiperiodic Spins / 329 \\ Self-Similar Winding Numbers / 330 \\ Circle Maps and Arnold Tongues / 331 \\ Mediants, Farey Sequences, and the Farey Tree / 334 \\ The Golden-Mean Route to Chaos / 340 \\ 15: Percolation: From Forest Fires to Epidemics / 345 \\ Critical Conflagration on a Square Lattice / 346 \\ Universality / 350 \\ The Critical Density / 353 \\ The Fractal Perimeters of Percolation / 353 \\ Finite-Size Scaling / 354 \\ 16: Phase Transitions and Renormalization / 357 \\ A First-Order Markov Process / 357 \\ Self-Similar and Non-Self-Similar Markov Processes / 358 \\ The Scaling of Markov Output's / 360 \\ Renormalization and Hierarchical Lattices / 362 \\ The Percolation Threshold of the Bethe Lattice / 363 \\ A Simple Renormalization / 367 \\ 17: Cellular Automata / 371 \\ The Game of Life / 373 \\ Cellular Growth and Decay / 375 \\ Biological Pattern Formation / 382 \\ Self-Similarity from a Cellular Automaton / 383 \\ A Catalytic Converter as a Cellular Automaton / 386 \\ Pascal's Triangle Modulo $N$ / 387 \\ Bak's Self-Organized Critical Sandpiles / 389 \\ Appendix / 391 \\ References / 395 \\ Author Index / 411 \\ Subject Index / 417", } @Article{Trubnikov:1991:SDZ, author = "B. A. Trubnikov and I. A. Rumynski{\u\i}", title = "A simple derivation of the {Zipf--Krylov} law for words and the possibility of its ``evolution'' interpretation", journal = j-DOKL-AKAD-NAUK, volume = "321", number = "2", pages = "270--275", year = "1991", CODEN = "DANKAS", ISSN = "0002-3264", ISSN-L = "0002-3264", MRclass = "00A69 (92K20)", MRnumber = "1153554", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Doklady Akademii Nauk SSSR", journal-URL = "http://istina.msu.ru/journals/366838/", } @Article{Basu:1992:RHD, author = "Aparna Basu", title = "Research: Hierarchical distributions and {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "43", number = "7", pages = "494--500", month = aug, year = "1992", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<494::AID-ASI4>3.0.CO%3B2-F", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:51 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @TechReport{Busta:1992:TRN, author = "B. Busta and R. Sundheim", title = "Tax return numbers tend to obey {Benford}'s law", type = "Working Paper", number = "W93-106-94", institution = "Center for Business Research, St. Cloud State University", address = "St. Cloud, MN, USA", year = "1992", bibdate = "Sat Feb 16 17:29:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Dehaene:1992:CLR, author = "Stanislas Dehaene and Jacques Mehler", title = "Cross-linguistic regularities in the frequency of number words", journal = j-COGNITION, volume = "43", number = "1", pages = "1--29", year = "1992", CODEN = "CGTNAU", DOI = "https://doi.org/10.1016/0010-0277(92)90030-L", ISSN = "0010-0277 (print), 1873-7838 (electronic)", ISSN-L = "0010-0277", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/001002779290030L", abstract = "We examine the frequency of numerals and ordinals in seven different languages and/or cultures. Many cross-cultural and cross-linguistic patterns are identified. The most striking is a decrease of frequency with numerical magnitude, with local increases for reference numerals such as 10, 12, 15, 20, 50 or 100. Four explanations are considered for this effect: sampling artifacts, notational regularities, environmental biases and psychological limitations on number representations. The psychological explanation, which appeals to a Fechnerian encoding of numerical magnitudes and to the existence of numerical points of reference, accounts for most of the data. Our finding also has practical importance since it reveals the frequent confound of two experimental variables: numerical magnitude and numeral frequency.", acknowledgement = ack-nhfb, fjournal = "Cognition", keywords = "Benford's Law", } @Article{Goto:1992:SEB, author = "Kazuo Got{\^o}", title = "Some examples of {Benford} sequences", journal = "Math. J. Okayama Univ.", volume = "34", pages = "225--232 (1994)", year = "1992", CODEN = "MJOKAP", ISSN = "0030-1566", ISSN-L = "0030-1566", MRclass = "11K36", MRnumber = "1272624 (95c:11097)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Mathematical Journal of Okayama University", } @Article{Gunther:1992:PCZ, author = "R. G{\"u}nther and B. Schapiro and P. Wagner", title = "Physical complexity and {Zipf}'s law", journal = j-INT-J-THEOR-PHYS, volume = "31", number = "3", pages = "525--543", year = "1992", CODEN = "IJTPBM", DOI = "https://doi.org/10.1007/BF00740003", ISSN = "0020-7748 (print), 1572-9575 (electronic)", ISSN-L = "0020-7748", MRclass = "58F40", MRnumber = "1154668 (92k:58252)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Theoretical Physics", journal-URL = "http://link.springer.com/journal/10773", } @Article{Jech:1992:LDL, author = "Thomas Jech", title = "The logarithmic distribution of leading digits and finitely additive measures", journal = j-DISCRETE-MATH, volume = "108", number = "1--3", pages = "53--57", month = "????", year = "1992", CODEN = "DSMHA4", ISSN = "0012-365X (print), 1872-681X (electronic)", ISSN-L = "0012-365X", bibdate = "Fri Nov 18 12:12:57 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Discrete Mathematics", } @Article{Lagarias:1992:PTS, author = "J. C. Lagarias and A. Weiss", title = "The $ 3 x + 1 $ Problem: Two Stochastic Models", journal = j-ANN-APPL-PROBAB, volume = "2", number = "1", pages = "229--261", month = feb, year = "1992", CODEN = "????", ISSN = "1050-5164 (print), 2168-8737 (electronic)", ISSN-L = "1050-5164", bibdate = "Fri Jun 6 11:35:34 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/annapplprobab.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.aoap/1177005779", acknowledgement = ack-nhfb, fjournal = "Annals of Applied Probability", journal-URL = "http://projecteuclid.org/all/euclid.aoap/; http://www.jstor.org/journals/10505164.html", } @Article{Li:1992:RTE, author = "W. Li", title = "Random texts exhibit {Zipf}'s-law-like word frequency distribution", journal = j-IEEE-TRANS-INF-THEORY, volume = "38", number = "6", pages = "1842--1845", month = "????", year = "1992", CODEN = "IETTAW", DOI = "https://doi.org/10.1109/18.165464", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", bibdate = "Fri Nov 18 12:32:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Information Theory", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18", } @Article{Longfellow:1992:LER, author = "Charles A. {Longfellow, Jr.}", title = "Letters to the {Editor}: Regarding {``Lotka's Law and the Kolmogorov--Smirnov Test: An Error in Calculation''}", journal = j-J-AM-SOC-INF-SCI, volume = "43", number = "7", pages = "518--518", month = aug, year = "1992", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<518::AID-ASI7>3.0.CO%3B2-#", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:51 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", note = "See \cite{Loughner:1992:BCL}.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Loughner:1992:BCL, author = "William Loughner", title = "Brief Communications: {Lotka's Law} and the {Kolmogorov--Smirnov} test: an error in calculation", journal = j-J-AM-SOC-INF-SCI, volume = "43", number = "2", pages = "149--150", month = mar, year = "1992", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199203)43:2<149::AID-ASI4>3.0.CO%3B2-Y", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:49 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", note = "See comment \cite{Longfellow:1992:LER}.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @PhdThesis{Nigrini:1992:DIE, author = "Mark John Nigrini", title = "The detection of income tax evasion through an analysis of digital distributions", type = "{Ph.D.} Dissertation", school = "Department of Accounting\slash Business Law, University of Cincinnati", address = "Cincinnati, OH, USA", pages = "xvi + 309", day = "28", month = aug, year = "1992", bibdate = "Sat Nov 12 15:47:41 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://search.proquest.com/docview/304052348", acknowledgement = ack-nhfb, advisor = "Wallace R. Wood", remark = "There are more than 230 mentions of Frank Benford, and 8 of Simon Newcomb, but no mention of Pareto or Zipf.", } @Article{Rousseau:1992:RBR, author = "Ronald Rousseau", title = "Research: Breakdown of the robustness property of {Lotka's Law}: the case of adjusted counts for multiauthorship attribution", journal = j-J-AM-SOC-INF-SCI, volume = "43", number = "10", pages = "645--647", month = dec, year = "1992", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199212)43:10<645::AID-ASI1>3.0.CO%3B2-X", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:48 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Sanders:1992:PPU, author = "Robert Sanders", title = "The {Pareto Principle}: its Use and Abuse", journal = j-J-PROD-BRAND-MANAG, volume = "1", number = "2", pages = "37--40", month = "????", year = "1992", CODEN = "????", DOI = "https://doi.org/10.1108/10610429210036762", ISSN = "1061-0421", ISSN-L = "1061-0421", bibdate = "Fri Nov 25 06:50:32 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Product \& Brand Management", keywords = "80/20 rule", } @Article{Too:1992:UDM, author = "Yeu-Hua Too", title = "On the uniform distribution modulo one of some log-like sequences", journal = "Proceedings of the Japan Academy, Series A. Mathematical Sciences", volume = "68", number = "9", pages = "269--272", month = "????", year = "1992", DOI = "https://doi.org/10.3792/pjaa.68.269", ISSN = "0021-4280", ISSN-L = "0021-4280", bibdate = "Mon Feb 18 06:55:06 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.pja/1195511634", acknowledgement = ack-nhfb, } @Article{Trachtenberg:1992:WFR, author = "M. Trachtenberg", title = "Why failure rates observe {Zipf}'s law in operational software", journal = j-IEEE-TRANS-RELIAB, volume = "41", number = "3", pages = "386--389", year = "1992", CODEN = "IEERAJ", DOI = "https://doi.org/10.1109/24.159803", ISSN = "0018-9529 (print), 1558-1721 (electronic)", ISSN-L = "0018-9529", bibdate = "Sat Nov 12 10:50:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0825.68222", acknowledgement = ack-nhfb, classmath = "68M15 (Reliability and testing of computer systems) 68N01 (General)", fjournal = "IEEE Transactions on Reliability", } @Article{Anonymous:1993:WFR, author = "Anonymous", title = "Why failure rates observe {Zipf}'s law in operational software: {M. Trachtenberg. IEEE Transactions on Reliability, {\bf 41}(3), 386 (1992)}", journal = j-MICROELECT-RELIABILITY, volume = "33", number = "13", pages = "2062--2062", month = oct, year = "1993", CODEN = "MCRLAS", DOI = "https://doi.org/10.1016/0026-2714(93)90406-O", ISSN = "0026-2714 (print), 1872-941X (electronic)", ISSN-L = "0026-2714", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/002627149390406O", acknowledgement = ack-nhfb, fjournal = "Microelectronics and Reliability", keywords = "Zipf's Law", } @Article{Buck:1993:IBF, author = "B. Buck and A. C. Merchant and S. M. Perez", title = "An illustration of {Benford}'s first digit law using alpha decay half lives", journal = j-EUR-J-PHYS, volume = "14", number = "2", pages = "59--63", month = "????", year = "1993", CODEN = "EJPHD4", DOI = "https://doi.org/10.1088/0143-0807/14/2/003", ISSN = "0143-0807 (print), 1361-6404 (electronic)", ISSN-L = "0143-0807", bibdate = "Mon Nov 14 17:32:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/1993EJPh...14...59B", acknowledgement = ack-nhfb, fjournal = "European Journal of Physics", journal-URL = "http://iopscience.iop.org/0143-0807/", } @Article{Christian:1993:NES, author = "C. W. Christian and S. Gupta", title = "New Evidence on ``Secondary Evasion''", journal = "Journal of the {American Taxation Association}", volume = "15", number = "??", pages = "72--93", month = "????", year = "1993", ISSN = "0198-9073 (print), 1558-8017 (electronic)", ISSN-L = "0198-9073", bibdate = "Thu Oct 13 06:50:53 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "J. Amer. Tax. Assoc.", fjournal = "Journal of the {American Taxation Association}", journal-URL = "http://aaajournals.org/loi/atax", remark = "No journal issues online before 1999.", } @Article{Deakin:1993:ADB, author = "Michael A. B. Deakin", title = "Another derivation of {Benford}'s law", journal = j-AUSTRALIAN-MATH-SOC-GAZ, volume = "20", number = "5", pages = "162--163", year = "1993", CODEN = "????", ISSN = "0311-0729 (print), 1326-2297 (electronic)", ISSN-L = "0311-0729", MRclass = "11K36", MRnumber = "1268513 (95j:11072)", MRreviewer = "Jean-Loup Mauclaire", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Australian Mathematical Society Gazette", journal-URL = "http://www.austms.org.au/gazette", } @Article{Nigrini:1993:CBL, author = "Mark Nigrini", title = "Can {Benford's Law} be used in Forensic Accounting?", journal = "The Balance Sheet", volume = "??", number = "??", pages = "7--8", month = jun, year = "1993", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 21 22:03:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Oluic-Vukovic:1993:LEW, author = "Vesna Olui{\'c}-Vukovi{\'c}", title = "Letters to the {Editor}: Why has {Bradford's Law} been an elusive phenomenon so far?", journal = j-J-AM-SOC-INF-SCI, volume = "44", number = "3", pages = "182--183", month = apr, year = "1993", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199304)44:3<182::AID-ASI9>3.0.CO%3B2-S", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:54 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @TechReport{Stewart:1993:LAN, author = "Ian Stewart", title = "The law of anomalous numbers", type = "Working paper", institution = "Mathematics Institute, University of Warwick", address = "Warwick, UK", year = "1993", bibdate = "Fri Mar 22 09:15:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Published in Spektrum der Wissenschaft (April 1994)", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @TechReport{Sundheim:1993:FNT, author = "R. Sundheim and B. Busta", title = "{Fibonacci} numbers tend to obey {Benford's Law}: an extension of {Wlodarski} and {Sentance}", type = "Working Paper", institution = "St. Cloud State University", address = "St. Cloud, MN, USA", month = "????", year = "1993", bibdate = "Mon Feb 18 06:37:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Sury:1993:FPD, author = "B. Sury", title = "Fractional parts of $ \log p $ and a digit function", journal = j-EXPO-MATH, volume = "11", number = "4", pages = "381--384", month = "????", year = "1993", DOI = "????", ISSN = "0723-0869 (print), 1878-0792 (electronic)", ISSN-L = "0723-0869", bibdate = "Mon Feb 18 06:39:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", ZMnumber = "0787.11003", acknowledgement = ack-nhfb, ajournal = "Expo. Math.", fjournal = "Expositiones Mathematicae", journal-URL = "http://www.sciencedirect.com/science/journal/07230869", keywords = "decimal expansion; sum of digits", ZMclass = "11A63 (Radix representation; digital problems)", ZMreviewer = "G. Larcher (Salzburg)", } @Article{Wolf:1993:PHJ, author = "Joel L. Wolf and Philip S. Yu and John Turek and Daniel M. Dias", title = "A parallel hash join algorithm for managing data skew", journal = j-IEEE-TRANS-PAR-DIST-SYS, volume = "4", number = "12", pages = "1355--1371", month = dec, year = "1993", CODEN = "ITDSEO", DOI = "https://doi.org/10.1109/71.250117", ISSN = "1045-9219 (print), 1558-2183 (electronic)", ISSN-L = "1045-9219", bibdate = "Fri Apr 11 15:20:39 MDT 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib", acknowledgement = ack-nhfb, affiliation = "IBM T. J. Watson Research Cent", affiliationaddress = "Yorktown Heights, NY, USA", classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P (Parallel programming and algorithm theory); C4250 (Database theory); C6160D (Relational DBMS)", corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights, NY, USA", fjournal = "IEEE Transactions on Parallel and Distributed Systems", journal-URL = "http://www.computer.org/tpds/archives.htm", journalabr = "IEEE Trans Parallel Distrib Syst", keywords = "Algorithms; combinatorial; Combinatorial mathematics; Combinatorial optimization; Complex queries; complex queries; Computational complexity; Data handling; Data skew; data skew; database theory; hash; Hash joins; hashing; heuristic optimization; hierarchical; join column; joins; load balancing; Load balancing; optimization; parallel algorithms; parallel hash join algorithm; Parallel processing systems; Program processors; Query languages; query processing; Relational database systems; relational databases; resource allocation; scheduling; Zipf-like distribution", treatment = "T Theoretical or Mathematical", } @Article{Wolf:1993:PSM, author = "Joel L. Wolf and Daniel M. Dias and Philip S. Yu", title = "Parallel sort merge join algorithm for managing data skew", journal = j-IEEE-TRANS-PAR-DIST-SYS, volume = "4", number = "1", pages = "70--86", month = jan, year = "1993", CODEN = "ITDSEO", DOI = "https://doi.org/10.1109/71.205654", ISSN = "1045-9219 (print), 1558-2183 (electronic)", ISSN-L = "1045-9219", bibdate = "Fri Apr 11 15:20:39 MDT 1997", bibsource = "Compendex database; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib", acknowledgement = ack-nhfb, affiliation = "IBM", affiliationaddress = "Yorktown Heights, NY, USA", classification = "723.1; 723.3; 921.5; C4240P (Parallel programming and algorithm theory); C4250 (Database theory); C6130 (Data handling techniques); C6160B (Distributed DBMS); C6160D (Relational DBMS)", corpsource = "IBM T. J. Watson Res. Center. Yorktown Heights, NY, USA", fjournal = "IEEE Transactions on Parallel and Distributed Systems", journal-URL = "http://www.computer.org/tpds/archives.htm", journalabr = "IEEE Trans Parallel Distrib Syst", keywords = "Algorithms; Computer systems programming; Data skew; data skew management; distributed databases; Divide and conquer approach; divide-and-conquer; join phases; load balancing; merging; multiple processors; Multiprocessing programs; Optimization; parallel; Parallel algorithms; parallel algorithms; Parallel sort merge join algorithm; parallelizable optimization algorithm; phase; Query processing; relational algebra; Relational database systems; relational databases; scheduling; Scheduling; sort merge join algorithm; sort phase; sorting; Sorting; transfer phase; Zipf-like distribution", treatment = "T Theoretical or Mathematical", } @Book{Arthur:1994:IRP, author = "W. Brian Arthur", title = "Increasing returns and path dependence in the economy", publisher = pub-U-MICHIGAN, address = pub-U-MICHIGAN:adr, pages = "xx + 201", year = "1994", ISBN = "0-472-09496-3, 0-472-06496-7 (paperback)", ISBN-13 = "978-0-472-09496-7, 978-0-472-06496-0 (paperback)", LCCN = "HD69.S5 A77 1994", bibdate = "Wed Feb 27 07:08:40 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", note = "With a foreword by Kenneth J. Arrow.", series = "Economics, cognition, and society", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Economies of scale; Mathematical models; Economic development; Economics, Mathematical", } @Article{Basu:1994:LEE, author = "Aparna Basu", title = "Letters to the {Editor}: The elusive phenomenon of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "45", number = "1", pages = "59--60", month = jan, year = "1994", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199401)45:1<59::AID-ASI8>3.0.CO%3B2-F", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:03:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Bookstein:1994:TMD, author = "A. Bookstein", title = "Towards a multi-disciplinary {Bradford Law}", journal = j-SCIENTOMETRICS, volume = "30", number = "1", pages = "353--361", month = may, year = "1994", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02017233", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Thu Sep 3 07:35:17 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib", URL = "http://link.springer.com/article/10.1007/BF02017233", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Boyle:1994:AFS, author = "Jeff Boyle", title = "An application of {Fourier} series to the most significant digit problem", journal = j-AMER-MATH-MONTHLY, volume = "101", number = "9", pages = "879--886", month = nov, year = "1994", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "60F99", MRnumber = "1 300 493", bibdate = "Wed Dec 3 17:17:33 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Egghe:1994:RSF, author = "L. Egghe", title = "Research: Special features of the author--publication relationship and a new explanation of {Lotka's Law} based on convolution theory", journal = j-J-AM-SOC-INF-SCI, volume = "45", number = "6", pages = "422--427", month = jul, year = "1994", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199407)45:6<422::AID-ASI8>3.0.CO%3B2-C", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:01 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Fuchs:1994:PDP, author = "Aim{\'e} Fuchs and Giorgio Letta", title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour les nombres premiers. ({French}) [The problem for the first decimal digit of prime numbers]", journal = "Rendiconti della Accademia Nazionale delle Scienze detta dei XL. Serie V. Memorie di Matem{\`a}tica", volume = "18", number = "1", pages = "81--87", month = "????", year = "1994", bibdate = "Sat Feb 16 17:40:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf", ZMnumber = "0838.11004", acknowledgement = ack-nhfb, ajournal = "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.", keywords = "asymptotic densities; logarithmic density; primes; relative densities", language = "French", xxjournal = "Rend. Acad. Naz. Sci. Detta", xxvolume = "XL", ZMclass = "11B05 (Topology etc. of sets of numbers); 11K16 (Normal numbers, etc.)", ZMreviewer = "I. Z. Ruzsa (Budapest)", } @Article{Ley:1994:TPB, author = "Eduadro Ley and Hal R. Varian", title = "Are there psychological barriers in the {Dow--Jones} index?", journal = j-APPL-FINANC-ECON, volume = "4", number = "3", pages = "217--224", month = "????", year = "1994", CODEN = "????", DOI = "https://doi.org/10.1080/758526902", ISSN = "0960-3107 (print), 1466-4305 (electronic)", ISSN-L = "0960-3107", bibdate = "Sat Feb 16 18:29:52 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/758526902", acknowledgement = ack-nhfb, fjournal = "Applied Financial Economics", } @Article{Mantegna:1994:LFN, author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger and S. Havlin and C. K. Peng and M. Simons and H. E. Stanley", title = "Linguistic Features of Noncoding {DNA} Sequences", journal = j-PHYS-REV-LET, volume = "73", number = "??", pages = "3169--??", day = "5", month = dec, year = "1994", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.73.3169", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See comment \cite{Voss:1996:CLF} and reply \cite{Mantegna:1996:MAR}.", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Nigrini:1994:UDF, author = "Mark J. Nigrini", title = "Using digital frequencies to detect fraud", journal = "The White Paper", volume = "??", number = "2", pages = "3--6", month = apr # "\slash " # may, year = "1994", bibdate = "Sat Feb 16 18:53:08 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, remark = "The White Paper is the precursor to Fraud Magazine; I cannot find it in the Library of Congress catalog.", } @Article{Pedrotti:1994:ALU, author = "A. Pedrotti", title = "Analysis of a list-update strategy", journal = j-INFO-PROC-LETT, volume = "52", number = "3", pages = "115--121", day = "11", month = nov, year = "1994", CODEN = "IFPLAT", ISSN = "0020-0190 (print), 1872-6119 (electronic)", ISSN-L = "0020-0190", bibdate = "Wed Nov 11 12:16:26 MST 1998", bibsource = "Compendex database; http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, affiliation = "Scuola Normale Superiore", affiliationaddress = "Pisa, Italy", classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C (Computational complexity); C6130 (Data handling techniques)", corpsource = "Scuola Normale Superiore, Pisa, Italy", fjournal = "Information Processing Letters", journal-URL = "http://www.sciencedirect.com/science/journal/00200190", journalabr = "Inf Process Lett", keywords = "Algorithms; analysis of algorithms; average-case complexity; BIT; competitive algorithms; Computational complexity; computational complexity; convergence; Convergence of numerical methods; Data handling; Function evaluation; Heuristic methods; list processing; list update; Markov chains; Move to front algorithm; move-to-front; Probability; Random number generation; searching; Theorem proving; transpose; Zipf's law", treatment = "T Theoretical or Mathematical", } @Article{Sheppard:1994:TNA, author = "Lee A. Sheppard", title = "{Tax Notes} audits the {Clintons}", journal = "Tax Notes Today", volume = "??", number = "??", pages = "18--23", day = "4", month = apr, year = "1994", bibdate = "Fri Mar 22 09:13:48 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.bankler.com/docs/Tax_Notes_Audits_the_Clintons.pdf", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Article{Tritch:1994:MAC, author = "Teresa Tritch and Mary L. Sprouse", title = "{Money} audits the {Clintons}", journal = "Money Magazine", volume = "??", number = "??", pages = "84--98", day = "1", month = apr, year = "1994", bibdate = "Fri Mar 22 09:16:28 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://money.cnn.com/magazines/moneymag/moneymag_archive/1994/04/01/88775/index.htm", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Article{Berton:1995:HGT, author = "L. Berton", title = "He's Got their Number. {Scholar} Uses Math to Foil Financial Fraud", journal = j-WALL-ST-J, volume = "??", number = "??", pages = "??--??", day = "10", month = jul, year = "1995", CODEN = "WSJOAF", ISSN = "0099-9660", ISSN-L = "0099-9660", bibdate = "Sat Dec 10 11:17:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Wall Street Journal", } @Book{Bologna:1995:FAF, author = "Jack Bologna and Robert J. Lindquist", title = "Fraud auditing and forensic accounting: new tools and techniques", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "xv + 249", year = "1995", ISBN = "0-471-10646-1 (hardcover)", ISBN-13 = "978-0-471-10646-3 (hardcover)", LCCN = "HV8079.W47 B65 1995", bibdate = "Tue Nov 22 10:31:53 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/wiley042/95005510.html; http://www.loc.gov/catdir/description/wiley033/95005510.html; http://www.loc.gov/catdir/toc/onix04/95005510.html", acknowledgement = ack-nhfb, remark = "This book does not discuss Benford's Law, but may be helpful background for application of that law to the detection of fraud.", subject = "white collar crime investigation; United States; forensic accounting; fraud investigation", } @Article{Chen:1995:LED, author = "Ye-Sho Chen", title = "Letters to the {Editor}: On the dynamic behavior of {Bradford's Law} --- response", journal = j-J-AM-SOC-INF-SCI, volume = "46", number = "10", pages = "799--800", month = dec, year = "1995", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<799::AID-ASI19>3.0.CO%3B2-P", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:04 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Chen:1995:RDB, author = "Ye-Sho Chen and P. Pete Chong and Morgan Y. Tong", title = "Research: Dynamic behavior of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "46", number = "5", pages = "370--383", month = jun, year = "1995", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<370::AID-ASI7>3.0.CO%3B2-J", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:06 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Czirok:1995:CBS, author = "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo Havlin and H. Eugene Stanley", title = "Correlations in binary sequences and a generalized {Zipf} analysis", journal = j-PHYS-REV-E, volume = "52", number = "??", pages = "446--??", day = "1", month = jul, year = "1995", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.52.446", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.446", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Filipponi:1995:SPA, author = "Piero Filipponi and Renato Menicocci", title = "Some Probabilistic Aspects of the Terminal Digits of {Fibonacci} Numbers", journal = j-FIB-QUART, volume = "33", number = "4", pages = "325--331", month = aug, year = "1995", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:02:19 MDT 2011", bibsource = "http://www.fq.math.ca/33-4.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Havlin:1995:DBZ, author = "Shlomo Havlin", title = "The distance between {Zipf} plots", journal = j-PHYSICA-A, volume = "216", number = "1--2", pages = "148--150", day = "1", month = jun, year = "1995", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/0378-4371(95)00069-J", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/037843719500069J", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Hill:1995:BII, author = "Theodore P. Hill", title = "Base-invariance implies {Benford's Law}", journal = j-PROC-AM-MATH-SOC, volume = "123", number = "3", pages = "887--895", month = mar, year = "1995", CODEN = "PAMYAR", DOI = "https://doi.org/10.2307/2160815", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "60A10 (28D05)", MRnumber = "1233974 (95d:60006)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/2160815", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @Article{Hill:1995:SDP, author = "Theodore P. Hill", title = "The significant-digit phenomenon", journal = j-AMER-MATH-MONTHLY, volume = "102", number = "4", pages = "322--327", month = apr, year = "1995", CODEN = "AMMYAE", DOI = "https://doi.org/10.2307/2974952", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11K99 (60E99)", MRnumber = "96f:11101", MRreviewer = "Jean-Loup Mauclaire", bibdate = "Wed Dec 3 17:17:33 MST 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Hill:1995:SDS, author = "Theodore P. Hill", title = "A statistical derivation of the significant-digit law", journal = j-STAT-SCI, volume = "10", number = "4", pages = "354--363", year = "1995", CODEN = "STSCEP", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", MRclass = "60E99 (60A10 62E99)", MRnumber = "1421567 (98a:60021)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 10:09:36 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "2-P&origin=MSN; http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO", ZMnumber = "Zbl 0955.60509", acknowledgement = ack-nhfb, fjournal = "Statistical Science. A Review Journal of the Institute of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.ss", } @Article{Kanter:1995:MPL, author = "I. Kanter and D. A. Kessler", title = "{Markov} Processes: Linguistics and {Zipf's Law}", journal = j-PHYS-REV-LET, volume = "74", number = "??", pages = "4559--??", day = "29", month = may, year = "1995", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.74.4559", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Koenig:1995:BCL, author = "Michael Koenig and Toni Harrell", title = "Brief Communications: {Lotka's Law}, {Price}'s urn, and electronic publishing", journal = j-J-AM-SOC-INF-SCI, volume = "46", number = "5", pages = "386--388", month = jun, year = "1995", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<386::AID-ASI9>3.0.CO%3B2-V", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:06 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Makse:1995:MUG, author = "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene Stanley", title = "Modelling urban growth patterns", journal = j-NATURE, volume = "377", number = "6550", pages = "608--612", day = "19", month = oct, year = "1995", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/377608a0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Wed Feb 27 06:06:25 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Berlin (Germany) population; London (UK) population; Zipf's Law", } @Article{Mantegna:1995:SAC, author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger and S. Havlin and C.-K. Peng and M. Simons and H. E. Stanley", title = "Systematic analysis of coding and noncoding {DNA} sequences using methods of statistical linguistics", journal = j-PHYS-REV-E, volume = "52", number = "??", pages = "2939--??", day = "1", month = sep, year = "1995", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.52.2939", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.52.2939", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Mosimann:1995:DFC, author = "James E. Mosimann and Claire V. Wiseman and Ruth E. Edelman", title = "Data Fabrication: Can People Generate Random Digits?", journal = j-ACCOUNT-RES, volume = "4", number = "1", pages = "31--55", month = "????", year = "1995", CODEN = "ARQAEZ", DOI = "https://doi.org/10.1080/08989629508573866", ISSN = "0898-9621 (print), 1545-5815 (electronic)", ISSN-L = "0898-9621", bibdate = "Sat Dec 10 11:56:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866", acknowledgement = ack-nhfb, fjournal = "Accountability in Research", journal-URL = "http://www.tandfonline.com/toc/gacr20", keywords = "Benford's Law", remark = "The abstract ends with: ``The difficulty that people have in creating random error digits supports the utility of examining such digits in investigations of scientific misconduct.''", } @Article{Oluic-Vukovic:1995:LED, author = "Vesna Olui{\'c}-Vukovi{\'c}", title = "Letters to the {Editor}: On the dynamic behavior of {Bradford's Law}", journal = j-J-AM-SOC-INF-SCI, volume = "46", number = "10", pages = "798--799", month = dec, year = "1995", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<798::AID-ASI18>3.0.CO%3B2-T", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:04 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "4 Jan 1999", } @Article{Stanley:1995:ZPS, author = "Michael H. R. Stanley and Sergey V. Buldyrev and Shlomo Havlin and Rosario N. Mantegna and Michael A. Salinger and H. Eugene Stanley", title = "{Zipf} plots and the size distribution of firms", journal = j-ECONOM-LETT, volume = "49", number = "4", pages = "453--457", day = "15", month = oct, year = "1995", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/0165-1765(95)00696-D", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/016517659500696D", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Wagner-Dobler:1995:DLL, author = "Roland Wagner-D{\"o}bler and Jan Berg", title = "The Dependence of {Lotka's Law} on the Selection of Time Periods in the Development of Scientific Areas and Authors", journal = j-J-DOC, volume = "51", number = "1", pages = "28--43", month = "????", year = "1995", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/eb026941", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:29:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{Zornig:1995:URZ, author = "Peter Z{\"o}rnig and Gabriel Altmann", title = "Unified representation of {Zipf} distributions", journal = j-COMPUT-STAT-DATA-ANAL, volume = "19", number = "4", pages = "461--473", day = "1", month = apr, year = "1995", CODEN = "CSDADW", DOI = "https://doi.org/10.1016/0167-9473(94)00009-8", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", MRclass = "62E10 (62F10)", MRnumber = "1333065 (96f:62029)", MRreviewer = "Friedrich Liese", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0167947394000098", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", keywords = "Zipf's Law", } @Book{Bak:1996:HNW, author = "Per Bak", title = "How nature works: the science of self-organized criticality", publisher = "Copernicus", address = "New York, NY, USA", pages = "xiii + 212 + 8", year = "1996", ISBN = "0-387-94791-4 (hardcover)", ISBN-13 = "978-0-387-94791-4 (hardcover)", LCCN = "QC173.4.C74 B34 1996", bibdate = "Thu Nov 24 13:34:22 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Critical phenomena (Physics); Complexity (Philosophy); Physics; Philosophy", } @Article{Beirlant:1996:TIE, author = "Jan Beirlant and Petra Vynckier and Jozef L. Teugels", title = "Tail Index Estimation, {Pareto} Quantile Plots, and Regression Diagnostics", journal = j-J-AM-STAT-ASSOC, volume = "91", number = "436", pages = "1659--??", month = "????", year = "1996", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon May 5 08:26:17 MDT 1997", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Bonhoeffer:1996:NSH, author = "Sebastian Bonhoeffer and Andreas V. M. Herz and Maarten C. Boerlijst and Sean Nee and Martin A. Nowak and Robert M. May", title = "No Signs of Hidden Language in Noncoding {DNA}", journal = j-PHYS-REV-LET, volume = "76", number = "11", pages = "1977--1977", month = mar, year = "1996", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.76.1977", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Sat Sep 10 17:27:23 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1977", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Burgos:1996:ZSB, author = "Javier D. Burgos and Pedro Moreno-Tovar", title = "{Zipf}-scaling behavior in the immune system", journal = j-BIOSYSTEMS, volume = "39", number = "3", pages = "227--232", day = "15", month = nov, year = "1996", CODEN = "BSYMBO", DOI = "https://doi.org/10.1016/0303-2647(96)01618-8", ISSN = "0303-2647 (print), 1872-8324 (electronic)", ISSN-L = "0303-2647", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/0303264796016188", acknowledgement = ack-nhfb, fjournal = "Biosystems (A6E)", journal-URL = "http://www.sciencedirect.com/science/journal/03032647", keywords = "Zipf's Law", } @Article{Campanino:1996:IIM, author = "Massimo Campanino and Stefano Isola", title = "Infinite invariant measures for non-uniformly expanding transformations of $ [0, 1] $: Weak law of large numbers with anomalous scaling", journal = j-FORUM-MATH, volume = "8", number = "1", pages = "71--92", year = "1996", CODEN = "FOMAEF", DOI = "https://doi.org/10.1515/form.1996.8.71", ISSN = "0933-7741 (print), 1435-5337 (electronic)", ISSN-L = "0933-7741", bibdate = "Sat Nov 12 10:33:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0837.60022", abstract = "We consider a class of maps of $ [0, 1] $ with an indifferent fixed point at 0 and expanding everywhere else. Using the invariant ergodic probability measure of a suitable, everywhere expanding, induced transformation we are able to study the infinite invariant measure of the original map in some detail. Given a continuous function with compact support in $]0, 1]$, we prove that its time averages satisfy a `weak law of large numbers' with anomalous scaling $ n / \log n $ and give an upper bound for the decay of correlations.", acknowledgement = ack-nhfb, ajournal = "Forum Math.", classmath = "60F05 (Weak limit theorems) 28D05 (Measure-preserving transformations) 37A99 (Ergodic theory)", fjournal = "Forum Mathematicum", keywords = "decay of correlations; invariant ergodic probability measure; weak law of large numbers", } @Article{Czirok:1996:POP, author = "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and Tam{\'a}s Vicsek", title = "Possible origin of power-law behavior in $n$-tuple {Zipf} analysis", journal = j-PHYS-REV-E, volume = "53", number = "??", pages = "6371--??", day = "1", month = jun, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.53.6371", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.6371", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Fuchs:1996:PDP, author = "Aim{\'e} Fuchs and Giorgio Letta", title = "Le probl{\`e}me du premier chiffre d{\'e}cimal pour les nombres premiers. ({French}) [The problem for the first decimal digit of prime numbers]", journal = j-ELECT-J-COMB, volume = "3", number = "2", pages = "R25:1--R25:7", month = "????", year = "1996", ISSN = "1077-8926 (print), 1097-1440 (electronic)", ISSN-L = "1077-8926", bibdate = "Sat Feb 16 17:40:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The Foata Festschrift volume.", URL = "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf", ZMnumber = "0853.11006", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Combinatorics", language = "French", xxpages = "601--607", } @Article{Gunther:1996:ZLE, author = "R. G{\"u}nther and L. Levitin and B. Schapiro and P. Wagner", title = "{Zipf}'s law and the effect of ranking on probability distributions", journal = j-INT-J-THEOR-PHYS, volume = "35", number = "2", pages = "395--417", year = "1996", CODEN = "IJTPBM", DOI = "https://doi.org/10.1007/BF02083823", ISSN = "0020-7748 (print), 1572-9575 (electronic)", ISSN-L = "0020-7748", bibdate = "Sat Nov 12 10:53:57 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0843.60002", abstract = "Ranking procedures are widely used in the description of many different types of complex systems. Zipf's law is one of the most remarkable frequency-rank relationships and has been observed independently in physics, linguistics, biology, demography, etc. We show that ranking plays a crucial role in making it possible to detect empirical relationships in systems that exist in one realization only, even when the statistical ensemble to which the systems belong has a very broad probability distribution. Analytical results and numerical simulations are presented which clarify the relations between the probability distributions and the behavior of expected values for unranked and ranked random variables. This analysis is performed, in particular, for the evolutionary model presented in our previous papers which leads to Zipf's law and reveals the underlying mechanism of this phenomenon in terms of a system with interdependent and interacting components as opposed to the ``ideal gas'' models suggested by previous researchers. The ranking procedure applied to this model leads to a new, unexpected phenomenon: a characteristic ``staircase'' behavior of the mean values of the ranked variables (ranked occupation numbers). This result is due to the broadness of the probability distributions for the occupation numbers and does not follow from the ``ideal gas'' model. Thus, it provides an opportunity, by comparison with empirical data, to obtain evidence as to which model relates to reality.", acknowledgement = ack-nhfb, classmath = "60A99 (Foundations of probability theory)", fjournal = "International Journal of Theoretical Physics", journal-URL = "http://link.springer.com/journal/10773", keywords = "numerical simulations; ranking procedures; Zipf's law", } @TechReport{Hill:1996:NDT, author = "Theodore P. Hill", title = "A note on distributions of true versus fabricated data", type = "Preprint", institution = "Department of Mathematics, Georgia Institute of Technology", address = "Atlanta, GA, USA", pages = "4", year = "1996", bibdate = "Sat Feb 16 17:47:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr", acknowledgement = ack-nhfb, } @Article{Israeloff:1996:CZD, author = "N. E. Israeloff and M. Kagalenko and K. Chan", title = "Can {Zipf} Distinguish Language From Noise in Noncoding {DNA}?", journal = j-PHYS-REV-LET, volume = "76", number = "11", pages = "1976--??", day = "11", month = mar, year = "1996", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.76.1976", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Krugman:1996:CMU, author = "Paul Krugman", title = "Confronting the Mystery of Urban Hierarchy", journal = j-J-JPN-INT-ECON, volume = "10", number = "4", pages = "399--418", month = dec, year = "1996", CODEN = "JJIEBD", DOI = "https://doi.org/10.1006/jjie.1996.0023", ISSN = "0889-1583 (print), 1095-8681 (electronic)", ISSN-L = "0889-1583", bibdate = "Wed Feb 27 06:15:55 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0889158396900234", acknowledgement = ack-nhfb, fjournal = "Journal of the {Japanese} and International Economies", keywords = "Zipf's Law", } @Book{Krugman:1996:SOE, author = "Paul R. Krugman", title = "The Self-Organizing Economy", publisher = "Blackwell Publishers", address = "Cambridge, MA, USA", pages = "vi + 122", year = "1996", ISBN = "1-55786-699-6 (paperback)", ISBN-13 = "978-1-55786-699-8 (paperback)", LCCN = "HB199 .K75 1996", bibdate = "Wed Feb 27 07:08:14 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, keywords = "Zipf's Law", subject = "Economics; Self-organizing systems", } @Article{Ley:1996:PDU, author = "Eduardo Ley", title = "On the Peculiar Distribution of the {U.S.} Stock Indexes' Digits", journal = j-AMER-STAT, volume = "50", number = "4", pages = "311--313", month = nov, year = "1996", CODEN = "ASTAAJ", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Nov 14 15:09:04 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.jstor.org/stable/2684926", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Mantegna:1996:MAR, author = "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger and S. Havlin and C.-K. Peng and M. Simons and H. E. Stanley", title = "{Mantegna} {\em et al.} Reply", journal = j-PHYS-REV-LET, volume = "76", pages = "1979--1981", month = mar, year = "1996", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.76.1979", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Sat Sep 10 17:28:12 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mantegna:1994:LFN,Voss:1996:CLF}", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1979", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", issue = "11", journal-URL = "http://prl.aps.org/browse", } @Article{Newman:1996:ASC, author = "M. E. J. Newman and Kim Sneppen", title = "Avalanches, scaling, and coherent noise", journal = j-PHYS-REV-E, volume = "54", number = "6", pages = "6226--6231", month = dec, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.54.6226", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:44:51 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.6226", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @InProceedings{Nigrini:1996:DAR, author = "Mark J. Nigrini", editor = "M. Ettredge", booktitle = "{Proceedings of the 1996 Deloitte \& Touche I University of Kansas Symposium on Auditing Problems}", title = "Digital Analysis and the Reduction of Auditor Litigation Risk", publisher = "University of Kansas", address = "Lawrence, KS, USA", pages = "69--81", year = "1996", bibdate = "Sat Sep 10 15:20:48 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Nigrini:1996:TCA, author = "Mark J. Nigrini", title = "A Taxpayer Compliance Application of {Benford's Law}", journal = "Journal of the {American Taxation Association}", volume = "18", number = "1", pages = "72--91", month = "????", year = "1996", CODEN = "????", ISSN = "0198-9073 (print), 1558-8017 (electronic)", ISSN-L = "0198-9073", bibdate = "Mon Nov 14 16:30:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "J. Amer. Tax. Assoc.", fjournal = "Journal of the {American Taxation Association}", journal-URL = "http://aaajournals.org/loi/atax", remark = "No journal issues online before 1999.", } @Article{Perline:1996:ZLC, author = "Richard Perline", title = "{Zipf}'s law, the {Central Limit Theorem}, and the random division of the unit interval", journal = j-PHYS-REV-E, volume = "54", number = "1", pages = "220--223", day = "1", month = jul, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.54.220", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.220", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Mandelbrot's monkey-at-the-typewriter model of Zipf's inverse power law; Zipf's Law", } @Article{Sole:1996:ESO, author = "Ricard V. Sol{\'e} and Susanna C. Manrubia", title = "Extinction and self-organized criticality in a model of large-scale evolution", journal = j-PHYS-REV-E, volume = "54", number = "1", pages = "R42--R45", month = jul, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.54.R42", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:32:32 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.R42", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Solomon:1996:SSE, author = "Sorin Solomon and Moshe Levy", title = "Spontaneous Scaling Emergence in Generic Stochastic Systems", journal = j-INT-J-MOD-PHYS-C, volume = "7", number = "5", pages = "745--752", month = oct, year = "1996", CODEN = "IJMPEO", DOI = "https://doi.org/10.1142/S0129183196000624", ISSN = "0129-1831 (print), 1793-6586 (electronic)", bibdate = "Thu Feb 28 10:20:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624", acknowledgement = ack-nhfb, fjournal = "International Journal of Modern Physics C [Physics and Computers]", journal-URL = "http://www.worldscientific.com/loi/ijmpc", } @Article{Voss:1996:CLF, author = "Richard F. Voss", title = "Comment on {``Linguistic Features of Noncoding DNA Sequences''}", journal = j-PHYS-REV-LET, volume = "76", number = "11", pages = "1978--1978", month = mar, year = "1996", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.76.1978", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Sat Sep 10 14:35:50 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mantegna:1994:LFN} and reply \cite{Mantegna:1996:MAR}.", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.76.1978", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Benford's Law", } @Article{Watanabe:1996:EZL, author = "Makoto S. Watanabe", title = "Erratum: {Zipf}'s law in percolation", journal = j-PHYS-REV-E, volume = "54", number = "??", pages = "4483--4483", day = "1", month = oct, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.54.4483", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite {Watanabe:1996:ZLP}.", URL = "http://link.aps.org/doi/10.1103/PhysRevE.54.4483", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Watanabe:1996:ZLP, author = "Makoto S. Watanabe", title = "{Zipf}'s law in percolation", journal = j-PHYS-REV-E, volume = "53", number = "??", pages = "4187--4190", day = "1", month = apr, year = "1996", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.53.4187", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See erratum \cite {Watanabe:1996:EZL}.", URL = "http://link.aps.org/doi/10.1103/PhysRevE.53.4187", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Allaart:1997:ISC, author = "Pieter C. Allaart", title = "An Invariant-Sum Characterization of {Benford's Law}", journal = j-J-APPL-PROBAB, volume = "34", number = "1", pages = "288--291", month = mar, year = "1997", CODEN = "JPRBAM", DOI = "https://doi.org/10.2307/3215195", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "60E05", MRnumber = "1429075 (98d:60029)", MRreviewer = "Peter Schatte", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3215195", abstract = "The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit $ d (d = 1, 2, \ldots, 9) $ is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits $ d_1, \ldots, d_k $ is constant for every fixed $k$.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", journal-URL = "http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Castillo:1997:FGP, author = "Enrique Castillo and Ali S. Hadi", title = "Fitting the Generalized {Pareto} Distribution to Data", journal = j-J-AM-STAT-ASSOC, volume = "92", number = "440", pages = "1609--1620", month = dec, year = "1997", CODEN = "JSTNAL", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Mon Oct 30 06:57:36 MST 2000", bibsource = "http://www.amstat.org/publications/jasa/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib", URL = "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM; http://www.jstor.org/stable/2965432", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Chen:1997:NHS, author = "Weishing Chen and Tai-Hsi Wu", title = "A non-homogeneous software reliability model based on {Zipf}'s law", journal = "International Journal of Quality \& Reliability Management", volume = "14", number = "4", pages = "409--431", month = "????", year = "1997", DOI = "https://doi.org/10.1108/02656719710170666", ISSN = "0265-671X (print), 1758-6682 (electronic)", ISSN-L = "0265-671X", bibdate = "Fri Nov 25 07:08:17 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Denisov:1997:FBS, author = "S. Denisov", title = "Fractal binary sequences: {Tsallis} thermodynamics and the {Zipf} law", journal = j-PHYS-LET-A, volume = "235", number = "5", pages = "447--451", day = "17", month = nov, year = "1997", CODEN = "PYLAAG", DOI = "https://doi.org/10.1016/S0375-9601(97)00688-9", ISSN = "0375-9601 (print), 1873-2429 (electronic)", ISSN-L = "0375-9601", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0375960197006889", acknowledgement = ack-nhfb, fjournal = "Physics Letters A", journal-URL = "http://www.sciencedirect.com/science/journal/03759601", keywords = "Zipf's Law", } @InCollection{Gell-Mann:1997:ETZ, author = "Murray Gell-Mann", title = "Empirical Theory --- {Zipf}'s Law", crossref = "Gell-Mann:1997:QJA", pages = "92--97", year = "1997", bibdate = "Mon Sep 01 10:20:00 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InCollection{Hill:1997:BL, author = "Theodore Hill", editor = "Michiel Hazewinkel", booktitle = "Encyclopedia of Mathematics, Supplement {I}", title = "{Benford's Law}", volume = "1", publisher = pub-SV, address = pub-SV:adr, pages = "102--103", year = "1997", ISBN = "90-481-4896-0", ISBN-13 = "978-90-481-4896-7", LCCN = "????", bibdate = "Wed Nov 16 10:29:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Irmay:1997:RBZ, author = "Shragga Irmay", title = "The relationship between {Zipf}'s law and the distribution of first digits", journal = j-J-APPL-STAT, volume = "24", number = "4", pages = "383--393", day = "1", month = aug, year = "1997", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", MRclass = "62E15", MRnumber = "1491308 (98h:62015)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.catchword.co.uk/titles/carfax/02664763/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", URL = "http://www.tandfonline.com/doi/abs/10.1080/02664769723594", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", keywords = "Benford's Law; Zipf's Law", xxpages = "383--394", } @Article{Jeevanand:1997:BEB, author = "E. S. Jeevanand", title = "{Bayes} Estimation of {$ P(X_2 < X_1) $} for a Bivariate {Pareto} Distribution", journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN, volume = "46", number = "1", pages = "93--99", month = "????", year = "1997", CODEN = "????", DOI = "https://doi.org/10.2307/2988496", ISSN = "0039-0526 (print), 1467-9884 (electronic)", ISSN-L = "0039-0526", bibdate = "Thu Jan 22 18:10:24 MST 2015", bibsource = "http://www.jstor.org/stable/i349996; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-d-1990.bib", URL = "http://www.jstor.org/stable/2988496", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series D (The Statistician)", journal-URL = "http://www.jstor.org/journals/00390526.html", } @Manual{Nigrini:1997:DAT, author = "Mark J. Nigrini", title = "Digital Analysis Tests and Statistics", organization = "The Nigrini Institute, Inc.", address = "Allen, TX, USA", month = "????", year = "1997", bibdate = "Sat Feb 16 18:55:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nigrini.com/data_software/Program_Details_2009.docx", acknowledgement = ack-nhfb, } @Article{Nigrini:1997:UBL, author = "Mark J. Nigrini and L. J. Mittermaier", title = "The Use of {Benford's Law} as an Aid in Analytical Procedures", journal = j-AUDITING, volume = "16", number = "2", pages = "52--67", month = "????", year = "1997", CODEN = "????", ISSN = "0278-0380 (print), 1558-7991 (electronic)", ISSN-L = "0278-0380", bibdate = "Sun Nov 13 11:37:48 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaapubs.org/loi/ajpt", acknowledgement = ack-nhfb, fjournal = "Auditing: A Journal of Practice \& Theory", remark = "No journal issues online before 1999.", } @Article{Oluic-Vukovic:1997:BDC, author = "Vesna Olui{\'c}-Vukovi{\'c}", title = "{Bradford}'s distribution: {From} the classical bibliometric ``law'' to the more general stochastic models", journal = j-J-AM-SOC-INF-SCI, volume = "48", number = "9", pages = "833--842", month = sep, year = "1997", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(199709)48:9<833::AID-ASI7>3.0.CO%3B2-S", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:21 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "7 Dec 1998", } @Book{Robertson:1997:FEM, author = "Jack C. Robertson", title = "Fraud Examination for Managers and Auditors", publisher = "Viesca Books", address = "Austin, TX, USA", edition = "1997", pages = "vii + 564", year = "1997", ISBN = "0-9656785-0-4", ISBN-13 = "978-0-9656785-0-6", LCCN = "HV8079.F7 R63 1997", bibdate = "Thu Oct 13 09:04:19 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Fraud investigation", } @Article{Salsburg:1997:DPB, author = "David Salsburg", title = "Digit Preferences in the {Bible}", journal = j-CHANCE, volume = "10", number = "4", pages = "46--48", month = "????", year = "1997", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.1997.10542065", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Sat Feb 16 19:08:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", } @InCollection{Smith:1997:EBL, author = "Steven W. Smith", booktitle = "The Scientist and Engineer's Guide to Digital Signal Processing", title = "Explaining {Benford's Law}", chapter = "34", publisher = "California Technical Publishing", address = "San Diego, CA, USA", bookpages = "xiv + 626", pages = "701--722", year = "1997", ISBN = "0-9660176-3-3", ISBN-13 = "978-0-9660176-3-2", LCCN = "TK5102.9 .S57 1997", bibdate = "Sat Sep 10 16:54:35 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.dspguide.com/ch34.htm", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "Chapters appear to stop at 31 in 1997 edition (according to Amazon book preview), so a later addition should have a new ISBN (the 2002 edition from Newnes is \booktitle{Digital Signal Processing: A Practical Guide for Engineers and Scientists}, with ISBN 0-7506-7444-X). However, the Web site says it is the same book. The Web edition has 34 chapters, and all are freely downloadable.", } @Article{Tsonis:1997:ZLS, author = "A. A. Tsonis and C. Schultz and P. A. Tsonis", title = "{Zipf's Law} and the structure and evolution of languages", journal = j-COMPLEXITY, volume = "2", number = "5", pages = "12--13", year = "1997", CODEN = "COMPFS", DOI = "https://doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO%3B2-C", ISSN = "1076-2787 (print), 1099-0526 (electronic)", ISSN-L = "1076-2787", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Complexity", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0526", } @Article{Zanette:1997:RIU, author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia", title = "Role of Intermittency in Urban Development: A Model of Large-Scale City Formation", journal = j-PHYS-REV-LET, volume = "79", number = "3", pages = "523--526", day = "3", month = jul, year = "1997", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.79.523", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Thu Feb 28 10:40:44 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.79.523", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Bach:1998:EPM, author = "Eric Bach", title = "Efficient prediction of {Marsaglia--Zaman} random number generators", journal = j-IEEE-TRANS-INF-THEORY, volume = "44", number = "3", pages = "1253--1257", year = "1998", CODEN = "IETTAW", DOI = "https://doi.org/10.1109/18.669305", ISSN = "0018-9448 (print), 1557-9654 (electronic)", ISSN-L = "0018-9448", MRclass = "65C10", MRnumber = "99b:65007", bibdate = "Thu Dec 22 07:42:24 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", ZMnumber = "0915.65003", abstract = "This paper presents two properties of the random number generator by {\em G. Marsaglia} and {\em A. Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl 0733.65005)]. First, it is shown that its successive digits are digits of certain rational $b$-adic numbers. Then, an efficient algorithm is derived to predict an unknown pseudorandom sequence of this type. Two examples of the prediction are given.", acknowledgement = ack-nhfb, classmath = "*65C10 Random number generation 11K45 Pseudo-random numbers, etc.", fjournal = "IEEE Transactions on Information Theory", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18", keywords = "$b$-adic number; algorithm; continued fraction; pseudo-random number generator", ZMreviewer = "K. Uosaki (Tottori)", } @Article{Browne:1998:FBL, author = "Malcolm W. Browne", title = "Following {Benford's Law}, or Looking Out for {No. 1}", journal = j-NY-TIMES, volume = "??", number = "??", pages = "F4--F4", day = "4", month = aug, year = "1998", CODEN = "NYTIAO", ISSN = "0362-4331 (print), 1542-667X, 1553-8095", ISSN-L = "0362-4331", bibdate = "Sat Feb 16 14:29:48 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Science section.", URL = "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1", acknowledgement = ack-nhfb, fjournal = "New York Times", journal-URL = "http://www.nytimes.com/", } @Article{Busta:1998:UBL, author = "Bruce Busta and Randy Weinberg", title = "Using {Benford's Law} and Neural Networks as a Review Procedure", journal = "Managerial Auditing Journal", volume = "13", number = "6", pages = "356--366", month = "????", year = "1998", CODEN = "????", DOI = "https://doi.org/10.1108/02686909810222375", ISSN = "0268-6902 (print), 1758-7735 (electronic)", ISSN-L = "0268-6902", bibdate = "Tue Nov 22 18:50:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Chongde:1998:EMB, author = "Wang Chongde and Wang Zhe", title = "Evaluation of the models for {Bradford's Law}", journal = j-SCIENTOMETRICS, volume = "42", number = "1", pages = "89--95", month = may, year = "1998", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/BF02465014", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:03:59 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib", URL = "http://link.springer.com/article/10.1007/BF02465014", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{DeCeuster:1998:HPB, author = "Marc J. K. {De Ceuster} and Geert Dhaene and Tom Schatteman", title = "On the hypothesis of psychological barriers in stock markets and {Benford's Law}", journal = j-J-EMPIR-FINANCE, volume = "5", number = "3", pages = "263--279", month = sep, year = "1998", CODEN = "JEFIEC", DOI = "https://doi.org/10.1016/S0927-5398(97)00024-8", ISSN = "0927-5398 (print), 1879-1727 (electronic)", ISSN-L = "0927-5398", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0927539897000248", abstract = "We consider the hypothesis of psychological barriers at round numbers of a stock index. This hypothesis is often examined by testing the uniformity of the distribution of the trailing digits in the stock index, a rejection being interpreted as evidencing the existence of psychological barriers. By virtue of Benford's Law, we show that the uniform distribution is not the right benchmark against which to test. As an alternative we propose a test based on the cyclical permutations of the actual returns. Applying this test to the Dow Jones 30 Industrial Average, the Financial Times Stock Exchange 100 and the Nikkei Stock Average 225, we find no convincing evidence of psychological barriers, contrary to previous findings.", acknowledgement = ack-nhfb, fjournal = "Journal of Empirical Finance", keywords = "Benford's Law; Psychological barriers", } @Article{Herman:1998:TRI, author = "Tom Herman", title = "Tax report: An {IRS} blooper startles thousands of taxpayers", journal = j-WALL-ST-J, volume = "??", number = "??", pages = "1--1", day = "18", month = feb, year = "1998", CODEN = "WSJOAF", ISSN = "0099-9660", bibdate = "Fri Mar 22 09:17:50 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://online.wsj.com/article/SB887753996209804500.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Wall Street Journal", keywords = "Benford's Law", remark = "From the article: ``[a taxpayer] was expecting a \$513 tax refund. Instead, he recently received a letter from the Internal Revenue Service informing him that he owes the government \$300,000,007.57. \ldots{} about 3,000 other people around the nation got similar erroneous notices, each showing a balance due of `three hundred million dollars and change.'\,''", } @Article{Hill:1998:FDP, author = "Theodore P. Hill", title = "The First Digit Phenomenon", journal = j-AM-SCI, volume = "86", number = "4", pages = "358--363", month = jul # "\slash " # aug, year = "1998", CODEN = "AMSCAC", DOI = "https://doi.org/10.1511/1998.4.358", ISSN = "0003-0996 (print), 1545-2786 (electronic)", ISSN-L = "0003-0996", bibdate = "Sat Dec 10 11:54:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf; http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf", abstract = "A century ago, Simon Newcomb observed an unexpected pattern in the first digits of logarithm tables: The digit $1$ is significantly more likely to occur than $2$, $2$ than $3$, and so on. More than a half-century later, Frank Benford rediscovered the first-digit phenomenon and found that it applied to many tables of numerical data, including the stock market, census statistics and accounting figures. New mathematical insights establish the empirical law developed by Newcomb and Benford as part of modern probability theory, and recent applications include testing of mathematical models, design of computers and detection of fraud in accounting.", acknowledgement = ack-nhfb, fjournal = "American Scientist", journal-URL = "http://www.americanscientist.org/issues/past.aspx", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Book{Knuth:1998:SA, author = "Donald E. Knuth", title = "Seminumerical Algorithms", volume = "2", publisher = pub-AW, address = pub-AW:adr, edition = "Third", pages = "xiii + 762", year = "1998", ISBN = "0-201-89684-2", ISBN-13 = "978-0-201-89684-8", LCCN = "QA76.6 .K64 1997", bibdate = "Fri Jul 11 15:41:22 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/css.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib; https://www.math.utah.edu/pub/tex/bib/texbook2.bib", note = "See section 4.2.4V, The Fraction Parts, pages 254--262, for a discussion of Benford's Law.", price = "US\$52.75", series = "The Art of Computer Programming", acknowledgement = ack-nhfb, remark = "Knuth comments on page 255: ``The fact that the leading digits tend to be small makes the most obvious techniques of ``average error'' estimation for floating point calculations invalid. The relative error due to rounding is usually a little more than expected.", tableofcontents = "3: Random Numbers / 1 \\ 3.1. Introduction / 1 \\ 3.2. Generating Uniform Random Numbers / 10 \\ 3.2.1. The Linear Congruential Method / 10 \\ 3.2 1.1. Choice of modulus / 12 \\ 3.2.1.2 Choice of multiplier / 16 \\ 3.2.1.3. Potency / 23 \\ 3.2.2. Other Methods / 26 \\ 3.3. Statistical Tests / 41 \\ 3.3.1. General Test Procedures for Studying Random Data / 41 \\ 3.3.2. Empirical Tests / 61 \\ *3.3.3. Theoretical Tests / 80 \\ 3.3.4. The Spectral Test / 93 \\ 3.4. Other Types of Random Quantities / 119 \\ 3.4 1. Numerical Distributions / 119 \\ 3.4.2. Random Sampling and Shuffling / 142 \\ *3.5. What Is a Random Sequence? / 149 \\ 3.6. Summary / 184 \\ 4: Arithmetic / 194 \\ 4.1. Positional Number Systems / 195 \\ 4.2. Floating Point Arithmetic / 214 \\ 4.2.1. Single-Precision Calculations / 214 \\ 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\ *4.2.3. Double-Precision Calculations / 246 \\ 4.2.4. Distribution of Floating Point Numbers / 253 \\ 4.3 Multiple Precision Arithmetic / 265 \\ 4.3.1. The Classical Algorithms / 265 \\ *4.3.2. Modular Arithmetic / 284 \\ *4.3.3. How Fast Can We Multiply? / 294 \\ 4.4. Radix Conversion / 319 \\ 4.5. Rational Arithmetic / 330 \\ 4.5.1. Fractions / 330 \\ 4.5.2. The Greatest Common Divisor / 333 \\ *4.5.3. Analysis of Euclid's Algorithm / 356 \\ 4.5.4. Factoring into Primes / 379 \\ 4.6. Polynomial Arithmetic / 418 \\ 4.6.1. Division of Polynomials / 420 \\ *4.6.2. Factorization of Polynomials / 439 \\ 4.6.3. Evaluation of Powers / 461 \\ 4.6.4. Evaluation of Polynomials / 485 \\ *4.7. Manipulation of Power Series / 525 \\ Answers to Exercises / 538 \\ Appendix A: Tables of Numerical Quantities / 726 \\ 1. Fundamental Constants (decimal) / 726 \\ 2; Fundamental Constants ( octal) / 727 \\ 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers / 728 \\ Appendix B: Index to Notations / 730 \\ Index and Glossary / 735", } @Article{Manrubia:1998:IMU, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette", title = "Intermittency model for urban development", journal = j-PHYS-REV-E, volume = "58", number = "1", pages = "295--302", month = jul, year = "1998", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.58.295", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:42:23 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.295", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Marsili:1998:IIL, author = "Matteo Marsili and Yi-Cheng Zhang", title = "Interacting Individuals Leading to {Zipf's Law}", journal = j-PHYS-REV-LET, volume = "80", number = "??", pages = "2741--??", day = "23", month = mar, year = "1998", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.80.2741", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Nigrini:1998:DIB, author = "Mark J. Nigrini", title = "{Dow} Illustrates {Benford's Law}", journal = j-NY-TIMES, volume = "??", number = "??", pages = "F4--F4", day = "4", month = aug, year = "1998", CODEN = "NYTIAO", ISSN = "0362-4331 (print), 1542-667X, 1553-8095", ISSN-L = "0362-4331", bibdate = "Sat Feb 16 15:46:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1", acknowledgement = ack-nhfb, fjournal = "New York Times", journal-URL = "http://www.nytimes.com/", } @Article{NunesAmaral:1998:PLS, author = "Lu{\'\i}s A. {Nunes Amaral} and Sergey V. Buldyrev and Shlomo Havlin and Michael A. Salinger and H. Eugene Stanley", title = "Power Law Scaling for a System of Interacting Units with Complex Internal Structure", journal = j-PHYS-REV-LET, volume = "80", number = "7", pages = "1385--1388", day = "16", month = feb, year = "1998", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.80.1385", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Thu Feb 28 11:09:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "power law; scale invariance; Zipf's law", } @Article{Pietronero:1998:UDN, author = "L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani", title = "The Uneven Distribution of Numbers in Nature", journal = "ArXiv e-prints", pages = "9", day = "27", month = aug, year = "1998", bibdate = "Mon Nov 21 06:58:45 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/cond-mat/9808305", abstract = "Suppose you look at today's stock prices and bet on the value of the first digit. One could guess that a fair bet should correspond to the frequency of $ 1 / 9 = 11.11 \% $ for each digit from 1 to 9. This is by no means the case, and one can easily observe a strong prevalence of the small values over the large ones. The first three integers 1, 2 and 3 alone have globally a frequency of 60\% while the other six values 4, 5, 6, 7, 8 and 9 appear only in 40\% of the cases. This situation is actually much more general than the stock market and it occurs in a variety of number catalogs related to natural phenomena. The first observation of this property traces back to S. Newcomb in 1881 but a more precise account was given by F. Benford in 1938. In this note we illustrate these observations with the enlightening specific example of the stock market. We also identify the general mechanism for the origin of this uneven distribution in the multiplicative nature of fluctuations in economics and in many natural phenomena. This provides a natural explanation for the ubiquitous presence of the Benford's law in many different phenomena with the common element that their fluctuations refer to a fraction of their values. This brings us close to the problem of the spontaneous origin of scale invariant properties in various phenomena which is a debated question at the frontier of different fields.", acknowledgement = ack-nhfb, } @Article{Pocheau:1998:SRS, author = "A. Pocheau", title = "Scale ratios, statistical symmetries and intermittency", journal = j-EUROPHYS-LETT, volume = "43", number = "4", pages = "410--415", month = aug, year = "1998", CODEN = "EULEEJ", DOI = "https://doi.org/10.1209/epl/i1998-00103-6", ISSN = "0295-5075 (print), 1286-4854 (electronic)", ISSN-L = "0295-5075", bibdate = "Sat Feb 16 16:02:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Europhysics Letters", journal-URL = "http://iopscience.iop.org/0295-5075", } @Article{Ramsden:1998:ZLB, author = "J. J. Ramsden and J. Vohradsk{\'y}", title = "{Zipf}-like behavior in procaryotic protein expression", journal = j-PHYS-REV-E, volume = "58", number = "??", pages = "7777--??", day = "1", month = dec, year = "1998", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.58.7777", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.58.7777", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Rousset:1998:CPV, author = "Olivier G. Rousset and Yilong Ma and Alan C. Evans", title = "Correction for Partial Volume Effects in {PET}: Principle and Validation", journal = j-NUCL-MED, volume = "39", number = "5", pages = "904--911", month = may, year = "1998", CODEN = "JNMEAQ", ISSN = "0161-5505 (print), 1535-5667 (electronic)", ISSN-L = "0161-5505", bibdate = "Sat Sep 10 16:10:46 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jnm.snmjournals.org/content/39/5/904.full.pdf+html", acknowledgement = ack-nhfb, fjournal = "Journal of Nuclear Medicine", journal-URL = "http://jnm.snmjournals.org/content/by/year", keywords = "Benford's Law", } @Article{Schatte:1998:BLV, author = "P. Schatte", title = "On {Benford's law} to variable base", journal = j-STAT-PROB-LETT, volume = "37", number = "4", pages = "391--397", day = "30", month = mar, year = "1998", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/S0167-7152(97)00142-9", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "60F05 (60E15)", MRnumber = "1624423 (99e:60072)", MRreviewer = "Theodore P. Hill", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715297001429", abstract = "Benford's law is studied in dependence on the base $ b > 1 $. It can hold to large bases $b$ only approximately. The quality of approximation is estimated in cases of products and sums of random variables, respectively, and in case of some deterministic sequences. Always the approximation by Benford's law becomes worse as $ b \to \infty $, but as a rule also as $ b \to 1 + 0 $", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law; Discrepancy; First-digit problem; Mantissa distribution; Products of random variables; Sums of random variables", } @Article{Simon:1998:ADC, author = "Jonathan Simon", title = "An Analysis of the Distribution of Combinations Chosen by {UK National Lottery} Players", journal = j-J-RISK-UNCERT, volume = "17", number = "3", pages = "243--277", year = "1998", CODEN = "JRUNEN", DOI = "https://doi.org/10.1023/A:1007786901776", ISSN = "0895-5646 (print), 1573-0476 (electronic)", ISSN-L = "0895-5646", bibdate = "Sat Sep 10 14:35:50 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Risk and Uncertainty", journal-URL = "http://link.springer.com/journal/11166", keywords = "Benford's Law", } @Article{Slijepcevic:1998:NID, author = "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}", title = "A Note on Initial Digits of Recurrence Sequences", journal = j-FIB-QUART, volume = "36", number = "4", pages = "305--308", month = aug, year = "1998", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Oct 20 18:02:49 MDT 2011", bibsource = "http://www.fq.math.ca/36-4.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Scanned/36-4/slijepcevic.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Troll:1998:ZLC, author = "G. Troll and P. beim Graben", title = "{Zipf}'s law is not a consequence of the {Central Limit Theorem}", journal = j-PHYS-REV-E, volume = "57", number = "3", pages = "1347--1355", day = "1", month = feb, year = "1998", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.57.1347", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.57.1347; http://pre.aps.org/abstract/PRE/v57/i2/p1347_1", abstract = "It has been observed that the rank statistics of string frequencies of many symbolic systems (e.g., word frequencies of natural languages) follows Zipf's law in good approximation. We show that, contrary to claims in the literature, Zipf's law cannot be realized by the central limit theorem(s). The observation that a log-normal distribution of string frequencies yields an approximately Zipf-like rank statistics is actually misleading. Indeed, Zipf's law for the rank statistics is strictly equivalent to a power law distribution of frequencies. There are two natural ways to perform the infinite size limit for the vocabulary. The first one is the method of choice in the literature; it makes the upper word length bound tend to infinity and leads in the case of a multistate Bernoulli process via a central limit theorem to a log-normal frequency distribution. An alternative and for text samples actually better realizable way is to make the lower frequency bound tend to zero. This limit procedure leads to a power law distribution and hence to Zipf's law --- at least for Bernoulli processes and to a very good approximation for natural languages where it passes the $ \chi^2 $ test. For the Bernoulli case we will give a heuristic proof.", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Book{Wirsching:1998:DSG, author = "G{\"u}nther J. Wirsching", title = "The dynamical system generated by the $ 3 n + 1 $ function", volume = "1681", publisher = pub-SV, address = pub-SV:adr, pages = "vii + 158", year = "1998", ISBN = "3-540-63970-5 (softcover)", ISBN-13 = "978-3-540-63970-1 (softcover)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", LCCN = "QA3 .L28 no. 1681", bibdate = "Mon Nov 21 08:00:54 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = ser-LNM, URL = "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html; http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Sequences (Mathematics); Combinatorial probabilities; Convergence", } @Article{Ausloos:1999:PMK, author = "M. Ausloos and K. Ivanova", title = "Precise $ (m, k) $-{Zipf} diagram analysis of mathematical and financial time series when $ m = 6 $, $ k = 2 $", journal = j-PHYSICA-A, volume = "270", number = "3--4", pages = "526--542", day = "15", month = aug, year = "1999", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(99)00178-8", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437199001788", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{AyllonBurguillo:1999:PDS, author = "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera Dom{\'\i}nguez}", title = "El primer d{\'\i}gito significativo. ({Spanish}) [The first significant digit]", journal = "{Epsilon}: Revista de la {Sociedad Andaluza de Educaci{\'o}n Matem{\'a}tica ``Thales''}", volume = "15", number = "3(45)", pages = "339--352", month = "????", year = "1999", ISSN = "1131-9321", ISSN-L = "1131-9321", MRnumber = "K60xx", bibdate = "Sat Feb 16 14:32:14 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "MATHEDUC.02332710", acknowledgement = ack-nhfb, ajournal = "{Rev. Epsil{\'o}n SAEM `Thales'}", journal-URL = "http://thales.cica.es/epsilon/; http://dialnet.unirioja.es/servlet/revista?codigo=504", language = "Spanish", remark = "Reported in \cite{Torres:2007:HDN} to contain an extensive bibliography on Benford's Law. The publisher does not have issues before 2003, and no electronic copy has yet been found on the Internet. Attempts to get this paper via Interlibrary Loan failed on the grounds that ``We are unable to verify any owning libraries within the United States or those that we have ILL privileges.''", xxauthor = "Manuel {Perera Dom{\'\i}nguez} and Juan David {Ayll{\'o}n Burguillo}", } @Article{Barabasi:1999:ESR, author = "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka Albert", title = "Emergence of scaling in random networks", journal = j-SCIENCE, volume = "286", number = "5439", pages = "509--512", day = "15", month = oct, year = "1999", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.286.5439.509", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Tue Nov 15 09:57:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/286/5439/509", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "power-law distribution; Zipf's Law", } @Article{Brakman:1999:RZT, author = "Steven Brakman and Harry Garretsen and Charles {Van Marrewijk} and Marianne {Van Den Berg}", title = "The Return of {Zipf}: Towards a Further Understanding of the Rank--Size Distribution", journal = j-J-REG-SCI, volume = "39", number = "1", pages = "183--213", year = "1999", DOI = "https://doi.org/10.1111/1467-9787.00129", ISSN = "0022-4146 (print), 1467-9787 (electronic)", ISSN-L = "0022-4146", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Regional Science", } @Article{Coderre:1999:FDU, author = "David Coderre", title = "Fraud Detection Using Digital Analysis", journal = j-EDPACS, volume = "27", number = "3", pages = "1--8", month = "????", year = "1999", CODEN = "EDPCDF", DOI = "https://doi.org/10.1201/1079/43249.27.3.19990901/30268.1", ISSN = "0736-6981 (print), 1936-1009 (electronic)", ISSN-L = "0736-6981", bibdate = "Sat Jan 07 09:20:49 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1", acknowledgement = ack-nhfb, fjournal = "EDPACS", keywords = "Benford's Law", onlinedate = "21 Dec 2006", } @Article{Egghe:1999:LZM, author = "L. Egghe", title = "On the law of {Zipf--Mandelbrot} for multi-word phrases", journal = j-J-AM-SOC-INF-SCI, volume = "50", number = "3", pages = "233--241", month = "????", year = "1999", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Mon Sep 10 06:09:31 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "17 Feb 1999", } @Article{Egghe:1999:RLZ, author = "L. Egghe", title = "Research: On the law of {Zipf--Mandelbrot} for multi-word phrases", journal = j-J-AM-SOC-INF-SCI, volume = "50", number = "3", pages = "233--241", month = "????", year = "1999", CODEN = "AISJB6", DOI = "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8", ISSN = "0002-8231 (print), 1097-4571 (electronic)", ISSN-L = "0002-8231", bibdate = "Fri Sep 11 09:04:32 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasis.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "17 Feb 1999", } @Article{Gabaix:1999:ZLC, author = "Xavier Gabaix", title = "{Zipf}'s law for cities: An explanation", journal = j-Q-J-ECON, volume = "114", number = "3", pages = "739--767", year = "1999", CODEN = "QJECAT", DOI = "https://doi.org/10.1162/003355399556133", ISSN = "0033-5533 (print), 1531-4650 (electronic)", ISSN-L = "0033-5533", bibdate = "Sat Nov 12 10:57:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0952.91059", abstract = "Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than $S$ is proportional to $ 1 / S $. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically). This automatically leads their distribution to converge to Zipf's law.", acknowledgement = ack-nhfb, ajournal = "Q. J. Econ.", classmath = "91B62 (Dynamic economic models etc.) 91B72 (Spatial models)", fjournal = "The Quarterly Journal of Economics", keywords = "local growth; Zipf's law", } @Book{Gigerenzer:1999:SHM, author = "Gerd Gigerenzer and Peter M. Todd", title = "Simple heuristics that make us smart", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xv + 416", year = "1999", ISBN = "0-19-512156-2", ISBN-13 = "978-0-19-512156-8", LCCN = "BD260 .G54 1999", bibdate = "Sat Sep 10 11:19:26 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Evolution and cognition", URL = "http://www.loc.gov/catdir/enhancements/fy0640/98051084-d.html; http://www.loc.gov/catdir/enhancements/fy0640/98051084-t.html; http://www.loc.gov/catdir/enhancements/fy0726/98051084-b.html", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Heuristic", tableofcontents = "The ABC Research Group \\ I. The Research Agenda \\ 1. Fast and Frugal Heuristics: The Adaptive Toolbox / Gerd Gigerenzer and Peter M. Todd \\ II. Ignorance-Based Decision Making \\ 2. The Recognition Heuristic: How Ignorance Makes Us Smart / Daniel G. Goldstein and Gerd Gigerenzer \\ 3. Can Ignorance Beat the Stock Market? / Bernhard Borges et al. \\ III. One-Reason Decision Making \\ 4. Betting on One Good Reason: The Take The Best Heuristic / Gerd Gigerenzer and Daniel G. Goldstein \\ 5. How Good Are Simple Heuristics? / Jean Czerlinski, Gerd Gigerenzer, and Daniel G. Goldstein \\ 6. Why Does One-Reason Decision Making Work? A Case Study in Ecological Rationality / Laura Martignon and Ulrich Hoffrage \\ 7. When Do People Use Simple Heuristics, and How Can We Tell? / J{\"o}rg Rieskamp and Ulrich Hoffrage \\ 8. Bayesian Benchmarks for Fast and Frugal Heuristics / Laura Martignon and Kathryn Blackmond Laskey \\ IV. Beyond Choice: Memory, Estimation, and Categorization \\ 9. Hindsight Bias: A Price Worth Paying for Fast and Frugal Memory / Ulrich Hoffrage and Ralph Hertwig \\ 10. Quick Estimation: Letting the Environment Do the Work / Ralph Hertwig, Ulrich Hoffrage, and Laura Martignon \\ 11. Categorization by Elimination: Using Few Cues to Choose / Patricia M. Berretty, Peter M. Todd, and Laura Martignon \\ V. Social Intelligence \\ 12. How Motion Reveals Intention: Categorizing Social Interactions / Philip W. Blythe, Peter M. Todd, and Geoffrey F. Miller \\ 13. From Pride and Prejudice to Persuasion: Satisficing in Mate Search / Peter M. Todd and Geoffrey F. Miller \\ 14. Parental Investment by Simple Decision Rules / Jennifer Nerissa Davis and Peter M. Todd \\ VI. A Look Around, A Look Back, A Look Ahead \\ 15. Demons versus Heuristics in Artificial Intelligence, Behavioral Ecology, and Economics / Adam S. Goodie et al. \\ 16. What We Have Learned (So Far) / Peter M. Todd and Gerd Gigerenzer \\ References \\ Name Index \\ Subject Index", } @Article{Hill:1999:DFD, author = "Theodore P. Hill", title = "The Difficulty of Faking Data", journal = j-CHANCE, volume = "12", number = "3", pages = "27--31", month = "????", year = "1999", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.1999.10542154", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Tue Nov 22 18:54:44 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", keywords = "Benford's Law", xxnote = "Check: Hurlimann bibliography says v26 pp. 8--13??; that is wrong!", } @Article{Hill:1999:PCS, author = "Theodore P. Hill", title = "Le premier chiffre significatif fait sa loi. ({French}) [{The} first significant digit makes its law]", journal = "La Recherche: L'actualit{\'e} des sciences", volume = "2", number = "316", pages = "72--76", month = jan, year = "1999", CODEN = "RCCHBV", ISSN = "0029-5671 (print), 1625-9955 (electronic)", ISSN-L = "0029-5671", bibdate = "Sat Feb 16 17:51:25 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970", acknowledgement = ack-nhfb, language = "French", xxjournal = "La Recherche Hors S{\'e}rie", } @Article{Huberman:1999:IGD, author = "Bernardo A. Huberman and Lada A. Adamic", title = "{Internet}: Growth dynamics of the {World-Wide Web}", journal = j-NATURE, volume = "401", number = "6749", pages = "131--131", day = "9", month = sep, year = "1999", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/43604", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Tue Nov 15 09:52:36 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Zipf's Law", } @TechReport{Lowe:1999:FDL, author = "Tomas Lowe and Sally Murphy and Justin Hayward", title = "The First Digit Law", type = "Report", number = "??", institution = "Department of Computing, Imperial College", address = "London, UK", month = jun, year = "1999", bibdate = "Wed Nov 23 16:59:50 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf; http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html", acknowledgement = ack-nhfb, lastaccess = "23 November 2011", } @Article{Malcai:1999:PLD, author = "Ofer Malcai and Ofer Biham and Sorin Solomon", title = "Power-law distributions and {L{\'e}vy}-stable intermittent fluctuations in stochastic systems of many autocatalytic elements", journal = j-PHYS-REV-E, volume = "60", number = "2", pages = "1299--1303", month = aug, year = "1999", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.60.1299", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 10:25:38 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.1299", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", } @Article{Manrubia:1999:SMP, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette", title = "Stochastic multiplicative processes with reset events", journal = j-PHYS-REV-E, volume = "59", number = "5", pages = "4945--4948", month = may, year = "1999", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.59.4945", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:25:24 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.59.4945", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", issue = "5", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's law", } @Article{Manrubia:1999:TDS, author = "Susanna C. Manrubia and Dami{\'a}n H. Zanette and Ricard V. Sol{\'e}", title = "Transient Dynamics and Scaling Phenomena in Urban Growth", journal = j-FRACTALS, volume = "7", number = "1", pages = "1--8", month = mar, year = "1999", CODEN = "FRACEG", DOI = "https://doi.org/10.1142/S0218348X99000025", ISSN = "0218-348X", ISSN-L = "0218-348X", bibdate = "Wed Feb 27 07:11:42 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025", acknowledgement = ack-nhfb, fjournal = "Fractals", journal-URL = "http://www.worldscientific.com/loi/fractals", keywords = "Zipf's Law", } @Article{Matthews:1999:PO, author = "Robert Matthews", title = "The Power of One", journal = j-NEW-SCIENTIST, volume = "163", number = "2194", pages = "27--30", day = "10", month = jul, year = "1999", CODEN = "NWSCAL", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Mon Nov 14 16:04:36 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fortunecity.com/emachines/e11/86/one.html; http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", xxISSN = "0262-4079, 0028-6664", } @Article{Mercik:1999:SAI, author = "Szymon Mercik and Karina Weron and Zuzanna Siwy", title = "Statistical analysis of ionic current fluctuations in membrane channels", journal = j-PHYS-REV-E, volume = "60", number = "6", pages = "7343--7348", day = "1", month = dec, year = "1999", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.60.7343", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.60.7343", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Book{Miller:1999:JFM, author = "Irwin Miller and Marylees Miller", title = "{John E. Freund}'s mathematical statistics", publisher = pub-PH, address = pub-PH:adr, edition = "Sixth", pages = "xii + 624", year = "1999", ISBN = "0-13-123613-X", ISBN-13 = "978-0-13-123613-4", LCCN = "QA276 .M4726 1999", bibdate = "Thu Oct 13 07:00:13 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1928--", remark = "Revised edition of John E. Freund, \booktitle{Mathematical statistics}, 5th edition, 1992.", subject = "Mathematical statistics", } @Article{Nigrini:1999:AVD, author = "Mark J. Nigrini", title = "Adding value with digital analysis", journal = "The Internal Auditor: Journal of the {Institute of Internal Auditors}", volume = "56", number = "1", pages = "21--23", month = "????", year = "1999", CODEN = "ITAUAB", ISSN = "0020-5745", ISSN-L = "0020-5745", bibdate = "Sat Feb 16 18:56:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Nigrini:1999:IGY, author = "Mark J. Nigrini", title = "{I've} Got Your Number: How a Mathematical Phenomenon Can Help {CPAs} Uncover Fraud and Other Irregularities", journal = j-J-ACCOUNTANCY, volume = "187", number = "2", pages = "79--83", month = may, year = "1999", CODEN = "JACYAD", ISSN = "0021-8448 (print), 1945-0729 (electronic)", ISSN-L = "0021-8448", bibdate = "Mon Nov 14 16:31:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm; http://www.journalofaccountancy.com/issues/1999/may/nigrini.html", acknowledgement = ack-nhfb, fjournal = "Journal of Accountancy", journal-URL = "http://www.journalofaccountancy.com/", } @Article{Nigrini:1999:PPF, author = "Mark J. Nigrini", title = "Peculiar patterns of first digits", journal = j-IEEE-POT, volume = "18", number = "2", pages = "24--27", month = apr # "\slash " # may, year = "1999", CODEN = "IEPTDF", DOI = "https://doi.org/10.1109/45.755849", ISSN = "0278-6648 (print), 1558-1772 (electronic)", ISSN-L = "0278-6648", bibdate = "Mon Nov 21 22:18:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Despite seeing numbers all the time only occasionally would one say that a list of numbers seems odd. For this to occur, the numbers are typically highly rounded or implausible (too much of a coincidence). However digit pattern analysis, using a computer, can produce valuable findings not revealed at a mere glance. The most widely cited paper on digit frequencies was published by Frank Benford in 1938. With powerful, low-cost personal computers, Benford's law can help us to efficiently test the integrity of data. The first step is to assess whether Benford's law should apply to the data. If the data is expected to conform, then Benford's law becomes the expected distribution. Conformity means that the actual distribution closely approximates the expected distribution", acknowledgement = ack-nhfb, fjournal = "IEEE Potentials", } @Article{Okuyama:1999:ZLI, author = "K. Okuyama and M. Takayasu and H. Takayasu", title = "{Zipf}'s law in income distribution of companies", journal = j-PHYSICA-A, volume = "269", number = "1", pages = "125--131", day = "1", month = jul, year = "1999", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(99)00086-2", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437199000862", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Growth rate of assets; Income distribution; Zipf's Law", } @Article{Piqueira:1999:ZLO, author = "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C. de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E. G. Cruz", title = "{Zipf's Law} Organizes a Psychiatric Ward", journal = j-J-THEOR-BIOL, volume = "198", number = "3", pages = "439--443", day = "7", month = jun, year = "1999", CODEN = "JTBIAP", DOI = "https://doi.org/10.1006/jtbi.1999.0923", ISSN = "0022-5193 (print), 1095-8541 (electronic)", ISSN-L = "0022-5193", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022519399909232", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Biology", journal-URL = "http://www.sciencedirect.com/science/journal/00225193", keywords = "Zipf's Law", } @Article{Stanley:1999:SUR, author = "H. Eugene Stanley", title = "Scaling, universality, and renormalization: Three pillars of modern critical phenomena", journal = j-REV-MOD-PHYS, volume = "71", number = "2", pages = "S358--S366", month = mar, year = "1999", CODEN = "RMPHAT", DOI = "https://doi.org/10.1103/RevModPhys.71.S358", ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756", ISSN-L = "0034-6861", bibdate = "Wed May 23 10:16:18 MDT 2012", bibsource = "http://rmp.aps.org/toc/RMP/v71/i2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib", URL = "http://link.aps.org/doi/10.1103/RevModPhys.71.S358; http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1", acknowledgement = ack-nhfb, fjournal = "Reviews of Modern Physics", journal-URL = "http://rmp.aps.org/browse", } @Article{Vandewalle:1999:ZAF, author = "N. Vandewalle and M. Ausloos", title = "The $n$-{Zipf} analysis of financial data series and biased data series", journal = j-PHYSICA-A, volume = "268", number = "1--2", pages = "240--249", day = "1", month = jun, year = "1999", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(99)00031-X", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S037843719900031X", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Vardi:1999:PCS, author = "Ilan Vardi", title = "Premiers chiffres significatifs et nombres alg{\'e}briques. ({French}) [Significant leading digits and algebraic numbers]", journal = j-C-R-ACAD-SCI-I, volume = "328", number = "9", pages = "749--754", month = may, year = "1999", CODEN = "CASMEI", DOI = "https://doi.org/10.1016/S0764-4442(99)80265-1", ISSN = "0764-4442 (print), 1778-3577 (electronic)", ISSN-L = "0764-4442", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0764444299802651", abstract = "I show that there is a meromorphic continuation of $ \sigma \log_\beta n / a < \log_\beta a n^{-s} $ to the whole plane if and only if $ \beta $ is a Pisot number, $ \alpha \in Q(\beta) $, and either the second largest conjugate of $ \beta $ is real or the conjugate of $ \alpha $ corresponding to the second largest conjugate of $ \beta $ is positive.", acknowledgement = ack-nhfb, fjournal = "Comptes rendus de l'Acad{\'e}mie des sciences. S{\'e}rie I, Math{'e}matique", keywords = "Benford's Law", language = "French", } @Article{Walthoe:1999:LNO, author = "Jon Walthoe and Robert Hunt and Mike Pearson", title = "Looking out for number one", journal = "Plus Magazine", volume = "??", number = "??", pages = "1--9", month = sep, year = "1999", DOI = "????", bibdate = "Mon Feb 18 06:59:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Published by the University of Cambridge Millennium Mathematics Project.", URL = "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Banyard:2000:NAF, author = "Peter Banyard", title = "A New Aid for Fraud Detection", journal = "Credit Management: journal of the {Institute of Credit Management}", volume = "??", number = "??", address = "Stamford College, UK", pages = "32--33", month = mar, year = "2000", DOI = "", ISSN = "0265-2099", ISSN-L = "0265-2099", bibdate = "Thu Oct 13 08:34:05 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", abstract = "A simple mathematical curiosity, discovered about a century ago, may well prove a surefire way of sniffing out swindlers. Benford's Law was just an observation until the theory that proved it was discovered 3 years ago. It seems unlikely, but about 30\% of numbers start with the digit one. Another 18\% start with the digit 2 and only 4.6\% start with 9. It would be quite easy to build a Benford fraud buster into any analysis of figures, while it remains extremely difficult to produce an artificial set of figures that will comply with the law.", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "I cannot find a Web site for this journal, or for its archives, despite extensive searching.", } @Article{Blank:2000:PLC, author = "Aharon Blank and Sorin Solomon", title = "Power laws in cities population, financial markets and {Internet} sites (scaling in systems with a variable number of components)", journal = j-PHYSICA-A, volume = "287", number = "1--2", pages = "279--288", day = "15", month = nov, year = "2000", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(00)00464-7", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 06:24:21 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437100004647", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @InProceedings{Burns:2000:SSR, author = "B. D. Burns", editor = "Niels A. Taatgen and Hedderik van Rijn", booktitle = "{Proceedings of the 31st Annual Conference of the Cognitive Science Society 2009 (CogSci 2009): Amsterdam, Netherlands, 29 July--1 August 2009}", title = "Sensitivity to Statistical Regularities: People (Largely) Follow {Benford's Law}", publisher = "Cognitive Science Society", address = "Austin, TX, USA", pages = "2872--2877", year = "2010", ISBN = "1-61567-407-1", ISBN-13 = "978-1-61567-407-7", LCCN = "????", bibdate = "Sat Sep 10 10:53:37 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Drake:2000:CAA, author = "Philip D. Drake and Mark J. Nigrini", title = "Computer assisted analytical procedures using {Benford's Law}", journal = j-J-ACCOUNT-EDUC, volume = "18", number = "2", pages = "127--146", month = "Spring", year = "2000", CODEN = "????", DOI = "https://doi.org/10.1016/S0748-5751(00)00008-7", ISSN = "0748-5751 (print), 1873-1996 (electronic)", ISSN-L = "0748-5751", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0748575100000087; http://www.sciencedirect.com/science/journal/07485751", abstract = "This case introduces students to Benford's Law and Digital Analysis, which can be used as an analytical procedure and fraud detection tool. Digital Analysis (DA) is the analysis of digit and number patterns of a data set. Actual digit frequencies in a data set are compared to the expected frequencies according to Benford's Law [Benford, F. (1938). The law of the anomalous numbers, Proceedings of the American Philosophical Society, 78, 551 572.]. Minor differences suggest that the data have passed a reasonableness test, while major differences signal possible financial statement mis-statements. After describing Benford's Law and the basic {DA} tests, the case requires auditing students to download {DA} software and the actual accounts payable file of a software company from a designated Internet site. Students then, (1) analyse the data using three {DA} tests as an analytical procedure in an external audit context, and (2) graph and a report the results and audit-related conclusions. The teaching note includes the actual findings from the audit of that data set and guidance on using the case in an auditing course.", acknowledgement = ack-nhfb, fjournal = "Journal of Accounting Education", keywords = "Benford's Law", } @Article{Lanza:2000:UDA, author = "R. B. Lanza", title = "Using digital analysis to detect fraud: Review of the {DATAS\reg} statistical analysis tool", journal = j-J-FORENSIC-ACCOUNT, volume = "1", number = "??", pages = "291--296", month = "????", year = "2000", CODEN = "????", ISSN = "1524-5586", bibdate = "Tue Nov 22 10:47:45 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.rtedwards.com/journals/JFA/", acknowledgement = ack-nhfb, fjournal = "Journal of Forensic Accounting", } @Article{Leemis:2000:SDS, author = "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L. Evans", title = "Survival Distributions Satisfying {Benford's Law}", journal = j-AMER-STAT, volume = "54", number = "4", pages = "236--241", month = nov, year = "2000", CODEN = "ASTAAJ", DOI = "https://doi.org/10.2307/2685773", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRclass = "62E15 (62N05)", MRnumber = "1803620", bibdate = "Fri Jan 27 18:16:34 MST 2012", bibsource = "http://www.amstat.org/publications/tas/; http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326510; https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/amstat2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amstat.org/publications/tas/Leemis.htm; http://www.jstor.org/stable/2685773", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @InProceedings{Lei:2000:EIN, author = "Skylar Lei and Michael Smith and Giancarlo Succi", title = "Empirical investigation of a novel approach to check the integrity of software engineering measuring processes", crossref = "ACM:2000:PIC", pages = "773--773", year = "2000", DOI = "https://doi.org/10.1145/337180.337629", bibdate = "Sat Feb 16 18:28:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Lowe:2000:BLF, author = "R. Lowe", title = "{Benford's Law} and fraud detection", journal = "Chartered Accountants Journal of New Zealand", volume = "79", number = "10", pages = "32--36", month = "????", year = "2000", DOI = "", ISSN = "1172-9929", ISSN-L = "1172-9929", bibdate = "Thu Oct 13 08:55:37 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, journal-URL = "http://www.nzica.com/journalarchive.aspx", remark = "No archives online before 2012. Library of Congress says that publication ceased in July 2005 at volume 84, number 6.", } @Article{Lowe:2000:WBL, author = "R. Lowe", title = "When {Benford's Law} is broken", journal = "Chartered Accountants Journal of New Zealand", volume = "79", number = "11", pages = "24--27", month = "????", year = "2000", DOI = "", ISSN = "1172-9929", ISSN-L = "1172-9929", bibdate = "Thu Oct 13 08:55:37 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, journal-URL = "http://www.nzica.com/journalarchive.aspx", remark = "No archives online before 2012. Library of Congress says that publication ceased in July 2005 at volume 84, number 6.", } @TechReport{Nigrini:2000:CA, author = "Mark J. Nigrini", title = "Continuous Auditing", type = "Preprint", institution = "Ernst \& Young Center for Auditing Research and Advanced Technology, University of Kansas", address = "Lawrence, KS, USA", pages = "23", day = "30", month = aug, year = "2000", bibdate = "Sat Feb 16 18:57:40 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Book{Nigrini:2000:DAT, author = "Mark J. Nigrini", title = "Digital analysis tests and statistics: using digit and number patterns and Benford's law to detect errors, biases, fraud, irregularities, and processing inefficiencies", publisher = "Nigrini Institute Inc.", address = "Allen, TX, USA", pages = "242", year = "2000", LCCN = "????", bibdate = "Sat Jan 23 07:53:08 MST 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Nigrini:2000:DAU, author = "Mark John Nigrini", title = "Digital analysis using {Benford}'s law: tests and statistics for auditors", publisher = "Global Audit Publications", address = "Vancouver, BC, Canada", edition = "Second", pages = "xvii + 278", year = "2000", ISBN = "189449709 (??invalid ISBN??)", ISBN-13 = "189449709 (??invalid ISBN??)", LCCN = "????", bibdate = "Tue Nov 22 20:48:29 MST 2011", bibsource = "amicus.nlc-bnc.ca:210/NL; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, subject = "Numerical analysis; Data processing; Auditing; Statistical methods; Analyse num{\'e}rique; Informatique; V{\'e}rification comptable; M{\'e}thodes statistiques", } @Article{Padmanabhan:2000:CAD, author = "Venkata N. Padmanabhan and Lili Qiu", title = "The content and access dynamics of a busy {Web} server (poster session)", journal = j-SIGMETRICS, volume = "28", number = "1", pages = "122--123", month = jun, year = "2000", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/339331.339405", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Thu Jun 26 11:31:11 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "We study the MSNBC Web site, one of the busiest in the Internet today. We analyze the dynamics of content creation and modification as well as client accesses. Our key findings are (a) files tend to change little upon modification, (b) a small set of files get modified repeatedly, (c) file popularity follows a Zipf-like distribution with an $ \alpha $ much larger than reported in previous, proxy-based studies, and (d) there is significant temporal stability in file popularity but not much stability in the domains from which popular content is accessed. We discuss implications of these findings.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", } @Book{Sole:2000:SLH, author = "Ricard Vicente Sol{\'e} and Brian Goodwin", title = "Signs of Life: How Complexity Pervades Biology", publisher = pub-BASIC-BOOKS, address = pub-BASIC-BOOKS:adr, pages = "xi + 322", year = "2000", ISBN = "0-465-01927-7, 0-465-01928-5 (paperback)", ISBN-13 = "978-0-465-01927-4, 978-0-465-01928-1 (paperback)", LCCN = "QH501 .S65 2000", bibdate = "Thu Feb 28 09:59:50 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Mandelbrot; Zipf's law", tableofcontents = "Nonlinearity, chaos, and emergence \\ Order, complexity, disorder \\ Genetic networks, cell differentiation, and development \\ Physiology on the edge of chaos \\ Brain dynamics \\ Ants, brains, and chaos \\ The Baroque of nature \\ Life on the edge of catastrophe \\ Evolution and extinction \\ Fractal cities and market crashes", } @Article{Soliman:2000:BPP, author = "Ahmed A. Soliman", title = "{Bayes} Prediction in a {Pareto} Lifetime Model with Random Sample Size", journal = j-J-R-STAT-SOC-SER-D-STATISTICIAN, volume = "49", number = "1", pages = "51--62", month = "????", year = "2000", CODEN = "????", DOI = "https://doi.org/10.2307/2681255", ISSN = "0039-0526 (print), 1467-9884 (electronic)", ISSN-L = "0039-0526", bibdate = "Thu Jan 22 18:10:23 MST 2015", bibsource = "http://www.jstor.org/stable/i326257; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jrss-d-2000.bib", URL = "http://www.jstor.org/stable/2681255", acknowledgement = ack-nhfb, fjournal = "Journal of the Royal Statistical Society. Series D (The Statistician)", journal-URL = "http://www.jstor.org/journals/00390526.html", } @Article{Stanley:2000:SIU, author = "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan and P. Ch. Ivanov and T. H. Keitt and V. Plerou", title = "Scale invariance and universality: organizing principles in complex systems", journal = j-PHYSICA-A, volume = "281", number = "1--4", pages = "60--68", day = "15", month = jun, year = "2000", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(00)00195-3", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Thu Feb 28 09:52:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437100001953", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "power law; scale invariance; Zipf's law", } @Article{Tapp:2000:UTD, author = "D. J. Tapp and D. B. Burg", title = "Using technology to detect fraud", journal = "{Pennsylvania CPA} Journal", volume = "71", number = "4", pages = "20--23", month = "????", year = "2000", ISSN = "0746-1062", ISSN-L = "0746-1062", bibdate = "Thu Oct 13 09:05:22 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "https://www.picpa.org/keep-informed/pennsylvania-cpa-journal", keywords = "Benford's Law", remark = "No archives online before 2014.", } @Article{Tolle:2000:DDS, author = "Charles R. Tolle and Joanne L. Budzien and Randall A. Laviolette", title = "Do dynamical systems follow {Benford}'s law?", journal = j-CHAOS, volume = "10", number = "2", pages = "331--336", month = "????", year = "2000", CODEN = "CHAOEH", DOI = "https://doi.org/10.1063/1.166498", ISSN = "1054-1500", ISSN-L = "1054-1500", bibdate = "Mon Nov 14 17:35:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2000Chaos..10..331T; http://link.aip.org/link/chaoeh/v10/i2/p331/s1; http://link.aip.org/link/doi/10.1063/1.166498", abstract = "Data compiled from a variety of sources follow Benford's law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benford's law. Finally, three chaotic systems are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The Lorenz system generates trajectories that follow Benford's law. The H{\'e}non system generates trajectories that resemble neither the uniform distribution nor Benford's law. Finally, the R{\"o}ssler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others.", acknowledgement = ack-nhfb, fjournal = "Chaos (Woodbury, NY)", journal-URL = "http://scitation.aip.org/content/aip/journal/chaos", xxpages = "331--337", } @Article{Urzua:2000:SET, author = "Carlos M. Urz{\'u}a", title = "A simple and efficient test for {Zipf}'s law", journal = j-ECONOM-LETT, volume = "66", number = "3", pages = "257--260", day = "1", month = mar, year = "2000", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/S0165-1765(99)00215-3", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176599002153", ZMnumber = "0951.91059", abstract = "This paper presents a simple and locally optimal test for Zipf's law. Its use is illustrated in the case of the largest US metropolitan areas. An objection to the general relevance of that law is also presented.", acknowledgement = ack-nhfb, classmath = "91B82 (Statistical methods in economics) 91B74 (Models of real-world systems)", fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "rank-size law; Zipf's law", } @Article{Vogt:2000:BGS, author = "W. Vogt", title = "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf der Spur --- Zahlen l{\"u}gen nichts}. ({German}) [{Benford's Law}: tax and budget sinners lying on the track --- Numbers do not lie]", journal = "Schweizer Versicherung", volume = "9", number = "??", pages = "27--29", month = "????", year = "2000", DOI = "????", bibdate = "Mon Feb 18 06:57:07 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", acknowledgement = ack-nhfb, journal-URL = "http://www.schweizerversicherung.ch/de/archiv_suche", language = "German", remark = "No ISSN assigned. Not found in journal archive on 18 February 2013.", } @Article{York:2000:ATB, author = "D. York", title = "Auditing Technique --- {Benford}'s law", journal = j-ACCOUNTANCY, volume = "126", number = "1283", pages = "126--??", month = "????", year = "2000", CODEN = "ACTYAD", ISSN = "0001-4664", ISSN-L = "0001-4664", bibdate = "Wed Nov 23 11:30:54 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Accountancy", journal-URL = "https://www.cchdaily.co.uk/magazine", remark = "No archives online before 2014", } @Article{Axtell:2001:ZDU, author = "R. L. Axtell", title = "{Zipf} Distribution of {U.S.} Firm Sizes", journal = j-SCIENCE, volume = "293", number = "5536", pages = "1818--1820", day = "7", month = sep, year = "2001", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.1062081", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Wed Feb 27 06:38:34 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/293/5536/1818", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "Zipf's Law", } @Article{Dolgikh:2001:PCS, author = "Dmitry G. Dolgikh and Andrei M. Sukhov", title = "Parameters of cache systems based on a {Zipf}-like distribution", journal = j-COMP-NET-AMSTERDAM, volume = "37", number = "6", pages = "711--716", day = "15", month = dec, year = "2001", CODEN = "????", DOI = "https://doi.org/10.1016/S1389-1286(01)00243-2", ISSN = "1389-1286 (print), 1872-7069 (electronic)", ISSN-L = "1389-1286", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "http://www.elsevier.com/locate/issn/13891286; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html; http://www.sciencedirect.com/science/article/pii/S1389128601002432", acknowledgement = ack-nhfb, fjournal = "Computer Networks (Amsterdam, Netherlands: 1999)", journal-URL = "http://www.sciencedirect.com/science/journal/13891286", keywords = "Zipf's Law", } @Article{Dubinsky:2001:MFF, author = "Bruce G. Dubinsky", title = "Math formula fights fraud", journal = "Legal Times of {Washington}", volume = "XXIV", number = "9", pages = "??--??", day = "26", month = feb, year = "2001", ISSN = "0732-7536", ISSN-L = "0732-7536", bibdate = "Sat Feb 16 17:35:39 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", xxjournal = "Legal Times", } @Article{Gelbukh:2001:ZHL, author = "Alexander Gelbukh and Grigori Sidorov", title = "{Zipf} and {Heaps Laws}' Coefficients Depend on Language", journal = j-LECT-NOTES-COMP-SCI, volume = "2004", pages = "332--??", year = "2001", CODEN = "LNCSD9", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Feb 2 13:03:22 MST 2002", bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm; http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf", acknowledgement = ack-nhfb, fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @TechReport{Gent:2001:BL, author = "Ian Gent and Toby Walsh", title = "{Benford's Law}", type = "Report", institution = "School of Computer Science, University of St. Andrews, and Department of Computer Science, University of York", address = "St. Andrews, Scotland and York, England", pages = "7", day = "2", month = feb, year = "2001", bibdate = "Fri Nov 18 08:37:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf", abstract = "Benford's Law predicts the frequency of the leading digit in numbers met in a wide range of naturally occurring phenomena. In data following Benford's Law, numbers start with a small leading digit more often those with a large leading digit. Here we demonstrate that Benford's Law also describes a wide range of computational phenomena. In particular, we show that a number of different statistics associated with computation like space and runtime often follow Benford's Law. We also show that search cost on input data that follows Benford's Law is often very different to that on more uniform data. These results could be used to improve algorithm performance (for example, for load balancing or disk de-fragmentation), as well as to help model algorithm performance. Benford's Law can also be used to generate data for benchmarking algorithms that may be more realistic than purely random data.", acknowledgement = ack-nhfb, remark = "PDF file no longer at the St. Andrews URL on 18 November 2011, but recovered from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.", } @Article{Harremoes:2001:MEF, author = "Peter Harremo{\"e}s and Flemming Tops{\o}e", title = "Maximum Entropy Fundamentals", journal = j-ENTROPY, volume = "3", number = "3", pages = "191--226", month = sep, year = "2001", CODEN = "ENTRFG", DOI = "https://doi.org/10.3390/e3030191", ISSN = "1099-4300", ISSN-L = "1099-4300", bibdate = "Thu Feb 28 10:55:45 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.mdpi.com/1099-4300/3/3/191", acknowledgement = ack-nhfb, fjournal = "Entropy", journal-URL = "https://www.mdpi.com/journal/entropy/", keywords = "continuity of entropy; entropy loss; exponential family; game theoretical equilibrium; hyperbolic distributions; information topology; maximum entropy; minimum risk; Nash equilibrium code; partition function; Zipf's law", remark = "Open access journal.", } @Article{Hobza:2001:NBL, author = "Tom{\'a}{\v{s}} Hobza and Igor Vajda", title = "On the {Newcomb--Benford} law in models of statistical data", journal = "Revista Matem{\'a}tica Complutense", volume = "14", number = "2", pages = "407--420", year = "2001", CODEN = "????", DOI = "https://doi.org/10.5209/rev\_rema.2001.v14.n2.16992", ISSN = "1139-1138, 1696-8220, 1988-2807", ISSN-L = "1139-1138", MRclass = "62E10", MRnumber = "1871305 (2002j:62015)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Rev. Mat. Complut.", fjournal = "Revista Matem{\'a}tica Complutense", } @Article{Huang:2001:PLE, author = "Z. F. Huang and S. Solomon", title = "Power, {L{\'e}vy}, exponential and {Gaussian}-like regimes in autocatalytic financial systems", journal = j-EUR-PHYS-J-B, volume = "20", number = "4", pages = "601--607", month = apr, year = "2001", CODEN = "EPJBFY", DOI = "https://doi.org/10.1007/PL00011114", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Thu Feb 28 10:26:53 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/PL00011114", acknowledgement = ack-nhfb, fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", keywords = "power law; scale invariance; Zipf's law", } @MastersThesis{Jamain:2001:BL, author = "Adrien Jamain", title = "{Benford's Law}", type = "{Master}'s thesis", school = "Department of Mathematics, Imperial College of London and ENSIMAG", address = "London, UK", pages = "????", year = "2001", bibdate = "Sat Feb 16 18:06:41 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Not found in Imperial College Library or COPAC catalogs on 16 February 2013. URL link is broken too.", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf", acknowledgement = ack-nhfb, } @Article{Jansen:2001:RNP, author = "C. J. M. Jansen and M. M. W. Pollmann", title = "On Round Numbers: Pragmatic Aspects of Numerical Expressions", journal = j-J-QUANT-LINGUISTICS, volume = "8", number = "3", pages = "187--201", month = "????", year = "2001", DOI = "https://doi.org/10.1076/jqul.8.3.187.4095", ISSN = "0929-6174 (print), 1744-5035 (electronic)", ISSN-L = "0929-6174", bibdate = "Sat Jan 07 09:51:05 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095", abstract = "This paper describes and explains some regularities in the frequency of numbers in text. An analysis of number frequencies in text corpora in Dutch, English, German, and French confirms the expectation that frequency is highly dependent on two factors: magnitude and roundness. Roundness (defined as number frequency in an approximation context) proves to be related to three arithmetical properties: `10-ness', `2-ness', and `5-ness'. In predicting the frequency of numbers irrespective of their context `$ 2 1 / 2 $-ness' should be added to these factors, as is suggested in the work of Sigurd (1988). The role of the four number characteristics found in this study can be explained by the preference of the language user for using base numbers, and for doubling and halving quantities.", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Linguistics", onlinedate = "09 Aug 2010", } @Article{Jolion:2001:IBL, author = "Jean-Michel Jolion", title = "Images and {Benford}'s law", journal = j-J-MATH-IMAG-VIS, volume = "14", number = "1", pages = "73--81", year = "2001", CODEN = "JMIVEK", DOI = "https://doi.org/10.1023/A:1008363415314", ISSN = "0924-9907 (print), 1573-7683 (electronic)", ISSN-L = "0924-9907", MRclass = "94A08 (68U10)", MRnumber = "1818436 (2001m:94007)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See comments and extensions in \cite[Chapter 19]{Miller:2015:BLT}.", URL = "http://link.springer.com/article/10.1023/A%3A1008363415314", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Imaging and Vision: JMIV", } @Article{Knudsen:2001:ZLC, author = "Thorbj{\o}rn Knudsen", title = "{Zipf}'s law for cities and beyond: the case of {Denmark}", journal = j-AM-J-ECON-SOCIOL, volume = "60", number = "1", pages = "123--146", month = jan, year = "2001", CODEN = "AJESA3", DOI = "https://doi.org/10.1111/1536-7150.00057", ISSN = "0002-9246 (print), 1536-7150 (electronic)", ISSN-L = "0002-9246", bibdate = "Sat Feb 16 18:14:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/3487947", acknowledgement = ack-nhfb, fjournal = "The American Journal of Economics and Sociology", } @Article{Kretschmer:2001:RAI, author = "Hildrun Kretschmer and Ronald Rousseau", title = "Research: Author inflation leads to a breakdown of {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "52", number = "8", pages = "610--614", month = "????", year = "2001", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.1118", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:41:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "27 Apr 2001", } @Article{Levene:2001:ZLW, author = "Mark Levene and Jos{\'e} Borges and George Loizou", title = "{Zipf}'s law for {Web} surfers", journal = j-KNOWL-INFO-SYS, volume = "3", number = "1", pages = "120--129", year = "2001", CODEN = "KISNCR", DOI = "https://doi.org/10.1007/PL00011657", ISSN = "0219-1377", bibdate = "Sat Nov 12 11:00:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "0991.68622", abstract = "One of the main activities of Web users, known as `surfing', is to follow links. Lengthy navigation often leads to disorientation when users lose track of the context in which they are navigating and are unsure how to proceed in terms of the goal of their original query. Studying navigation patterns of Web users is thus important, since it can lead us to a better understanding of the problems users face when they are surfing. We derive Zipf's rank frequency law (i.e., an inverse power law) from an absorbing Markov chain model of surfers' behavior assuming that less probable navigation trails are, on average, longer than more probable ones. In our model the probability of a trail is interpreted as the relevance (or `value') of the trail. We apply our model to two scenarios: in the first the probability of a user terminating the navigation session is independent of the number of links he has followed so far, and in the second the probability of a user terminating the navigation session increases by a constant each time the user follows a link. We analyze these scenarios using two sets of experimental data sets showing that, although the first scenario is only a rough approximation of surfers' behavior, the data is consistent with the second scenario and can thus provide an explanation of surfers' behavior.", acknowledgement = ack-nhfb, classmath = "68U99 (Computing methodologies) 68P15 (Database theory) 68P20 (Information storage and retrieval)", fjournal = "Knowledge and Information Systems", keywords = "Markov chain; Web navigation; Zipf's law", } @Article{Losee:2001:TDB, author = "Robert M. Losee", title = "Term dependence: a basis for {Luhn} and {Zipf} models", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "52", number = "12", pages = "1019--1025", year = "2001", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.1155", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @Article{Malacarne:2001:QED, author = "L. C. Malacarne and R. S. Mendes and E. K. Lenzi", title = "$q$-exponential distribution in urban agglomeration", journal = j-PHYS-REV-E, volume = "65", number = "??", pages = "017106", day = "21", month = dec, year = "2001", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.65.017106", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.65.017106", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf--Mandelbrot law", } @Article{Montemurro:2001:BZM, author = "Marcelo A. Montemurro", title = "Beyond the {Zipf--Mandelbrot} law in quantitative linguistics", journal = j-PHYSICA-A, volume = "300", number = "3--4", pages = "567--578", day = "15", month = nov, year = "2001", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(01)00355-7", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437101003557", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @PhdThesis{Morters:2001:BGV, author = "Peter M{\"o}rters", title = "{Benford's Gesetz {\"u}ber die Verteilung der Ziffern}. (German) [{Benford}'s law on the distribution of digits]", type = "{Habilitationsvorlesung}", school = "????", address = "Kaiserslauten, Germany, and Bath, UK", pages = "4", month = "????", year = "2001", bibdate = "Sat Feb 16 18:47:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://people.bath.ac.uk/maspm/benford.ps", acknowledgement = ack-nhfb, language = "German", } @Article{Nigrini:2001:DAU, author = "Mark Nigrini", title = "Digital Analysis Using {Benford's} Law: Tests and Statistics for Auditors", journal = j-EDPACS, volume = "28", number = "9", pages = "1--2", month = "????", year = "2001", CODEN = "EDPCDF", DOI = "https://doi.org/10.1201/1079/43266.28.9.20010301/30389.4", ISSN = "0736-6981 (print), 1936-1009 (electronic)", ISSN-L = "0736-6981", bibdate = "Sat Jan 07 09:08:09 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4", acknowledgement = ack-nhfb, fjournal = "EDPACS", onlinedate = "21 Dec 2006", } @Article{Pietronero:2001:EUD, author = "L. Pietronero and E. Tosatti and V. Tosatti and A. Vespignani", title = "Explaining the uneven distribution of numbers in nature: the laws of {Benford} and {Zipf}", journal = j-PHYSICA-A, volume = "293", number = "1--2", pages = "297--304", day = "1", month = apr, year = "2001", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(00)00633-6", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2001PhyA..293..297P; http://www.sciencedirect.com/science/article/pii/S0378437100006336", abstract = "The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the Benford's law in terms of multiplicative processes. We show that this law can be also generalized to series of numbers generated from more complex systems like the catalogs of seismic activity. Finally, we derive a relation between the generalized Benford's law and the popular Zipf's law which characterize the rank order statistics and has been extensively applied to many problems ranging from city population to linguistics.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Reed:2001:PZO, author = "William J. Reed", title = "The {Pareto}, {Zipf} and other power laws", journal = j-ECONOM-LETT, volume = "74", number = "1", pages = "15--19", day = "20", month = dec, year = "2001", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/S0165-1765(01)00524-9", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176501005249", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @TechReport{Scott:2001:BLE, author = "P. D. Scott and M. Fasli", title = "{Benford's Law}: An Empirical Investigation and a Novel Explanation", type = "CSM Technical Report", number = "349", institution = "Department of Computer Science, University Essex", address = "Colchester, UK", day = "26", month = oct, year = "2001", bibdate = "Tue Nov 22 21:05:22 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf", acknowledgement = ack-nhfb, } @Article{Sellke:2001:CVT, author = "Thomas Sellke and M. J. Bayarri and James O. Berger", title = "Calibration of $p$ Values for Testing Precise Null Hypotheses", journal = j-AMER-STAT, volume = "55", number = "1", pages = "62--71", month = feb, year = "2001", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/000313001300339950", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Jan 27 18:16:34 MST 2012", bibsource = "http://www.amstat.org/publications/tas/; http://www.jstor.org/journals/00031305.html; http://www.jstor.org/stable/i326511; https://www.math.utah.edu/pub/tex/bib/amstat2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amstat.org/publications/tas/Sellke.htm; http://www.jstor.org/stable/2685531; http://www.tandfonline.com/doi/abs/10.1198/000313001300339950", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Snyder:2001:SAO, author = "Mark A. Snyder and James H. Curry and Anne M. Dougherty", title = "Stochastic aspects of one-dimensional discrete dynamical systems: {Benford}'s law", journal = j-PHYS-REV-E, volume = "64", number = "2", pages = "026222:1--026222:5", month = aug, year = "2001", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.64.026222", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Mon Nov 14 17:44:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S; http://pre.aps.org/abstract/PRE/v64/i2/e026222", abstract = "Benford's law owes its discovery to the ``Grubby Pages Hypothesis,'' a 19th century observation made by Simon Newcomb that the beginning pages of logarithm books were grubbier than the last few pages, implying that scientists referenced the values toward the front of the books more frequently. If a data set satisfies Benford's law, then its significant digits will have a logarithmic distribution, which favors smaller significant digits. In this article we demonstrate two ways of creating discrete one-dimensional dynamical systems that satisfy Benford's law. We also develop a numerical simulation methodology that we use to study dynamical systems when analytical results are not readily available.", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", pagecount = "5", } @InCollection{Solomon:2001:SPZ, author = "Sorin Solomon and Peter Richmond", booktitle = "Economics with heterogeneous interacting agents ({Marseille}, 2000)", title = "Stability of {Pareto--Zipf} law in non-stationary economies", volume = "503", publisher = pub-SV, address = pub-SV:adr, pages = "141--159", year = "2001", MRclass = "91B28 (91B62)", MRnumber = "1838925", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Econom. and Math. Systems", acknowledgement = ack-nhfb, } @Article{Zanette:2001:VTC, author = "Dami{\'a}n H. Zanette and Susanna C. Manrubia", title = "Vertical transmission of culture and the distribution of family names", journal = j-PHYSICA-A, volume = "295", number = "1--2", pages = "1--8", day = "1", month = jun, year = "2001", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(01)00046-2", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:03:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437101000462", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Abe:2002:STE, author = "Sumiyoshi Abe", title = "Stability of {Tsallis} entropy and instabilities of {R{\'e}nyi} and normalized {Tsallis} entropies: a basis for $q$-exponential distributions", journal = j-PHYS-REV-E, volume = "66", number = "??", pages = "046134", day = "24", month = oct, year = "2002", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.66.046134", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.046134", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Anonymous:2002:ZLM, author = "Anonymous", title = "{Zipf}'s law and maximum sustainable growth", journal = j-STAT-PROB-LETT, volume = "56", number = "2", pages = "??--??", day = "15", month = jan, year = "2002", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.jedc.2013.02.004", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165188913000341", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Zipf's Law", onlinedate = "19 February 2013", } @InProceedings{Bhattacharya:2002:KBT, author = "S. Bhattacharya", editor = "????", booktitle = "9th World Congress of Accounting Historians, Deakin University, Melbourne, Australia July 30--August 3, 2002", title = "From {Kautilya} to {Benford} --- Trends in Forensic and Investigative Accounting", publisher = "Accounting Association of Australia and New Zealand", address = "????", pages = "??--??", year = "2002", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:22:29 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "http://ach.sagepub.com/", remark = "I cannot find the published proceedings in online catalogs or bookstores, or in the Deakin University library catalogs. Where only selected papers published from the conference in the journal Accounting History??", review-doi = "https://doi.org/10.1177/103237320200700207", review-url = "http://dro.deakin.edu.au/view/DU:30012663; http://www.highbeam.com/doc/1G1-97484707.html", } @Article{Bolton:2002:SFD, author = "Richard J. Bolton and David J. Hand", title = "Statistical Fraud Detection: A Review", journal = j-STAT-SCI, volume = "17", number = "3", pages = "235--255", month = aug, year = "2002", CODEN = "STSCEP", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", bibdate = "Fri May 30 12:48:50 MDT 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statsci.bib", URL = "http://projecteuclid.org/euclid.ss/1042727940", acknowledgement = ack-nhfb, fjournal = "Statistical Science", journal-URL = "http://projecteuclid.org/all/euclid.ss", } @Article{Brown:2002:ICF, author = "Philip Brown and Angeline Chua and Jason Mitchell", title = "The influence of cultural factors on price clustering: Evidence from {Asia Pacific} stock markets", journal = "Pacific-Basin Finance Journal", volume = "10", number = "3", pages = "307--332", year = "2002", DOI = "https://doi.org/10.1016/S0927-538X(02)00049-5", ISSN = "0927-538X (print), 1879-0585 (electronic)", ISSN-L = "0927-538X", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "13th Annual PACAP/FMA Finance Conference", URL = "http://www.sciencedirect.com/science/article/pii/S0927538X02000495", abstract = "Price clustering is the tendency of prices to be observed more frequently at some numbers than others. It increases with haziness, or imprecision, about underlying value. Most research on price clustering has been conducted in Western financial markets, where there is manifest preference for trading at round numbers. We focus on number preferences under Chinese culture. Many Chinese believe some numbers are unlucky and to be avoided. For instance, the number 4 is inauspicious because the Cantonese pronunciation of 4 is similar to the phrase to die. We first document clustering of daily closing prices on six Asia Pacific stock markets, three with predominantly Chinese populations. Next, we fit binomial logit models within these markets to estimate the association between structural and economic factors, and culture, on price clustering. We find some support for the influence of Chinese culture and superstition on year-round number preferences of traders, but it is located solely in the Hong Kong market. Furthermore, in the Hong Kong market Chinese culture and superstition help explain the increased avoidance of the number 4 during the auspicious Chinese New Year, Dragon Boat and Mid-Autumn festivals.", acknowledgement = ack-nhfb, keywords = "Attraction; Benford's Law; Haziness; Negotiation; Price clustering", } @TechReport{Diekmann:2002:DFM, author = "Andreas Diekmann", title = "{Diagnose von Fehlerquellen und methodische Qualit{\"a}t in der sozialwissenschaftlichen Forschung}. ({German}) [{Diagnosis} of errors and methodological quality in social science research]", type = "Report", number = "ITA-02-04", institution = "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung", address = "Vienna, Austria", pages = "????", year = "2002", bibdate = "Thu Nov 17 19:11:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Egghe:2002:DRC, author = "L. Egghe and I. K. Ravichandra Rao", title = "Duality revisited: {Construction} of fractional frequency distributions based on two dual {Lotka} laws", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "53", number = "10", pages = "789--801", month = "????", year = "2002", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.10103", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:41:59 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "11 Jun 2002", } @Article{FerreriCancho:2002:ZLR, author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}", title = "{Zipf}'s law and random texts", journal = j-ADV-COMPLEX-SYST, volume = "5", number = "1", pages = "1--6", year = "2002", CODEN = "????", DOI = "https://doi.org/10.1142/S0219525902000468", ISSN = "0219-5259", bibdate = "Sat Nov 12 11:00:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1090.91595", abstract = "Random-text models have been proposed as an explanation for the power law relationship between word frequency and rank, the so-called Zipf's law. They are generally regarded as null hypotheses rather than models in the strict sense. In this context, recent theories of language emergence and evolution assume this law as a priori information with no need of explanation. Here, random texts and real texts are compared through (a) the so-called lexical spectrum and (b) the distribution of words having the same length. It is shown that real texts fill the lexical spectrum much more efficiently and regardless of the word length, suggesting that the meaningfulness of Zipf's law is high.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics)", fjournal = "Advances in Complex Systems", journal-URL = "http://www.worldscinet.com/acs/acs.shtml", keywords = "Human language; monkey languages; random texts; scaling; Zipf's law", } @Article{Gottwald:2002:NBL, author = "Georg A. Gottwald and Matthew Nicol", title = "On the nature of {Benford's Law}", journal = j-PHYSICA-A, volume = "303", number = "3--4", pages = "387--396", day = "15", month = jan, year = "2002", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(01)00497-6", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "60C05 (28D05 60E05 82B05)", MRnumber = "1917635 (2003d:60015)", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://adsabs.harvard.edu/abs/2002PhyA..303..387G; http://www.sciencedirect.com/science/article/pii/S0378437101004976", abstract = "We study multiplicative and affine sequences of real numbers defined by $ N(j + 1) = \zeta (j) N(j) + \eta (j) $, where \{\zeta(j)\} and \{\eta(j)\} are sequences of positive real numbers (in the multiplicative case $ \eta (j) = 0 $ for all $j$). We investigate the conditions under which the leading digits $k$ of \{N(j)\} have the following probability distribution, known as Benford's Law, $ P(k) = \log_{10}((k + 1) / k)$. We present two main results. First, we show that contrary to the usual assumption in the literature, \{\zeta(j)\} does not necessarily need to come from a chaotic or independent random process for Benford's Law to hold. The multiplicative driving force may be a deterministic quasiperiodic or even periodic forcing. Second, we give conditions under which the distribution of the first digits of an affine process displays Benford's Law. Our proofs use techniques from ergodic theory.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Law of Anomalous Numbers; Multiplicative process; Scaling laws; Zipf's Law", } @Article{Hasan:2002:ADA, author = "Bassam Hasan", title = "Assessing data authenticity with {Benford}'s law", journal = "Information Systems Control Journal", volume = "6", pages = "??--??", year = "2002", CODEN = "ISYJFS", ISSN = "1526-7407", bibdate = "Sat Feb 16 17:45:21 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx", acknowledgement = ack-nhfb, journal-URL = "http://www.isaca.org/", remark = "Journal publication ceased at volume 6 in 2008, according to one library catalog, but volumes up to 2013 are available at journal Web site.", } @InProceedings{Hill:2002:RAB, author = "T. P. Hill", editor = "????", booktitle = "Conference, Leiden University", title = "Recent applications of {Benford}'s law", publisher = "????", address = "????", pages = "??--??", year = "2002", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:55:46 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hoyle01042002, author = "David C. Hoyle and Magnus Rattray and Ray Jupp and Andrew Brass", title = "Making sense of microarray data distributions", journal = j-BIOINFORMATICS, volume = "18", number = "4", pages = "576--584", year = "2002", DOI = "https://doi.org/10.1093/bioinformatics/18.4.576", ISSN = "1367-4803 (print), 1367-4811 (electronic)", ISSN-L = "1367-4803", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bioinformatics.oxfordjournals.org/content/18/4/576.abstract", abstract = "Motivation: Typical analysis of microarray data has focused on spot by spot comparisons within a single organism. Less analysis has been done on the comparison of the entire distribution of spot intensities between experiments and between organisms.Results: Here we show that mRNA transcription data from a wide range of organisms and measured with a range of experimental platforms show close agreement with Benford's law (Benford, Proc. Am. Phil. Soc., 78, 551 572, 1938) and Zipf's law (Zipf, The Psycho-biology of Language: an Introduction to Dynamic Philology, 1936 and Human Behaviour and the Principle of Least Effort, 1949). The distribution of the bulk of microarray spot intensities is well approximated by a log-normal with the tail of the distribution being closer to power law. The variance, 2, of log spot intensity shows a positive correlation with genome size (in terms of number of genes) and is therefore relatively fixed within some range for a given organism. The measured value of 2 can be significantly smaller than the expected value if the mRNA is extracted from a sample of mixed cell types. Our research demonstrates that useful biological findings may result from analyzing microarray data at the level of entire intensity distributions. Contact: david.c.hoyle@man.ac.uk", acknowledgement = ack-nhfb, fjournal = "Bioinformatics", journal-URL = "http://bioinformatics.oxfordjournals.org/", keywords = "Zipf's Law", } @Article{Hoyle:2002:MSM, author = "David C. Hoyle and Magnus Rattray and Ray Jupp and Andrew Brass", title = "Making sense of microarray data distributions", journal = j-BIOINFORMATICS, volume = "18", number = "4", pages = "576--584", month = apr, year = "2002", ISSN = "1367-4803 (print), 1367-4811 (electronic)", ISSN-L = "1367-4803", bibdate = "Fri Nov 25 11:16:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Bioinformatics", journal-URL = "http://bioinformatics.oxfordjournals.org/", keywords = "Benford's Law; mRNA transcription data", } @Article{Huber:2002:NMG, author = "John C. Huber", title = "A new model that generates {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "53", number = "3", pages = "209--219", month = "????", year = "2002", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.10025", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:02 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "28 Dec 2001", } @Article{Jones:2002:LDR, author = "B. K. Jones", title = "Logarithmic distributions in reliability analysis", journal = j-MICROELECT-RELIABILITY, volume = "42", number = "4--5", pages = "779--786", month = apr # "\slash " # may, year = "2002", CODEN = "MCRLAS", DOI = "https://doi.org/10.1016/S0026-2714(02)00031-8", ISSN = "0026-2714 (print), 1872-941X (electronic)", ISSN-L = "0026-2714", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0026271402000318", abstract = "Real-life systems are complex, with many independent parameters which can affect the system. Their behaviour can therefore be very variable. This is especially true of the more involved processes which occur in reliability and degradation processes. However, there are some characteristics which are observed which can be understood simply because they are characteristic of complex systems. These include distributions that are very often logarithmic rather than uniform, log normal failure distributions and $ 1 g / f $ noise. A wide variety of diverse examples is given to illustrate the common occurrence of such observations together with the underlying unifying themes. There are several basic reasons for the origin of logarithmic distributions. One is that they arise from multiplicative processes. Another is that although basic science is often introduced as linear, with non-linear effects added as a correction, complex systems are often inherently non-linear. This produces multiplicative effects, such as harmonic generation and fractal behaviour.", acknowledgement = ack-nhfb, fjournal = "Microelectronics and Reliability", keywords = "Benford's Law; Pareto distribution; Zipf's Law", } @Article{Kawamura:2002:UZL, author = "Kenji Kawamura and Naomichi Hatano", title = "Universality of {Zipf}'s law", journal = j-J-PHYS-SOC-JAP, volume = "71", number = "5", pages = "1211--1213", year = "2002", CODEN = "JUPSAU", DOI = "https://doi.org/10.1143/JPSJ.71.1211", ISSN = "0031-9015 (print), 1347-4073 (electronic)", ISSN-L = "0031-9015", bibdate = "Sat Nov 12 11:00:54 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jpsj.ipap.jp/", ZMnumber = "1063.60114", abstract = "The aim of the present paper is to propose and simulate a simple and generic model that reproduces Zipf's law. In the proposed model, the time evolution is considered to be a random walk in the logarithmic scale reflecting the company asset distribution and/or the evolution of city populations (e.g. Zipf's law for income distribution asserts that the size and number of companies are in inverse proportional relationship). The paper explains theoretically and shows by numerical simulation that the introduced model of Zipf's law has a very robust behaviour when applied to various natural and social phenomena. The authors do not investigate the famous case of Zipf's law application to the frequency of English words, but they speculate that this case might be also explained within the same time development of the proposed model.", acknowledgement = ack-nhfb, classmath = "60J60 (Diffusion processes) 60J70 (Appl. of diffusion theory) 76R50 (Diffusion) 82C24 (Interface problems (dynamic and non-equilibrium))", fjournal = "Journal of the Physical Society of Japan", keywords = "city population evolution; company asset distribution; diffusion; generic model of Zipf's law; natural and social phenomena; random walk in logarithmic scale", ZMreviewer = "Neculai Curteanu (Ia\c si)", } @TechReport{Kreiner:2002:FDL, author = "W. A. Kreiner", title = "First digit law", type = "Preprint", institution = "Abteilung Chemische Physik, Arbeitsgruppe Laseranwendungen, Universit{\"a}t Ulm", address = "Ulm, Germany", pages = "7", day = "3", month = may, year = "2002", bibdate = "Sat Feb 16 18:18:49 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law; First Digit Law; Newcomb; Statistisches Fraktal", language = "German", } @Article{Li:2002:ZLI, author = "Wentian Li and Yaning Yang", title = "{Zipf's Law} in Importance of Genes for Cancer Classification Using Microarray Data", journal = j-J-THEOR-BIOL, volume = "219", number = "4", pages = "539--551", day = "21", month = dec, year = "2002", CODEN = "JTBIAP", DOI = "https://doi.org/10.1006/jtbi.2002.3145", ISSN = "0022-5193 (print), 1095-8541 (electronic)", ISSN-L = "0022-5193", MRclass = "92C40 (92D10)", MRnumber = "2044066", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022519302931450", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Biology", journal-URL = "http://www.sciencedirect.com/science/journal/00225193", keywords = "Zipf's Law", } @Book{Livio:2002:GRS, author = "Mario Livio", title = "The Golden Ratio: the Story of Phi, the World's Most Astonishing Number", publisher = "Broadway Books", address = "New York, NY, USA", pages = "viii + 294", year = "2002", ISBN = "0-7679-0815-5", ISBN-13 = "978-0-7679-0815-3", LCCN = "QA466 .L58 2002", bibdate = "Tue Jul 08 12:29:44 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", note = "Benford's Law is treated on pages 231--237.", price = "US\$24.95, CAN\$37.95", abstract = "Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, the author tells the tale of a number at the heart of that mystery: phi, or 1.6180339887\ldots{}. This curious mathematical relationship, widely known as ``The Golden Ratio,'' was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! This book is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, the author reveals the world as a place where order, beauty, and eternal mystery will always coexist.", acknowledgement = ack-nhfb, tableofcontents = "Prelude to a number \\ The pitch and the pentagram \\ Under a star-Y-pointing pyramid? \\ The second treasure \\ Son of good nature \\ The divine proportion \\ Painters and poets have equal license \\ From the tiles to the heavens \\ Is God a mathematician?", } @InProceedings{Manaris:2002:PTR, author = "B. Manaris and T. Purewal and C. McCormick", editor = "{IEEE}", booktitle = "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002, Embassy Suites Hotel, Columbia, South Carolina, USA", title = "Progress Towards Recognizing and Classifying Beautiful Music with Computers: {MIDI}-Encoded Music and the {Zipf-Mandelbrot Law}", publisher = pub-IEEE, address = pub-IEEE:adr, bookpages = "xviii + 482", pages = "52--57", year = "2002", DOI = "https://doi.org/10.1109/.2002.995557", ISBN = "0-7803-7252-2", ISBN-13 = "978-0-7803-7252-8", LCCN = "TK7801 .I56 2002", bibdate = "Mon Feb 18 10:40:27 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=7814", acknowledgement = ack-nhfb, } @Article{Mochty:2002:AMI, author = "L. Mochty", title = "{Die Aufdeckung von Manipulationen im Rechnungswesen --- Was leistet das Benford's Law?}. ({German}) [{The} disclosure of accounting manipulations --- what does {Benford's Law} mean?]", journal = "Die Wirtschaftspr{\"u}fung", volume = "14", number = "??", pages = "725--736", month = "????", year = "2002", CODEN = "????", ISSN = "0043-6313", ISSN-L = "0043-6313", bibdate = "Thu Nov 17 19:20:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Mosimann:2002:TDE, author = "James Mosimann and John Dahlberg and Nancy Davidian and John Krueger", title = "Terminal Digits and the Examination of Questioned Data", journal = j-ACCOUNT-RES, volume = "9", number = "2", pages = "75--92", month = "????", year = "2002", CODEN = "ARQAEZ", DOI = "https://doi.org/10.1080/08989620212969", ISSN = "0898-9621 (print), 1545-5815 (electronic)", ISSN-L = "0898-9621", bibdate = "Sat Sep 10 15:08:21 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/08989620212969", acknowledgement = ack-nhfb, fjournal = "Accountability in Research", journal-URL = "http://www.tandfonline.com/toc/gacr20", keywords = "Benford's Law", } @Book{Newman:2002:ME, author = "M. E. J. (Mark E. J.) Newman and Richard G. Palmer", title = "Modeling extinction", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xii + 102", year = "2002", ISBN = "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)", ISBN-13 = "978-0-19-515946-2 (paperback), 978-0-19-515945-5 (hardcover)", LCCN = "QH78 .N48 2002", bibdate = "Thu Feb 28 10:36:25 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; library.ox.ac.uk:210/ADVANCE", series = "Santa Fe Institute studies in the sciences of complexity", acknowledgement = ack-nhfb, keywords = "power law; Zipf's law", subject = "Extinction (Biology); Statistical methods; Mathematical models", } @Misc{Popescu:2002:LNZ, author = "Ioan-Iovitz Popescu", title = "On the {Lavelette}'s nonlinear {Zipf}'s law", howpublished = "Web preprint.", month = feb, year = "2002", bibdate = "Sat Feb 16 19:02:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html", acknowledgement = ack-nhfb, } @Article{Reed:2002:GFG, author = "William J. Reed and Barry D. Hughes", title = "From gene families and genera to incomes and {Internet} file sizes: Why power laws are so common in nature", journal = j-PHYS-REV-E, volume = "66", number = "6", pages = "067103", month = dec, year = "2002", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.66.067103", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Wed Feb 27 06:58:05 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.66.067103", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Pareto's Law; rank-size property; Zipf's Law", pagecount = "4", } @Article{Sandon:2002:DPC, author = "F. Sandon", title = "Do Populations Conform to the Law of Anomalous Numbers?", journal = "Population", volume = "57", number = "4", pages = "755--761", month = "????", year = "2002", bibdate = "Sat Sep 10 16:15:28 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.persee.fr/doc/pop_1634-2941_2002_num_57_4_18419", acknowledgement = ack-nhfb, journal-URL = "http://www.persee.fr/collection/pop", keywords = "Benford's Law", } @Article{Sandron:2002:DPC, author = "Fr{\'e}d{\'e}ric Sandron", title = "Do populations conform to the {Law of Anomalous Numbers}?", journal = "Population", volume = "57", number = "4--5", pages = "755--761", month = "????", year = "2002", CODEN = "????", DOI = "????", ISSN = "1169-1018", ISSN-L = "1169-1018", bibdate = "Sat Feb 16 19:08:50 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Translation from French by S. R. Hayford.", URL = "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753", acknowledgement = ack-nhfb, journal-URL = "http://www.jstor.org/journals/11691018.html", } @Article{Sandron:2002:PSE, author = "Fr{\'e}d{\'e}ric Sandron", title = "Les populations suivent-elles la loi des nombres anomaux? ({French}). [{Do} populations conform to the {Law of Anomalous Numbers}?]", journal = "Population ({French} edition)", volume = "57", number = "4--5", pages = "761--768", month = "????", year = "2002", CODEN = "POPUAQ", DOI = "????", ISSN = "0032-4663 (print), 1957-7966 (electronic)", ISSN-L = "0032-4663", bibdate = "Sat Feb 16 19:08:50 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873", acknowledgement = ack-nhfb, language = "French", } @TechReport{Seaman:2002:BLB, author = "R. S. Seaman", title = "{Benford}'s law and and background field errors in data assimilation", type = "Preprint", institution = "Bureau of Meteorology Research Centre", address = "Melbourne, Australia", month = "????", year = "2002", bibdate = "Sun Feb 17 14:01:22 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf", acknowledgement = ack-nhfb, } @Article{Seaman:2002:RBL, author = "R. S. Seaman", title = "The relevance of {Benford's Law} to background field errors in data assimilation", journal = "Australian Meteorological Magazine", volume = "51", number = "1", pages = "25--33", month = "????", year = "2002", CODEN = "AMMGAS", ISSN = "0004-9743", ISSN-L = "0004-9743", bibdate = "Mon Nov 14 16:08:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.bom.gov.au/amm/docs/2002/seaman.pdf; http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf", acknowledgement = ack-nhfb, ajournal = "Aust. Met. Mag.", ajournal-2 = "Aust. Meteorol. Mag.", fjournal = "Australian Meteorological Magazine", journal-URL = "http://www.bom.gov.au/amm/", } @Article{Taylor:2002:STD, author = "Rosemary N. Taylor and Damian J. McEntegart and Eleanor C. Stillman", title = "Statistical techniques to detect fraud and other data irregularities in clinical questionnaire data", journal = "Drug Information Journal", volume = "36", number = "1", pages = "115--125", month = jan, year = "2002", DOI = "https://doi.org/10.1177/009286150203600115", ISSN = "0092-8615", ISSN-L = "0092-8615", bibdate = "Mon Feb 18 06:42:24 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{VanCaneghem:2002:EMI, author = "T. {Van Caneghem}", title = "Earnings Management Induced by Cognitive Reference Points", journal = "The British Accounting Review", volume = "34", number = "2", pages = "167--178", year = "2002", DOI = "https://doi.org/10.1006/bare.2002.0190", ISSN = "0890-8389 (print), 1095-8347 (electronic)", ISSN-L = "0890-8389", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0890838902901903", abstract = "Previous studies (Carslaw, 1988; Thomas, 1989; Niskanen \& Keloharju, 2000) have shown that companies' managers tend to round-up the first digits of reported earnings (i.e. for companies reporting profits). According to Carslaw (1988), this type of behaviour is inspired by the existence of the so-called `\$1.99' phenomenon where a price of \$1.99 is perceived as being abnormally lower than one of \$2.00. In the current study, we try to determine whether managers of UK-listed companies also engage in this type of `earnings rounding-up behaviour'. Analogous to the earlier studies, our study compares observed and expected frequencies for the second-from-the-left digit in reported earnings. Our results suggest that managers of UK-listed companies tend to round-up reported pre-tax income, in a way that increases the first digit by one, when they are faced with a nine in the second-from-the-left position for this particular earnings measure. The major contribution of the current study is that it introduces discretionary accruals in this line of research. Discretionary accruals were estimated using both the Jones model (1991) and the modified Jones model as proposed by Dechow et al. (1995). Our results clearly suggest that discretionary accruals are used in order to round-up reported earnings figures. Moreover, discretionary accruals enabled us to increase the power of the tests used in previous studies.", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Wallace:2002:AQD, author = "W. A. Wallace", title = "Assessing the quality of data used for benchmarking and decision making", journal = "Journal of Government Financial Management", volume = "51", number = "3", pages = "16--22", month = "????", year = "2002", DOI = "", ISSN = "1533-1385", ISSN-L = "1533-1385", bibdate = "Thu Oct 13 09:17:04 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, journal-URL = "https://www.agacgfm.org/Resources/Journal-of-Government-Financial-Management/Archives.aspx", keywords = "Benford's Law", remark = "Online archive access, even for journal metadata, requires member account!", } @Article{Yeh:2002:SMZ, author = "Hsiaw-Chan Yeh", title = "Six multivariate {Zipf} distributions and their related properties", journal = j-STAT-PROB-LETT, volume = "56", number = "2", pages = "131--141", day = "15", month = jan, year = "2002", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/S0167-7152(01)00149-3", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "62H10", MRnumber = "1881166 (2002m:62084)", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715201001493", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Zipf's Law", } @Article{Abdel-All:2003:GPP, author = "N. H. Abdel-All and M. A. W. Mahmoud and H. N. Abd-Ellah", title = "Geometrical properties of {Pareto} distribution", journal = j-APPL-MATH-COMP, volume = "145", number = "2--3", pages = "321--339", day = "25", month = dec, year = "2003", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Jan 9 08:41:12 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Alvarez-Ramirez:2003:ZMS, author = "Jose Alvarez-Ramirez and Monica Meraz and Gustavo Gallegos", title = "{Zipf--Mandelbrot} scaling law for world track records", journal = j-PHYSICA-A, volume = "328", number = "3--4", pages = "545--560", day = "15", month = oct, year = "2003", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(03)00579-X", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S037843710300579X", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Book{Anastasi:2003:NFI, author = "Joe Anastasi", title = "The new forensics: investigating corporate fraud and the theft of intellectual property", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xiv + 270", year = "2003", ISBN = "0-471-26994-8 (hardcover)", ISBN-13 = "978-0-471-26994-6 (hardcover)", LCCN = "HV8079.W47 A5 2003", bibdate = "Tue Nov 22 11:42:36 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/wiley044/2003001697.html; http://www.loc.gov/catdir/description/wiley037/2003001697.html; http://www.loc.gov/catdir/toc/wiley031/2003001697.html", acknowledgement = ack-nhfb, remark = "Brief mention of Benford's Law on pp. 184--185.", subject = "white collar crime investigation; data processing; case studies; fraud investigation; forensic accounting; computer security", } @Article{Ausloos:2003:SIZ, author = "M. Ausloos and Ph. Bronlet", title = "Strategy for investments from {Zipf} law(s)", journal = j-PHYSICA-A, volume = "324", number = "1--2", pages = "30--37", day = "1", month = jun, year = "2003", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(02)01845-9", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B82", MRnumber = "2030919", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "International Econophysics Conference IEC2002 (Bali)", URL = "http://www.sciencedirect.com/science/article/pii/S0378437102018459", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Book{Baldi:2003:MIW, author = "Pierre Baldi and Paolo Frasconi and Padhraic Smyth", title = "Modeling the {Internet} and the {Web}: probabilistic methods and algorithms", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xix + 285", year = "2003", ISBN = "0-470-86492-3 (e-book), 0-470-84906-1", ISBN-13 = "978-0-470-86492-0 (e-book), 978-0-470-84906-4", LCCN = "TK5105.875.I57 B35 2003eb", bibdate = "Fri Jun 3 10:03:23 MDT 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/pagerank.bib", acknowledgement = ack-nhfb, subject = "Internet; Mathematical models; Telecommunication; Traffic; World Wide Web; Cyberspace; Probabilities; Computers; Web; General; Networking; Intranets and Extranets", tableofcontents = "Mathematical Background \\ Probability and Learning from a Bayesian Perspective \\ Parameter Estimation from Data \\ Basic principles \\ A simple die example \\ Mixture Models and the Expectation Maximization Algorithm \\ Graphical Models \\ Bayesian networks \\ Belief propagation \\ Learning directed graphical models from data \\ Classification \\ Clustering \\ Power-Law Distributions \\ Scale-free properties (80/20 rule) \\ Applications to Languages: Zipf's and Heaps' Laws \\ Origin of power-law distributions and Fermi's model \\ Basic WWW Technologies \\ Web Documents \\ SGML and HTML \\ General structure of an HTML document \\ Links \\ Resource Identifiers: URI, URL, and URN \\ Protocols \\ Reference models and TCP/IP \\ The domain name system \\ The Hypertext Transfer Protocol \\ Programming examples \\ Log Files \\ Search Engines \\ Coverage \\ Basic crawling \\ Web Graphs \\ Internet and Web Graphs \\ Power-law size \\ Power-law connectivity \\ Small-world networks \\ Power law of PageRank \\ The bow-tie structure \\ Generative Models for the Web Graph and Other Networks \\ Web page growth \\ Lattice perturbation models: between order and disorder \\ Preferential attachment models, or the rich get richer \\ Copy models \\ PageRank models \\ Applications \\ Distributed search algorithms \\ Subgraph patterns and communities \\ Robustness and vulnerability \\ Notes and Additional Technical References \\ Text Analysis \\ Indexing \\ Compression techniques \\ Lexical Processing \\ Tokenization", } @TechReport{Berger:2003:BLP, author = "Arno Berger", title = "{Benford}'s law in power-like nonautonomous dynamical systems", type = "Preprint", institution = "Vienna University of Technology", address = "Vienna, Austria", year = "2003", bibdate = "Sat Feb 16 17:18:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Canessa:2003:TAFa, author = "Enrique Canessa", title = "Theory of Analogous Force on Number Sets", journal = "ArXiv e-prints", year = "2003", bibdate = "Mon Nov 21 06:56:01 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/cond-mat/0307703", abstract = "A general statistical thermodynamic theory that considers given sequences of $x$-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions $ p_x $ for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering $ p_x $ to describe complex phenomena, the theory leads to derive a distinct analogous force $ f_x $ on number sets proportional to $ (\frac {\partial p_x}{\partial x})_T $ at an analogous system temperature $T$. In particular, this yields to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.", acknowledgement = ack-nhfb, remark = "To appear in Phys. A.", } @Article{Canessa:2003:TAFb, author = "Enrique Canessa", title = "Theory of analogous force on number sets", journal = j-PHYSICA-A, volume = "328", number = "1--2", pages = "44--52", month = oct, year = "2003", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(03)00526-0", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103005260", abstract = "A general statistical thermodynamic theory that considers given sequences of $x$-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions $ p_x $ for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering $ p_x $ to describe complex phenomena, the theory leads to derive a distinct analogous force $ f_x $ on number sets proportional to $ (\partial p_x / \partial x)T $ at an analogous system temperature $T$. In particular, this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Fibonacci numbers; Number theory; prime numbers; Probability theory; Statistical physics and thermodynamics", } @Article{Das:2003:RRE, author = "Somnath Das and Huai Zhang", title = "Rounding-up in reported {EPS}, behavioral thresholds, and earnings management", journal = "Journal of Accounting and Economics", volume = "35", number = "1", pages = "31--50", year = "2003", DOI = "https://doi.org/10.1016/S0165-4101(02)00096-4", ISSN = "0165-4101 (print), 1879-1980 (electronic)", ISSN-L = "0165-4101", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165410102000964", abstract = "Reported earnings per share (EPS) are frequently rounded to the nearest cent. This paper provides evidence that firms manipulate earnings so that they can round-up and report one more cent of EPS. Specifically, we examine the digit immediately right of the decimal in the calculated {EPS} number expressed in cents. Evidence is presented that firms are more likely to round-up when managers ex ante expect rounding-up to meet analysts forecasts, report positive profits, or sustain recent performance. Further investigation provides evidence that working capital accruals are used to round-up EPS.", acknowledgement = ack-nhfb, keywords = "Behavioral threshold; Benford's Law; Earnings management; Earnings per share (EPS); Rounding", } @Article{Engel:2003:BLE, author = "Hans-Andreas Engel and Christoph Leuenberger", title = "{Benford}'s law for exponential random variables", journal = j-STAT-PROB-LETT, volume = "63", number = "4", pages = "361--365", day = "15", month = jul, year = "2003", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/S0167-7152(03)00101-9", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "60E99 (60C05)", MRnumber = "1996184 (2004d:60050)", MRreviewer = "Ulrich M. Hirth", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715203001019", abstract = "Benford's law assigns the probability $ \log_{10}(1 + 1 / d) $ for finding a number starting with specific significant digit $d$. We show that exponentially distributed numbers obey this law approximatively, i.e., within bounds of $ 0.03$.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law; Exponential distribution; Significant digit law", } @Article{FerreriCancho:2003:LEO, author = "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}", title = "Least effort and the origins of scaling in human language", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "100", number = "3", pages = "788--791", day = "4", month = feb, year = "2003", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.0335980100", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Tue Nov 15 09:44:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/search", keywords = "Zipf's Law", onlinedate = "January 22, 2003", } @Book{Fleiss:2003:SMR, author = "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho Paik", title = "Statistical Methods for Rates and Proportions", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Third", pages = "xxvii + 760", year = "2003", ISBN = "0-471-52629-0 (hardcover)", ISBN-13 = "978-0-471-52629-2 (hardcover)", LCCN = "QA279 .F58 2003", bibdate = "Fri Mar 22 08:46:57 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley series in probability and statistics", URL = "http://www.loc.gov/catdir/bios/wiley042/2002191005.html; http://www.loc.gov/catdir/description/wiley034/2002191005.html; http://www.loc.gov/catdir/toc/wiley031/2002191005.html", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Analysis of variance; Sampling (Statistics); Biometry", tableofcontents = "Preface \\ Preface to the Second Edition \\ Preface to the First Edition \\ 1. An Introduction to Applied Probability \\ 2. Statistical Inference for a Single Proportion \\ 3. Assessing Significance in a Fourfold Table \\ 4. Determining Sample Sizes Needed to Detect a Difference Between Two Proportions \\ 5. How to Randomize \\ \\ 6. Comparative Studies: Cross-Sectional, Naturalistic, or Multinomial Sampling \\ \\ 7. Comparative Studies: Prospective and Retrospective Sampling \\ 8. Randomized Controlled Trials \\ 9. The Comparison of Proportions from Several Independent Samples \\ 10. Combining Evidence from Fourfold Tables \\ 11. Logistic Regression \\ 12. Poisson Regression \\ 13. Analysis of Data from Matched Samples \\ 14. Regression Models for Matched Samples \\ 15. Analysis of Correlated Binary Data \\ 16. Missing Data \\ 17. Misclassification Errors: Effects, Control, and Adjustment \\ 18. The Measurement of Interrater Agreement \\ 19. The Standardization of Rates \\ Appendix A. Numerical Tables \\ Appendix B. The Basic Theory of Maximum Likelihood", } @Article{Furusawa:2003:ZLG, author = "Chikara Furusawa and Kunihiko Kaneko", title = "{Zipf's Law} in Gene Expression", journal = j-PHYS-REV-LET, volume = "90", number = "??", pages = "088102", day = "26", month = feb, year = "2003", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.90.088102", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", } @Article{Gabaix:2003:TPL, author = "Xavier Gabaix and Parameswaran Gopikrishnan and Vasiliki Plerou and H. Eugene Stanley", title = "A theory of power-law distributions in financial market fluctuations", journal = j-NATURE, volume = "423", number = "6937", pages = "267--270", day = "15", month = may, year = "2003", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/nature01624", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Wed Feb 27 06:45:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Zipf's Law", } @InProceedings{Grekos:2003:RSC, author = "G. Grekos and R. Giuliano-Antonini", editor = "????", booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July 6--12, 2003}", title = "Regular sets and conditional density: an extension of {Benford}'s law", publisher = "????", address = "????", pages = "??--??", year = "2003", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:43:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hassan:2003:EDA, author = "Bassam Hassan", title = "Examining data accuracy and authenticity with leading digit frequency analysis", journal = "Industrial Management + Data Systems", volume = "103", number = "2", pages = "121--125", month = "????", year = "2003", CODEN = "MDSD8F", ISSN = "0263-5577 (print), 1758-5783 (electronic)", ISSN-L = "0263-5577", bibdate = "Fri Nov 25 11:07:59 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Havil:2003:GEE, author = "Julian Havil", title = "{Gamma}: Exploring {Euler}'s Constant", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xxiii + 266", year = "2003", ISBN = "0-691-09983-9", ISBN-13 = "978-0-691-09983-5", LCCN = "QA41 .H23 2003", bibdate = "Thu Sep 25 16:52:46 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", price = "US\$29.95", URL = "http://www.loc.gov/catdir/description/prin031/2002192453.html", abstract = "Among the myriad of constants that appear in mathematics, $ \pi $, $e$, and $i$ are the most familiar. Following closely behind is $ \gamma $ or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707--1783), who figures prominently in this book, gamma is defined as the limit of the sum of $ 1 + 1 / 2 + 1 / 3 + \cdots + 1 / n - \ln n$, the numerical value being $ 0.5772156 \ldots {}$. But unlike its more celebrated colleagues $ \pi $ and $e$, the exact nature of gamma remains a mystery --- we don't even know if it can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today, the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.", acknowledgement = ack-nhfb, tableofcontents = "Foreword / xv \\ Acknowledgements / xvii \\ Introduction / xix \\ Chapter One: The Logarithmic Cradle / 1 \\ 1.1 A Mathematical Nightmare- and an Awakening / 1 \\ 1.2 The Baron's Wonderful Canon / 4 \\ 1.3 A Touch of Kepler / 11 \\ 1.4 A Touch of Euler / 13 \\ 1.5 Napier's Other Ideas / 16 \\ Chapter Two: The Harmonic Series / 21 \\ 2.1 The Principle / 21 \\ 2.2 Generating Function for $H_n$ / 21 \\ 2.3 Three Surprising Results / 22 \\ Chapter Three: Sub-Harmonic Series / 27 \\ 3.1 A Gentle Start / 27 \\ 3.2 Harmonic Series of Primes / 28 \\ 3.3 The Kempner Series / 31 \\ 3.4 Madelung's Constants / 33 \\ Chapter Four: Zeta Functions / 37 \\ 4.1 Where $n$ Is a Positive Integer / 37 \\ 4.2 Where $x$ Is a Real Number / 42 \\ 4.3 Two Results to End With / 44 \\ Chapter Five: Gamma's Birthplace / 47 \\ 5.1 Advent / 47 \\ 5.2 Birth / 49 \\ Chapter Six: The Gamma Function / 53 \\ 6.1 Exotic Definitions / 53 \\ 6.2 Yet Reasonable Definitions / 56 \\ 6.3 Gamma Meets Gamma / 57 \\ 6.4 Complement and Beauty / 58 \\ Chapter Seven: Euler's Wonderful Identity / 61 \\ 7.1 The All-Important Formula / 61 \\ 7.2 And a Hint of Its Usefulness / 62 \\ Chapter Eight: A Promise Fulfilled / 65 \\ Chapter Nine: What Is Gamma Exactly? / 69 \\ 9.1 Gamma Exists / 69 \\ 9.2 Gamma Is What Number? 739.3 A Surprisingly Good Improvement / 75 \\ 9.4 The Germ of a Great Idea / 78 \\ Chapter Ten: Gamma as a Decimal / 81 \\ 10.1 Bernoulli Numbers / 81 \\ 10.2 Euler--Maclaurin Summation / 85 \\ 10.3 Two Examples / 86 \\ 10.4 The Implications for Gamma / 88 \\ Chapter Eleven: Gamma as a Fraction / 91 \\ 11.1 A Mystery / 91 \\ 11.2 A Challenge / 91 \\ 11.3 An Answer / 93 \\ 11.4 Three Results / 95 \\ 11.5 Irrationals / 95 \\ 11.6 Pell's Equation Solved / 97 \\ 11.7 Filling the Gaps / 98 \\ 11.8 The Harmonic Alternative / 98 \\ Chapter Twelve: Where Is Gamma? / 101 \\ 12.1 The Alternating Harmonic Series Revisited / 101 \\ 12.2 In Analysis / 105 \\ 12.3 In Number Theory / 112 \\ 12.4 In Conjecture / 116 \\ 12.5 In Generalization / 116 \\ Chapter Thirteen: It's a Harmonic World / 119 \\ 13.1 Ways of Means / 119 \\ 13.2 Geometric Harmony / 121 \\ 13.3 Musical Harmony / 123 \\ 13.4 Setting Records / 125 \\ 13.5 Testing to Destruction / 126 \\ 13.6 Crossing the Desert / 127 \\ 13.7 Shuffiing Cards / 127 \\ 13.8 Quicksort / 128 \\ 13.9 Collecting a Complete Set / 130 \\ 13.10 A Putnam Prize Question / 131 \\ 13.11 Maximum Possible Overhang / 132 \\ 13.12 Worm on a Band / 133 \\ 13.13 Optimal Choice / 134 \\ Chapter Fourteen: It's a Logarithmic World / 139 \\ 14.1 A Measure of Uncertainty / 139 \\ 14.2 Benford's Law / 145 \\ 14.3 Continued-Fraction Behaviour / 155 \\ Chapter Fifteen: Problems with Primes / 163 \\ 15.1 Some Hard Questions about Primes / 163 \\ 15.2 A Modest Start / 164 \\ 15.3 A Sort of Answer / 167 \\ 15.4 Picture the Problem / 169 \\ 15.5 The Sieve of Eratosthenes / 171 \\ 15.6 Heuristics / 172 \\ 15.7 A Letter / 174 \\ 15.8 The Harmonic Approximation / 179 \\ 15.9 Different-and Yet the Same / 180 \\ 15.10 There are Really Two Questions, Not Three / 182 \\ 15.11 Enter Chebychev with Some Good Ideas / 183 \\ 15.12 Enter Riemann, Followed by Proof(s) / 186 \\ Chapter Sixteen: The Riemann Initiative / 189 \\ 16.1 Counting Primes the Riemann Way / 189 \\ 16.2 A New Mathematical Tool / 191 \\ 16.3 Analytic Continuation / 191 \\ 16.4 Riemann's Extension of the Zeta Function / 193 \\ 16.5 Zeta's Functional Equation / 193 \\ 16.6 The Zeros of Zeta / 193 \\ 16.7 The Evaluation of $\Pi(x)$ and $\pi(x)$ / 196 \\ 16.8 Misleading Evidence / 197 \\ 16.9 The Von Mangoldt Explicit Formula --- and How It Is Used to Prove the Prime Number Theorem / 200 \\ 16.10 The Riemann Hypothesis / 202 \\ 16.11 Why Is the Riemann Hypothesis Important? / 204 \\ 16.12 Real Alternatives / 206 \\ 16.13 A Back Route to Immortality-Partly Closed / 207 \\ 16.14 Incentives, Old and New / 210 \\ 16.15 Progress / 213 \\ Appendix A: The Greek Alphabet / 217 \\ Appendix B: Big Oh Notation / 219 \\ Appendix C: Taylor Expansions / 221 \\ C.1 Degree 1 / 221 \\ C.2 Degree 2 / 221 \\ C.3 Examples / 223 \\ C.4 Convergence / 223 \\ Appendix D: Complex Function Theory / 225 \\ D.1 Complex Differentiation / 225 \\ D.2 Weierstrass Function / 230 \\ D.3 Complex Logarithms / 231 \\ D.4 Complex Integration / 232 \\ D.5 A Useful Inequality / 235 \\ D.6 The Indefinite Integral / 235 \\ D.7 The Seminal Result / 237 \\ D.8 An Astonishing Consequence / 238 \\ D.9 Taylor Expansions-and an Important Consequence / 239 \\ D.10 Laurent Expansions --- and Another Important Consequence / 242 \\ D.11 The Calculus of Residues / 245 \\ D.12 Analytic Continuation / 247 \\ Appendix E: Application to the Zeta Function / 249 \\ E.1 Zeta Analytically Continued / 249 \\ E.2 Zeta's Functional Relationship / 253", } @Article{Hurlimann:2003:GBL, author = "Werner H{\"u}rlimann", title = "A generalized {Benford} law and its application", journal = j-ADV-APPL-STAT, volume = "3", number = "3", pages = "217--228", year = "2003", CODEN = "????", ISSN = "0972-3617", ISSN-L = "0972-3617", MRclass = "11K31 (11B73)", MRnumber = "2034405 (2004k:11125)", MRreviewer = "Vydas {\v{C}}ekanavi{\v{c}}ius", bibdate = "Wed Aug 16 07:36:50 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Advances and Applications in Statistics", journal-URL = "http://www.pphmj.com/journals/contents/adas.htm", } @Article{Ioannides:2003:ZLC, author = "Yannis M. Ioannides and Henry G. Overman", title = "{Zipf}'s law for cities: an empirical examination", journal = j-REG-SCI-URBAN-ECON, volume = "33", number = "2", pages = "127--137", day = "1", month = mar, year = "2003", CODEN = "RSUEDM", DOI = "https://doi.org/10.1016/S0166-0462(02)00006-6", ISSN = "0166-0462 (print), 1879-2308 (electronic)", ISSN-L = "0166-0462", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0166046202000066", acknowledgement = ack-nhfb, fjournal = "Regional Science and Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/01660462", keywords = "Zipf's Law", } @Article{Kreiner:2003:NBL, author = "W. A. Kreiner", title = "On the {Newcomb--Benford} law", journal = j-Z-NATURFORSCH, volume = "58a", number = "11", pages = "618--622", month = "????", year = "2003", CODEN = "ZNTFA2", ISSN = "0372-9516", ISSN-L = "0372-9516", bibdate = "Sat Feb 16 18:19:41 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf", acknowledgement = ack-nhfb, fjournal = "{Zeitschrift f{\"u}r Naturforschung}", journal-URL = "http://www.degruyter.com/view/j/zna", } @InCollection{Kumar:2003:BLA, author = "Kuldeep Kumar and Sukanto Bhattacharya", editor = "Cheng-Few Lee", booktitle = "Advances in Financial Planning and Forecasting", title = "{Benford}'s law and its application in financial fraud detection", volume = "11", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, bookpages = "ix + 177", pages = "57--70", year = "2003", ISBN = "0-7623-1016-2", ISBN-13 = "978-0-7623-1016-6", ISSN = "1046-5847", LCCN = "????", bibdate = "Wed Nov 23 16:45:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Lagarias:2003:PAB, author = "Jeffrey C. Lagarias", title = "The $ 3 x + 1 $ problem: An annotated bibliography (1963--1999) (sorted by author)", journal = "arxiv.org", volume = "??", number = "??", month = sep, year = "2003", bibdate = "Sat Sep 10 12:58:10 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math/0309224", abstract = "The $ 3 x + 1 $ problem concerns iteration of the map on the integers given by $ T(n) = (3 n + 1) / 2 $ if $n$ is odd; $ T(n) = n / 2$ if $n$ is even. The $ 3 x + 1$ Conjecture asserts that for every positive integer $ n > 1$ the forward orbit of $n$ under iteration by $T$ includes the integer 1. This paper is an annotated bibliography of work done on the $ 3 x + 1$ problem and related problems from 1963 through 1999. At present the $ 3 x + 1$ Conjecture remains unsolved.", acknowledgement = ack-nhfb, pagecount = "74", remark = "At least 13 updates have been made up to 11-Jan-2011.", } @Article{Lanza:2003:FSP, author = "Richard B. Lanza", title = "Fear Not the Software: Proactively Detecting Occupational Fraud Using Computer Audit Reports", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = sep # "\slash " # feb, year = "2003", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:14:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967868", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @InProceedings{Manaris:2003:EMZ, author = "Bill Manaris and Dallas Vaughan and Christopher Wagner and Juan Romero and Robert B. Davis", title = "Evolutionary Music and the {Zipf--Mandelbrot Law}: Developing Fitness Functions for Pleasant Music", crossref = "Raidl:2003:AEC", pages = "522--534", year = "2003", bibdate = "Mon Feb 18 10:49:54 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{McAllister:2003:ARE, author = "James W. McAllister", title = "Algorithmic randomness in empirical data", journal = j-STUD-HIST-PHILOS-SCI, volume = "34", number = "3", pages = "633--646", month = sep, year = "2003", CODEN = "SHPSB5", DOI = "https://doi.org/10.1016/S0039-3681(03)00047-5", ISSN = "0039-3681 (print), 1879-2510 (electronic)", ISSN-L = "0039-3681", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/shps-a.bib; http://www.sciencedirect.com/science/journal/00393681", note = "See replies \cite{Twardy:2005:EDS,McAllister:2005:ACE}.", URL = "http://www.sciencedirect.com/science/article/pii/S0039368103000475", abstract = "According to a traditional view, scientific laws and theories constitute algorithmic compressions of empirical data sets collected from observations and measurements. This article defends the thesis that, to the contrary, empirical data sets are algorithmically incompressible. The reason is that individual data points are determined partly by perturbations, or causal factors that cannot be reduced to any pattern. If empirical data sets are incompressible, then they exhibit maximal algorithmic complexity, maximal entropy and zero redundancy. They are therefore maximally efficient carriers of information about the world. Since, on algorithmic information theory, a string is algorithmically random just if it is incompressible, the thesis entails that empirical data sets consist of algorithmically random strings of digits. Rather than constituting compressions of empirical data, scientific laws and theories pick out patterns that data sets exhibit with a certain noise.", acknowledgement = ack-nhfb, fjournal = "Studies in History and Philosophy of Science Part {A}", journal-URL = "http://www.sciencedirect.com/science/journal/00393681", keywords = "Algorithmic randomness; Benford's Law; Compression; Empirical data; Information; Law; Pattern", } @Article{Mitzenmacher:2003:BHG, author = "Michael Mitzenmacher", title = "A Brief History of Generative Models for Power Law and Lognormal Distributions", journal = j-INTERNET-MATH, volume = "1", number = "2", pages = "226--251", month = dec, year = "2003", CODEN = "????", DOI = "https://doi.org/10.1080/15427951.2004.10129088", ISSN = "1542-7951 (print), 1944-9488 (electronic)", ISSN-L = "1542-7951", bibdate = "Thu Nov 24 13:38:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.im/1089229510; http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf; http://www.tandfonline.com/toc/uinm20/1/2", acknowledgement = ack-nhfb, ajournal = "Internet Math.", fjournal = "Internet Mathematics", journal-URL = "http://projecteuclid.org/info/euclid.im", keywords = "Fibonacci sequence; lognormal distribution; monkeys typing randomly; Pareto distribution; power-law distribution; Yule distribution; Zipf's Law", remark = "This is a survey article with a six-page bibliography of earlier work, and a clear description of the differences between lognormal and power-law distributions, which otherwise look similar on log-log plots. Lognormal distributions have finite means and moments, while power-law distributions may have infinite means and/or moments, depending on the exponent. The preprint at author's Web site (last URL) contains additional material on the acrimonious debate between Beno{\^\i}t Mandelbrot and Herbert A. Simon (see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and other references in Mitzenmacher's paper) on the derivation and modeling of Zipf's Law distributions.", } @PhdThesis{Muller:2003:AZP, author = "Mathias M{\"u}ller", title = "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}. ({German}) [Applications of the digit analysis in the audit practice with a focus on {Benford's Law}]", type = "{Diplomarbeit}", school = "Wirtschaftsuniversit{\"a}t Wien", address = "Wien, Austria", pages = "v + 75", month = "????", year = "2003", bibdate = "Sat Feb 16 18:44:50 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://permalink.obvsg.at/wuw/AC03895842", acknowledgement = ack-nhfb, language = "German", } @Article{Naldi:2003:CIZ, author = "M. Naldi", title = "Concentration indices and {Zipf}'s law", journal = j-ECONOM-LETT, volume = "78", number = "3", pages = "329--334", month = mar, year = "2003", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/S0165-1765(02)00251-3", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "91B82", MRnumber = "1959355", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176502002513", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Newby:2003:OSS, author = "Gregory B. Newby and Jane Greenberg and Paul Jones", title = "Open source software development and {Lotka's Law}: {Bibliometric} patterns in programming", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "54", number = "2", pages = "169--178", day = "15", month = jan, year = "2003", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.10177", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:09 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", note = "See comments \cite{Burrell:2004:LEF}.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "10 Dec 2002", } @Article{Nguyen:2003:DPL, author = "H. T. Nguyen and V. Kreinovich and L. Longpre", title = "Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals", journal = j-IEEE-TRANS-FUZZY-SYSTEMS, volume = "1", pages = "67--73", year = "2003", CODEN = "IEFSEV", DOI = "https://doi.org/10.1109/FUZZ.2003.1209339", ISSN = "1063-6706 (print), 1941-0034 (electronic)", ISSN-L = "1063-6706", bibdate = "Sat Feb 16 18:51:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The 12th IEE International Conference on Fuzzy Systems. FUZZ'03", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Fuzzy Systems", xxnote = "Is this the listed journal, or a conference paper??", } @Article{Peter:2003:ADE, author = "Manfred Peter", title = "The asymptotic distribution of elements in automatic sequences", journal = j-THEOR-COMP-SCI, volume = "301", number = "1 3", pages = "285--312", year = "2003", CODEN = "TCSCDI", DOI = "https://doi.org/10.1016/S0304-3975(02)00587-X", ISSN = "0304-3975 (print), 1879-2294 (electronic)", ISSN-L = "0304-3975", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S030439750200587X", abstract = "In an automatic sequence an element need not have an asymptotic density. In this paper a necessary and sufficient criterion is proved for the existence of the asymptotic density of a given element. If it does not exist the asymptotic distribution of the element can be described in terms of a function H whose graph is self-similar. An algorithm is given to decide whether H is piecewise continuously differentiable, and in this case it can be computed effectively. Finally, it is shown that the H -density of an element in an automatic sequence always exists and equals its logarithmic density.", acknowledgement = ack-nhfb, fjournal = "Theoretical Computer Science", journal-URL = "http://www.sciencedirect.com/science/journal/03043975", keywords = "Asymptotics; Automata; Benford's Law; Density; H{\"o}lder mean; Oscillating sum; Self-similarity", } @Article{Quick:2003:BLD, author = "Reiner Quick and Matthias Wolz", title = "{Benford's Law in deutschen Rechnungslegungsdaten}. ({German}) [{Benford's Law} in {German} accounting data]", journal = "Betriebswirtschaftliche Forschung und Praxis", volume = "55", number = "2", pages = "208--224", month = "????", year = "2003", CODEN = "????", ISSN = "0340-5370", ISSN-L = "0340-5370", bibdate = "Sat Dec 10 12:01:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", remark = "Betriebswirtschaftliche Forschung und Praxis == Business Research and Practice.", } @Article{Reed:2003:PLI, author = "William J. Reed", title = "The {Pareto} law of incomes---an explanation and an extension", journal = j-PHYSICA-A, volume = "319", number = "1--4", pages = "469--486", year = "2003", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/S0378-4371(02)01507-8", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B70", MRnumber = "1965596", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Rose:2003:TEF, author = "Anna M. Rose and Jacob M. Rose", title = "Turn {Excel} into a financial sleuth: an easy-to-use digital analysis tool can red-flag irregularities", journal = j-J-ACCOUNTANCY, volume = "196", number = "2", pages = "58--??", month = aug, year = "2003", CODEN = "JACYAD", ISSN = "0021-8448 (print), 1945-0729 (electronic)", ISSN-L = "0021-8448", bibdate = "Sat Feb 16 19:07:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth", acknowledgement = ack-nhfb, fjournal = "Journal of Accountancy", journal-URL = "http://www.journalofaccountancy.com/", } @Article{Sinai:2003:SP, author = "Ya. G. Sinai", title = "Statistical $ (3 x + 1) $ problem", journal = j-COMM-PURE-APPL-MATH, volume = "56", number = "7", pages = "1016--1028", month = jul, year = "2003", CODEN = "CPAMAT, CPMAMV", DOI = "https://doi.org/10.1002/cpa.10084", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", bibdate = "Mon Nov 21 07:52:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Dedicated to the memory of J{\"u}rgen K. Moser.", acknowledgement = ack-nhfb, fjournal = "Communications on Pure and Applied Mathematics (New York)", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", } @InProceedings{Swanson:2003:DPF, author = "David Swanson and Moon Jung Cho and John Eltinge", editor = "????", booktitle = "Proceedings of the Survey Research Section", title = "Detecting possibly fraudulent or error-prone survey data using {Benford's Law}", publisher = "American Statistical Association", address = "Washington, DC, USA", pages = "4172--4177", year = "2003", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Wed Nov 16 10:21:39 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.", acknowledgement = ack-nhfb, } @Article{Wales:2003:IWI, author = "Elspeth Wales", title = "Is it Worth Investing in Software to Combat Fraud?", journal = "Computer Fraud \& Security", volume = "2003", number = "5", pages = "6--8", year = "2003", DOI = "https://doi.org/10.1016/S1361-3723(03)05009-7", ISSN = "1361-3723 (print), 1873-7056 (electronic)", ISSN-L = "1361-3723", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1361372303050097", abstract = "Despite the tendency for businesses to keep fraud to themselves, the consensus is that the problem is becoming worse. On the plus side though software solutions that can detect potential fraudulent activity are evolving in their scope and ability to automatically track transactions in real-time.", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InCollection{Warren:2003:DLD, author = "Henry S. Warren", title = "The distribution of leading digits", crossref = "Warren:2003:HD", chapter = "15.3", pages = "264--267", year = "2003", bibdate = "Fri Mar 16 08:02:56 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, } @Article{Wu:2003:IPD, author = "Shuo-Jye Wu and Chun-Tao Chang", title = "Inference in the {Pareto} distribution based on progressive {Type II} censoring with random removals", journal = j-J-APPL-STAT, volume = "30", number = "2", pages = "163--172", month = "????", year = "2003", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Tue Dec 16 15:40:48 MST 2003", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Wu:2003:PDC, author = "Wei Biao Wu and Chinya V. Ravishankar", title = "The performance of difference coding for sets and relational tables", journal = j-J-ACM, volume = "50", number = "5", pages = "665--693", month = sep, year = "2003", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/876638.876641", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Mon Sep 8 17:55:23 MDT 2003", bibsource = "http://portal.acm.org/; http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "We characterize the performance of difference coding for compressing sets and database relations through an analysis of the problem of estimating the number of bits needed for storing the spacings between values in sets of integers. We provide analytical expressions for estimating the effectiveness of difference coding when the elements of the sets or the attribute fields in database tuples are drawn from the uniform and Zipf distributions. We also examine the case where a uniformly distributed domain is combined with a Zipf distribution, and with an arbitrary distribution. We present limit theorems for most cases, and probabilistic convergence results in other cases. We also examine the effects of attribute domain reordering on the compression ratio. Our simulations show excellent agreement with theory.", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Computing Machinery", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Aoyama:2004:KDP, author = "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma", title = "Kinematics and dynamics of {Pareto--Zipf}'s law and {Gibrat}'s law", journal = j-PHYSICA-A, volume = "344", number = "1--2", pages = "117--121", day = "1", month = dec, year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2004.06.099", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009185", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @TechReport{Berger:2004:DDU, author = "A. Berger", title = "Dynamics and digits: on the ubiquity of {Benford's Law}", type = "Preprint", institution = "Institute of Mechanics, Vienna University of Technology", address = "Vienna, Austria", pages = "3", day = "19", month = nov, year = "2004", bibdate = "Sat Feb 16 17:20:58 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf", acknowledgement = ack-nhfb, } @Article{Burrell:2004:LEF, author = "Quentin L. Burrell", title = "Letters to the {Editor}: Fitting {Lotka's Law}: {Some} cautionary observations on a recent paper by {Newby} et al. (2003)", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "55", number = "13", pages = "1209--1210", month = nov, year = "2004", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20086", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:16 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", note = "See \cite{Newby:2003:OSS}.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "17 Aug 2004", } @Article{Challet:2004:BPD, author = "Damien Challet and Andrea Lombardoni", title = "Bug propagation and debugging in asymmetric software structures", journal = j-PHYS-REV-E, volume = "70", number = "4", pages = "046109", month = oct, year = "2004", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.70.046109", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Thu Feb 28 08:15:07 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.046109; http://pre.aps.org/abstract/PRE/v70/i4/e046109", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", issue = "4", journal-URL = "http://pre.aps.org/browse", keywords = "Linux; Unix; Zipf's Law", pagecount = "5", } @Article{Chen:2004:MFM, author = "Yanguang Chen and Yixing Zhou", title = "Multi-fractal measures of city-size distributions based on the three-parameter {Zipf} model", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "22", number = "4", pages = "793--805", day = "1", month = nov, year = "2004", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2004.02.059", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0960077904001031", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", keywords = "Zipf's Law", } @Article{Cong:2004:WTP, author = "Lin Cong and Zhipeng Li", title = "On {Wilson}'s theorem and {Polignac} conjecture", journal = "ArXiv e-prints", day = "2", month = aug, year = "2004", bibdate = "Mon Feb 18 07:03:53 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math.NT/0408018", abstract = "We introduce Wilson's theorem and Clement's result and present a necessary and sufficient condition for $p$ and $ p + 2 k $ to be primes where $k$ is a positive integer. By using Simiov's Theorem, we derive an improved version of Clement's result and characterizations of Polignac twin primes which parallel previous characterizations.", acknowledgement = ack-nhfb, } @TechReport{Diekmann:2004:DEE, author = "Andreas Diekmann", title = "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit der Benford Verteilung}. ({German}) [{Data} falsification. {Results} from experiments with the {Benford} distribution]", type = "Report", institution = "ETH Z{\"u}rich", address = "Z{\"u}rich, Switzerland", year = "2004", bibdate = "Fri Nov 18 12:09:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @TechReport{Diekmann:2004:FDU, author = "Andreas Diekmann", title = "Not the First Digit! {Using} {Benford's Law} to Detect Fraudulent Scientific Data", type = "Report", institution = "ETH Z{\"u}rich", address = "Z{\"u}rich, Switzerland", pages = "26", month = oct, year = "2004", bibdate = "Sat Dec 10 11:12:29 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf", abstract = "Digits in statistical data produced by natural or social processes are often distributed in a manner described by ``Benford's law''. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that real data follow the Benford distribution while fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking digit frequencies in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). These experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, the digits of the published regression coefficients were approximately Benford distributed. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first and more on the second and higher-digits", acknowledgement = ack-nhfb, } @Article{Durtschi:2004:EUB, author = "C. Durtschi and W. Hillison and C. Pacini", title = "The Effective Use of {Benford's Law} to Assist in Detecting Fraud in Accounting Data", journal = j-J-FORENSIC-ACCOUNT, volume = "5", number = "1", pages = "17--34", month = "????", year = "2004", CODEN = "????", ISSN = "1524-5586", bibdate = "Sun Nov 13 11:35:18 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Forensic Accounting", } @Article{Fontanari:2004:SNM, author = "J. F. Fontanari and L. I. Perlovsky", title = "Solvable null model for the distribution of word frequencies", journal = j-PHYS-REV-E, volume = "70", number = "??", pages = "042901", day = "25", month = oct, year = "2004", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.70.042901", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.70.042901", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Fujiwara:2004:DPZ, author = "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki Aoyama and Mauro Gallegati and Wataru Souma", title = "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An} analysis with {European} firms", journal = j-PHYSICA-A, volume = "335", number = "1--2", pages = "197--216", day = "1", month = apr, year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2003.12.015", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011294", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Fujiwara:2004:GPZ, author = "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di Guilmi} and Wataru Souma and Mauro Gallegati", title = "{Gibrat} and {Pareto--Zipf} revisited with {European} firms", journal = j-PHYSICA-A, volume = "344", number = "1--2", pages = "112--116", day = "1", month = dec, year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2004.06.098", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104009173", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Fujiwara:2004:ZLF, author = "Yoshi Fujiwara", title = "{Zipf} law in firms bankruptcy", journal = j-PHYSICA-A, volume = "337", number = "1--2", pages = "219--230", day = "1", month = jun, year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2004.01.037", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B38", MRnumber = "2092316", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437104001165", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Garcia-Berthou:2004:IBT, author = "Emili Garc{\'i}a-Berthou and Carles Alcaraz", title = "Incongruence between test statistics and {$P$} values in medical papers", journal = "BMC Medical Research Methodology", volume = "4", number = "1", pages = "1--5", year = "2004", DOI = "https://doi.org/10.1186/1471-2288-4-13", ISSN = "1471-2288", ISSN-L = "1471-2288", bibdate = "Sat Sep 10 11:16:07 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers.", acknowledgement = ack-nhfb, journal-URL = "http://bmcmedresmethodol.biomedcentral.com/", keywords = "Benford's Law; digit frequencies", } @Article{Geyer:2004:DFD, author = "Christina Lynn Geyer and Patricia Pepple Williamson", title = "Detecting fraud in data sets using {Benford's Law}", journal = j-COMMUN-STAT-SIMUL-COMPUT, volume = "B33", number = "1", pages = "229--246", month = "????", year = "2004", CODEN = "CSSCDB", DOI = "https://doi.org/10.1081/SAC-120028442", ISSN = "0361-0918", ISSN-L = "0361-0918", MRclass = "62-07", MRnumber = "2044866", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", acknowledgement = ack-nhfb, ajournal = "Comm. Statist. Simulation Comput.", fjournal = "Communications in Statistics: Simulation and Computation", journal-URL = "http://www.tandfonline.com/loi/lssp20", keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Hurlimann:2004:IPB, author = "Werner H{\"u}rlimann", title = "Integer powers and {Benford}'s law", journal = j-INT-J-PURE-APPL-MATH, volume = "11", number = "1", pages = "39--46", year = "2004", CODEN = "????", ISSN = "1311-8080 (print), 1314-3395 (electronic)", ISSN-L = "1314-3395", MRclass = "62E15 (11B83 11K31 62E20)", MRnumber = "2033394 (2005c:62030)", MRreviewer = "I. N. Volodin", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Pure and Applied Mathematics", journal-URL = "http://ijpam.eu/", } @Article{Ismail:2004:SES, author = "Sanaa Isma{\"\i}l", title = "A Simple Estimator for the Shape Parameter of the {Pareto} Distribution with Economics and Medical Applications", journal = j-J-APPL-STAT, volume = "31", number = "1", pages = "3--13", month = jan, year = "2004", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Sat Dec 4 12:10:37 MST 2004", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Janvresse:2004:UDB, author = "{\'E}lise Janvresse and Thierry de la Rue", title = "From uniform distributions to {Benford}'s law", journal = j-J-APPL-PROBAB, volume = "41", number = "4", pages = "1203--1210", year = "2004", CODEN = "JPRBAM", DOI = "https://doi.org/10.1239/jap/1101840566", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", MRclass = "60J20 (60J10)", MRnumber = "2122815 (2006b:60161)", MRreviewer = "Michael Drmota", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566; http://www.jstor.org/stable/4141393; https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf", abstract = "We provide a new, probabilistic explanation for the appearance of Benford's law in everyday-life numbers, by showing that it arises naturally when we consider mixtures of uniform distributions. Then we connect our result to a result of Flehinger, for which we provide a shorter proof, and the speed of convergence.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Probability", journal-URL = "http://www.jstor.org/journals/00219002.html; http://projecteuclid.org/euclid.jap/", } @Book{Judson:2004:GBF, author = "Horace Freeland Judson", title = "The Great Betrayal: Fraud in Science", publisher = "Harcourt", address = "Orlando, FL, USA", pages = "xiv + 463", year = "2004", ISBN = "0-15-100877-9", ISBN-13 = "978-0-15-100877-3", LCCN = "Q175.37 .J84 2004", bibdate = "Sat Sep 10 12:29:21 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/har051/2004005906.html; http://www.loc.gov/catdir/description/har051/2004005906.html; http://www.loc.gov/catdir/samples/har051/2004005906.html; http://www.loc.gov/catdir/toc/ecip0416/2004005906.html", acknowledgement = ack-nhfb, remark = "No mention of Benford's Law or first digit phenomenon, but nevertheless relevant for applications of Benford's Law to detection of fraud in data.", subject = "Fraud in science", tableofcontents = "Preface / xi \\ Prologue / 1 \\ 1: A Culture of Fraud / 9 \\ 2: What's It Like? A Typology of Scientific Fraud / 43 \\ 3: Patterns of Complicity: Recent Cases / 98 \\ 4: Hard to Measure, Hard to Define: The Incidence of Scientific Fraud and the Struggle Over Its Definition / 155 \\ 5: The Baltimore Affair / 191 \\ 6: The Problems of Peer Review / 244 \\ 7: Authorship, Ownership: The Problems of Credit, Plagiarism, and Property / 287 \\ 8: The Rise of Open Publication on the Internet / 325 \\ 9: Laboratory to Law: The Problems of Institutions When Misconduct is Charged / 369 \\ Epilogue / 404 \\ Notes / 419 \\ Index / 447", } @TechReport{Kollath-Romano:2004:DSD, author = "P. Kollath-Romano", title = "On the distribution of significant digits in numbers", type = "Preprint", institution = "Rensselaer Polytechnic Institute", address = "Troy, NY, USA", year = "2004", bibdate = "Sat Feb 16 18:15:19 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InCollection{Kotz:2004:FDP, author = "Samuel Kotz and N. Balakrishnan and Campbell B. Read and Brani Vidakovic", editor = "Samuel Kotz and N. Balakrishnan and Campbell B. Read and Brani Vidakovic", booktitle = "Encyclopedia of Statistical Sciences", title = "First-Digit Problem", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Second", pages = "??--??", year = "2004", DOI = "https://doi.org/10.1002/0471667196.ess0783.pub2", ISBN = "0-471-66719-6 (e-book)", ISBN-13 = "978-0-471-66719-3 (e-book)", bibdate = "Sun Feb 24 10:49:25 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Kristiansen:2004:BTZ, author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T. Skjeltorp", title = "Braid theory and {Zipf} relation used in dynamics of magnetic microparticles", journal = j-ECONOM-LETT, volume = "30", number = "1", pages = "2387--2388", day = "1", month = may, year = "2004", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/j.jmmm.2003.12.1288", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0304885303019127", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Kristiansen:2004:EOZ, author = "Kai de Lange Kristiansen and Geir Helgesen and Arne T. Skjeltorp", title = "Experimental observation of {Zipf--Mandelbrot} relation", journal = j-PHYSICA-A, volume = "335", number = "3--4", pages = "413--420", day = "15", month = apr, year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2003.12.024", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "82D10 (76T99 82-05)", MRnumber = "2044153", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437103011804", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Kulikova:2004:OSS, author = "A. A. Kulikova and Yu. V. Prokhorov", title = "One-sided stable distributions and {Benford}'s law", journal = "Teor. Veroyatn. Primen.", volume = "49", number = "1", pages = "178--184", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1137/S0040585X97980944", ISSN = "0040-361X", ISSN-L = "0040-361X", MRclass = "60E07 (60F05)", MRnumber = "2141338 (2005m:60028)", MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya Veroyatnoste{\u\i} i ee Primeneniya", } @Article{Lanza:2004:CBS, author = "Richard B. Lanza", title = "Comparing Best Software for Fraud Examinations: Fraud Data Interrogation Tools", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = nov # "\slash " # dec, year = "2004", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:17:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967837", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @Article{Lehner:2004:DVG, author = "B. Lehner and P. Doll", title = "Development and validation of a global database of lakes", journal = j-J-HYDROL, volume = "296", number = "1--4", pages = "1--22", day = "20", month = aug, year = "2004", CODEN = "JHYDA7", DOI = "https://doi.org/10.1016/j.jhydrol.2004.03.028", ISSN = "0022-1694 (print), 1879-2707 (electronic)", ISSN-L = "0022-1694", bibdate = "Fri Mar 22 08:54:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022169404001404", acknowledgement = ack-mjn # "\slash " # ack-nhfb, fjournal = "Journal of Hydrology", journal-URL = "http://www.sciencedirect.com/science/journal/00221694", keywords = "Benford's Law", } @Article{Li:2004:DBL, author = "Zhi-peng Li and Lin Cong and Hua-jia Wang", title = "Discussion on {Benford's Law} and its Application", journal = "ArXiv e-prints", pages = "1--13", year = "2004", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 16:17:04 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2004math......8057L; http://arxiv.org/abs/math/0408057", abstract = "The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law $ {\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's Law from both theoretical and real-life sources on both science and social science areas are shown in detail with some novel ideas and generalizations developed solely by the authors of this paper. Three tests, Chi-Square test, total variation distance, and maximum deviations are adopted to examine the fitness of the datasets to Benford's distribution. Finally, applications of Benford's Law are summarized and explored to reveal the power of this mathematical principle.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "math/0408057", } @Article{Lindsay:2004:DFD, author = "D. H. Lindsay and P. S. Foote and A. Campbell and D. R. Reilly", title = "Detecting fraud in the data using automatic intervention detection", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2004", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sat Feb 16 18:32:22 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", } @Book{Miller:2004:JFM, author = "Irwin Miller and Marylees Miller", title = "{John E. Freund}'s mathematical statistics with applications", publisher = pub-PH, address = pub-PH:adr, edition = "Seventh", pages = "x + 614", year = "2004", ISBN = "0-13-142706-7", ISBN-13 = "978-0-13-142706-8", LCCN = "QA276 .M4726 2004", bibdate = "Thu Oct 13 07:01:49 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1928--", remark = "Revised edition of \cite{Miller:1999:JFM}.", subject = "Mathematical statistics", } @TechReport{Miller:2004:STB, author = "Steven J. Miller", title = "Some thoughts on {Benford}'s law", type = "Preprint", institution = "Williams College", address = "Williamstown, MA 01267 USA", year = "2004", bibdate = "Sat Feb 16 18:43:46 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf", acknowledgement = ack-nhfb, remark = "URL not found on 17 February 2013; perhaps in ReCALL 2004 proceedings", } @Article{Molchanov:2004:BEL, author = "Stanislav Molchanov and Xian Wang", title = "On the {Benford}'s empirical law", journal = "Random Oper. Stochastic Equations", volume = "12", number = "3", pages = "201--210", year = "2004", CODEN = "????", DOI = "https://doi.org/10.1163/1569397042222495", ISSN = "0926-6364 (print), 1569-397X (electronic)", ISSN-L = "0926-6364", MRclass = "11K16 (11B39 60B15)", MRnumber = "2084074 (2005h:11162)", MRreviewer = "A. N. Philippou", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Random Operators and Stochastic Equations", } @Article{Nabeshima:2004:ZLP, author = "Terutaka Nabeshima and Yukio-Pegio Gunji", title = "{Zipf}'s law in phonograms and {Weibull} distribution in ideograms: comparison of {English} with {Japanese}", journal = j-BIOSYSTEMS, volume = "73", number = "2", pages = "131--139", day = "20", month = feb, year = "2004", CODEN = "BSYMBO", DOI = "https://doi.org/10.1016/j.biosystems.2003.11.002", ISSN = "0303-2647 (print), 1872-8324 (electronic)", ISSN-L = "0303-2647", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0303264703002260", acknowledgement = ack-nhfb, fjournal = "Biosystems (A6E)", journal-URL = "http://www.sciencedirect.com/science/journal/03032647", keywords = "Zipf's Law", } @Article{Nguyen:2004:DPL, author = "Hung T. Nguyen and Vladik Kreinovich and Luc Longpr{\'e}", title = "Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals", journal = j-RELIABLE-COMPUTING, volume = "10", number = "2", pages = "83--106", month = apr, year = "2004", CODEN = "RCOMF8", DOI = "https://doi.org/10.1023/B:REOM.0000015848.19449.12", ISSN = "1385-3139 (print), 1573-1340 (electronic)", ISSN-L = "1385-3139", bibdate = "Mon Feb 6 07:42:05 MST 2012", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/rc.bib", URL = "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83; http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106", acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk, fjournal = "Reliable Computing = Nadezhnye vychisleniia", journal-URL = "http://link.springer.com/journal/11155", } @InProceedings{Pericchi:2004:LNB, author = "Luis R{\'a}ul Pericchi and David Torres", editor = "????", booktitle = "{Third Universidad Simon Bolivar Seminar on Statistical Analyses of the Venezuelan Recall Referendum}", title = "La {Ley de Newcomb--Benford} y sus aplicaciones al Referendum Revocatorio en {Venezuela}. ({Spanish}) [The {Newcomb--Benford Law} and its applications to the recall referendum in {Venezuela}]", publisher = "????", address = "????", pages = "1--7", day = "1", month = oct, year = "2004", bibdate = "Fri Feb 15 18:25:14 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reporte T{\'e}cnico no-definitivo 2a. Presented on September 23, 2004.", URL = "http://esdata.info/pdf/pericchi-torres.pdf; https://sites.google.com/a/upr.edu/probability-and-statistics/home/techical-reports", acknowledgement = ack-nhfb, language = "Spanish", } @TechReport{Posch:2004:BBH, author = "Peter N. Posch", title = "{Benford} or not-{Benford}? {How} to test for the first digit law", type = "Working paper.", institution = "Department of Finance, University of Ulm", address = "Ulm, Germany", year = "2004", bibdate = "Sat Feb 16 19:05:45 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @TechReport{Posch:2004:SSD, author = "Peter N. Posch", title = "A survey on sequences and distribution functions satisfying {Benford}'s law", type = "Working paper.", institution = "Department of Finance, University of Ulm", address = "Ulm, Germany", day = "25", month = oct, year = "2004", bibdate = "Sat Feb 16 19:05:45 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.posch.org/paper/posch_benforddist.pdf", acknowledgement = ack-nhfb, } @TechReport{Posch:2004:ZFB, author = "Peter N. Posch", title = "{Ziffernanalyse in der F{\"a}lschungsaufsp{\"u}rung. Benford's Gesetz und Steuererkl{\"a}rungen in Theorie und Praxis}. ({German}) [Digit analysis in fake tracing. {Benford's Law} and tax returns in theory and practice]", type = "Arbeitspapier", institution = "Abteilung Finanzwirtschaft, University Ulm", address = "Ulm, Germany", month = oct, year = "2004", bibdate = "Sat Feb 16 19:03:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Pustet:2004:ZHH, author = "Regina Pustet", title = "{Zipf} and his heirs", journal = j-LANG-SCI, volume = "26", number = "1", pages = "1--25", day = "1", month = jan, year = "2004", CODEN = "????", DOI = "https://doi.org/10.1016/S0388-0001(03)00018-4", ISSN = "0388-0001 (print), 1873-5746 (electronic)", ISSN-L = "0388-0001", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0388000103000184", abstract = "During the first half of this century, George Kingsley Zipf devised a comprehensive model of language mainly on the empirical basis of frequency counts in discourse. Although Zipf is remembered particularly for establishing the general formula the higher the discourse frequency of a linguistic item, the shorter it will be, his model is complex enough to merit re-evaluation especially in the light of more recent findings of discourse-based models of language and grammaticalization theory.", acknowledgement = ack-nhfb, fjournal = "Language Sciences", journal-URL = "http://www.sciencedirect.com/science/journal/03880001", keywords = "Benford's Law; Diachronic development of language; Discourse analysis; George Kingsley Zipf; Usage-based models of language; Word frequency; Zipf's Law", } @Article{Quarantelli:2004:ISA, author = "Mario Quarantelli and Karim Berkouk and Anna Prinster and Brigitte Landeau and Claus Svarer and Laszlo Balkay and Bruno Alfano and Arturo Brunetti and Jean-Claude Baron and Marco Salvatore", title = "Integrated Software for the Analysis of Brain {PET\slash SPECT} Studies with Partial-Volume Effect Correction", journal = j-NUCL-MED, volume = "45", number = "2", pages = "192--201", day = "1", month = feb, year = "2004", CODEN = "JNMEAQ", ISSN = "0161-5505 (print), 1535-5667 (electronic)", ISSN-L = "0161-5505", bibdate = "Sat Sep 10 15:45:29 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jnm.snmjournals.org/content/45/2/192.abstract", acknowledgement = ack-nhfb, fjournal = "Journal of Nuclear Medicine", journal-URL = "http://jnm.snmjournals.org/content/by/year", keywords = "Benford's Law", } @Article{Rawlings:2004:EBP, author = "Philip K. Rawlings and David Reguera and Howard Reiss", title = "Entropic basis of the {Pareto} law", journal = j-PHYSICA-A, volume = "343", number = "1--4", pages = "643--652", year = "2004", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2004.06.152", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B26 (91B82)", MRnumber = "2094418 (2005e:91065)", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Rodriguez:2004:FSD, author = "Ricardo J. Rodriguez", title = "First Significant Digit Patterns From Mixtures of Uniform Distributions", journal = j-AMER-STAT, volume = "58", number = "1", pages = "64--71", month = feb, year = "2004", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/0003130042782", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Fri Feb 20 06:14:28 MST 2004", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", keywords = "Benford's Law", } @TechReport{Saville:2004:SWN, author = "Adrian D. Saville", title = "Sorry, wrong number. {How} accounting data are wrong and how the numbers can be fixed", type = "Preprint", institution = "????", address = "????", month = "????", year = "2004", bibdate = "Sat Feb 16 19:11:00 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Sigurd:2004:WLS, author = "Bengt Sigurd and Mats Eeg-Olofsson and Joost {Van Weijer}", title = "Word length, sentence length and frequency --- {Zipf} revisited", journal = j-STUD-LINGUISTICA, volume = "58", number = "1", pages = "37--52", year = "2004", DOI = "https://doi.org/10.1111/j.0039-3193.2004.00109.x", ISSN = "0039-3193 (print), 1467-9582 (electronic)", ISSN-L = "0039-3193", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Studia Linguistica", } @Article{Skousen:2004:AUP, author = "Christopher J. Skousen and Liming Guan and T. Sterling Wetzel", title = "Anomalies and Unusual Patterns in Reported Earnings: {Japanese} Managers Round Earnings", journal = j-J-INT-FINANC-MANAG-ACCOUNT, volume = "15", number = "3", pages = "212--234", month = oct, year = "2004", CODEN = "????", DOI = "https://doi.org/10.1111/j.1467-646X.2004.00108.x", ISSN = "0954-1314 (print), 1467-646X (electronic)", ISSN-L = "0954-1314", bibdate = "Fri Nov 25 11:11:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of International Financial Management and Accounting", } @Book{Tijms:2004:UPC, author = "Henk C. Tijms", title = "Understanding probability: chance rules in everyday life", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "x + 380", year = "2004", ISBN = "0-521-83329-9 (hardcover), 0-521-54036-4 (paperback)", ISBN-13 = "978-0-521-83329-5 (hardcover), 978-0-521-54036-0 (paperback)", LCCN = "QA273 .T48 2004", bibdate = "Mon Feb 18 06:48:08 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Probabilities; Mathematical analysis; Chance; Wahrscheinlichkeit; (Math.); Gesamtdarstellung", } @Article{Vanichpun:2004:OCU, author = "Sarut Vanichpun and Armand M. Makowski", title = "The output of a cache under the independent reference model: where did the locality of reference go?", journal = j-SIGMETRICS, volume = "32", number = "1", pages = "295--306", month = jun, year = "2004", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/1012888.1005722", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Fri Jun 27 09:21:18 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "We consider a cache operating under a demand-driven replacement policy when document requests are modeled according to the Independent Reference Model (IRM). We characterize the popularity pmf of the stream of misses from the cache, the so-called output of the cache, for a large class of demand-driven cache replacement policies. We measure strength of locality of reference in a stream of requests through the skewness of its popularity distribution. Using the notion of majorization to capture this degree of skewness, we show that for the policy $ A_0 $ and the random policy, the output always has less locality of reference than the input. However, we show by counterexamples that this is not always the case under the LRU and CLIMB policies when the input is selected according to a Zipf-like pmf. In that case, conjectures are offered (and supported by simulations) as to when LRU or CLIMB caching indeed reduces locality of reference.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "locality of reference; majorization; output of a cache; popularity", } @InProceedings{Acebo:2005:BLN, author = "E. Acebo and M. Sbert", editor = "L. Neumann and M. Sbert and B. Gooch and W. Purgathofer", booktitle = "Conference: Computational Aesthetics 2005: Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging 2005, Girona, Spain, May 18--20, 2005", title = "{Benford's Law} for Natural and Synthetic Images", publisher = "????", address = "????", pages = "169--176", year = "2005", DOI = "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176", bibdate = "Sat Sep 10 11:34:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Alexanderson:2005:BRG, author = "Gerald L. Alexanderson", title = "Book Review: {{\booktitle{Gamma: Exploring Euler's Constant}}, by Julian Havil. Princeton, Princeton University Press 2003. xxiii + 266 pages. US \$29.95. ISBN 0-691-09983-9}", journal = j-MATH-INTEL, volume = "27", number = "1", pages = "86--88", month = dec, year = "2005", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/BF02984820", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/BF02984820", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", keywords = "Benford's Law", } @Article{Anonymous:2005:UZL, author = "Anonymous", title = "The use of {Zipf}'s law in animal communication analysis", journal = j-ANIM-BEHAV, volume = "69", number = "1", pages = "??--??", day = "20", month = jan, year = "2005", CODEN = "ANBEA8", DOI = "https://doi.org/10.1016/j.anbehav.2004.08.004", ISSN = "0003-3472 (print), 1095-8282 (electronic)", ISSN-L = "0003-3472", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0003347204003471", acknowledgement = ack-nhfb, fjournal = "Animal Behaviour", journal-URL = "http://www.sciencedirect.com/science/journal/00033472", keywords = "Zipf's Law", } @Article{Antonini:2005:RSC, author = "Rita Giuliano Antonini and Georges Grekos", title = "Regular sets and conditional density: an extension of {Benford}'s law", journal = j-COLLOQ-MATH, volume = "103", number = "2", pages = "173--192", year = "2005", CODEN = "CQMAAQ", DOI = "https://doi.org/10.4064/cm103-2-3", ISSN = "0010-1354 (print), 1730-6302 (electronic)", ISSN-L = "0010-1354", MRclass = "11B05 (11K99)", MRnumber = "2197847 (2006j:11012)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1092.11009", acknowledgement = ack-nhfb, fjournal = "Colloquium Mathematicum", keywords = "asymptotic density; Benford's law; conditional density; first digit problem; logarithmic density; regular set; regular varying function", ZMclass = "11B05 (Topology etc. of sets of numbers); 11K99 (Probabilistic theory)", } @Article{Berger:2005:BLP, author = "Arno Berger", title = "{Benford}'s law in power-like dynamical systems", journal = j-STOCH-DYNAM, volume = "5", number = "4", pages = "587--607", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1142/S0219493705001602", ISSN = "0219-4937", ISSN-L = "0219-4937", MRclass = "37B55 (11K06 37A50 37E05)", MRnumber = "2185507 (2008i:37029)", MRreviewer = "Peter Raith", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Stoch. Dyn.", fjournal = "Stochastics and Dynamics", } @InCollection{Berger:2005:DDU, author = "A. Berger", booktitle = "{EQUADIFF} 2003", title = "Dynamics and digits: on the ubiquity of {Benford}'s law", publisher = "World Sci. Publ., Hackensack, NJ", pages = "693--695", year = "2005", DOI = "https://doi.org/10.1142/9789812702067_0115", MRclass = "37A45 (11K55)", MRnumber = "2185113", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Berger:2005:MDD, author = "Arno Berger", title = "Multi-dimensional dynamical systems and {Benford}'s law", journal = j-DISCRETE-CONTIN-DYN-SYST, volume = "13", number = "1", pages = "219--237", year = "2005", CODEN = "????", DOI = "https://doi.org/10.3934/dcds.2005.13.219", ISSN = "1078-0947 (print), 1553-5231 (electronic)", ISSN-L = "1078-0947", MRclass = "37A45 (11K36 28D05 37A50 60F05)", MRnumber = "2128801 (2005m:37016)", MRreviewer = "Reinhard Winkler", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Discrete and Continuous Dynamical Systems. Series A", } @Article{Berger:2005:ODD, author = "Arno Berger and Leonid A. Bunimovich and Theodore P. Hill", title = "One-dimensional dynamical systems and {Benford}'s law", journal = j-TRANS-AM-MATH-SOC, volume = "357", number = "1", pages = "197--219", year = "2005", CODEN = "TAMTAM", DOI = "https://doi.org/10.1090/S0002-9947-04-03455-5", ISSN = "0002-9947 (print), 1088-6850 (electronic)", ISSN-L = "0002-9947", MRclass = "37A45 (11K06 37A50 37E05 60F05 82B05)", MRnumber = "2098092 (2005m:37017)", MRreviewer = "Peter Raith", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Transactions of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/tran/", } @Article{Bhattacharya:2005:CPA, author = "Sukanto Bhattacharya and Kuldeep Kumar and Florentin Smarandache", title = "Conditional probability of actually detecting a financial fraud --- a neutrosophic extension to {Benford}'s law", journal = j-INT-J-APPL-MATH, volume = "17", number = "1", pages = "7--14", year = "2005", CODEN = "????", ISSN = "1311-1728 (print), 1314-8060 (electronic)", MRclass = "62G10 (91B28)", MRnumber = "2170667", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math/0504520", abstract = "This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been actually committed, given that no Type I error occurred while rejecting the null hypothesis H0: The observed first-digit frequencies approximate a Benford distribution; and accepting the alternative hypothesis H1: The observed first-digit frequencies do not approximate a Benford distribution. We have also suggested a conceptual model to implement such a neutrosophic fraud detection system.", acknowledgement = ack-nhfb, ajournal = "Int. J. Appl. Math.", fjournal = "International Journal of Applied Mathematics", journal-URL = "http://www.diogenes.bg/ijam/", } @Article{Bhattacharyya:2005:COP, author = "P. Bhattacharyya and A. Chatterjee and B. K. Chakrabarti", title = "A common origin of the power law distributions in models of market and earthquake", journal = "ArXiv e-prints", year = "2005", bibdate = "Sat Feb 16 17:25:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/physics/0510038", acknowledgement = ack-nhfb, } @Article{Brown:2005:BLS, author = "Richard J. C. Brown", title = "{Benford}'s law and the screening of analytical data: the case of pollutant concentrations in ambient air", journal = j-ANALYST, volume = "130", number = "9", pages = "1280--1285", month = "????", year = "2005", CODEN = "ANALAO", DOI = "https://doi.org/10.1039/B504462F", ISSN = "0003-2654 (print), 1364-5528 (electronic)", ISSN-L = "0003-2654", bibdate = "Sat Feb 16 17:27:51 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ncbi.nlm.nih.gov/pubmed/16096674", acknowledgement = ack-nhfb, fjournal = "The Analyst", journal-URL = "http://pubs.rsc.org/en/journals/journalissues/an", } @Article{Campi:2005:ZLM, author = "X. Campi and H. Krivine", title = "{Zipf}'s law in multifragmentation", journal = j-PHYS-REV-C, volume = "72", number = "??", pages = "057602", day = "30", month = nov, year = "2005", CODEN = "PRVCAN", DOI = "https://doi.org/10.1103/PhysRevC.72.057602", ISSN = "0556-2813 (print), 1089-490X, 1538-4497", ISSN-L = "0556-2813", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevC.72.057602", acknowledgement = ack-nhfb, fjournal = "Physical Review C (Nuclear Physics)", journal-URL = "http://prc.aps.org/browse", keywords = "Zipf's Law", } @TechReport{Ciofalo:2005:EBF, author = "Michele Ciofalo", title = "Entropy, {Benford}'s first digit law, and the distribution of everything", type = "Report", institution = "Dipartimento di Ingegneria Nucleare, Universit{\`a} degli Studi di Palermo", address = "Palermo, Italy", pages = "34", year = "2005", bibdate = "Sun Feb 17 08:23:55 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf", acknowledgement = ack-nhfb, } @Article{Cleary:2005:ADA, author = "Richard Cleary and Jay C. Thibodeau", title = "Applying Digital Analysis Using {Benford's Law} to Detect Fraud: The Dangers of Type {I} Errors", journal = j-AUDITING, volume = "24", number = "1", pages = "77--81", month = may, year = "2005", CODEN = "????", DOI = "https://doi.org/10.2308/aud.2005.24.1.77", ISSN = "0278-0380 (print), 1558-7991 (electronic)", ISSN-L = "0278-0380", bibdate = "Tue Nov 15 09:17:46 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaapubs.org/loi/ajpt; http://link.aip.org/link/AJPTXX/v24/i1/p77/s1", acknowledgement = ack-nhfb, fjournal = "Auditing: A Journal of Practice \& Theory", } @Article{Cohen:2005:PCL, author = "Edith Cohen and Carsten Lund", title = "Packet classification in large {ISPs}: design and evaluation of decision tree classifiers", journal = j-SIGMETRICS, volume = "33", number = "1", pages = "73--84", month = jun, year = "2005", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/1064212.1064222", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Fri Jun 27 09:21:27 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Packet classification, although extensively studied, is an evolving problem. Growing and changing needs necessitate the use of larger filters with more complex rules. The increased complexity and size pose implementation challenges on current hardware solutions and drive the development of software classifiers, in particular, decision-tree based classifiers. Important performance measures for these classifiers are time and memory due to required high throughput and use of limited fast memory. We analyze Tier 1 ISP data that includes filters and corresponding traffic from over a hundred edge routers and thousands of interfaces. We provide a comprehensive view on packet classification in an operational network and glean insights that help us design more effective classification algorithms. We propose and evaluate decision tree classifiers with {\em common branches}. These classifiers have linear worst-case memory bounds and require much less memory than standard decision tree classifiers, but nonetheless, we show that on our data have similar average and worst-case time performance. We argue that common-branches exploit structure that is present in real-life data sets. We observe a strong Zipf-like pattern in the usage of rules in a classifier, where a very small number of rules resolves the bulk of traffic and most rules are essentially never used. Inspired by this observation, we propose {\em traffic-aware\/} classifiers that obtain superior average-case and bounded worst-case performance. Good average-case can boost performance of software classifiers that can be used in small to medium sized routers and are also important for traffic analysis and traffic engineering.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "access control lists; decision trees; packet filtering; routing", } @Article{Dahui:2005:TRZ, author = "Wang Dahui and Li Menghui and Di Zengru", title = "True reason for {Zipf}'s law in language", journal = j-PHYSICA-A, volume = "358", number = "2--4", pages = "545--550", day = "15", month = dec, year = "2005", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2005.04.021", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437105004085", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @InProceedings{DelAcebo:2005:BLN, author = "Esteve {Del Acebo} and Mateu Sbert", title = "{Benford's Law} for Natural and Synthetic Images", crossref = "Neumann:2005:CAE", pages = "169--176", year = "2005", DOI = "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176", bibdate = "Tue Nov 15 08:46:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf", acknowledgement = ack-nhfb, } @Book{Durrett:2005:PTE, author = "Richard Durrett", title = "Probability: theory and examples", publisher = "Thomson Brooks\slash Cole", address = "Belmont, CA, USA", edition = "Third", pages = "xi + 497", year = "2005", ISBN = "0-534-42441-4", ISBN-13 = "978-0-534-42441-1", LCCN = "QA273 .D865 2005", bibdate = "Mon Nov 21 10:00:11 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Duxbury advanced series", acknowledgement = ack-nhfb, remark = "Benford's Law is treated on pp. 337ff. Hill \cite[page 893]{Hill:1995:BII} reports that the 1991 edition has a proof that the $k$-th digit of powers of integers follows Benford's Law.", subject = "Probabilities", } @Book{Egghe:2005:PLI, author = "Leo Egghe", title = "Power laws in the information production process: {Lotkaian} informetrics", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "xvii + 427", year = "2005", ISBN = "0-12-088753-3, 0-08-048011-X (e-book)", ISBN-13 = "978-0-12-088753-8, 978-0-08-048011-4 (e-book)", LCCN = "Z669.8 .E44 2005", bibdate = "Mon Feb 25 10:42:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See pages 204--205 for Benford's Law discussion.", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject-dates = "Lotka, Alfred James, (1880--1949)", tableofcontents = "Basic theory of Lotkaian informetrics \\ Three-dimensional Lotkaian informetrics \\ Lotkaian concentration theory \\ Lotkaian fractal complexity theory \\ Lotkaian informetrics of systems in which items can have multiple sources \\ Further applications in Lotkaian informetrics \\ Lotkaian informetrics: an introduction", } @Article{Egghe:2005:PPL, author = "L. Egghe", title = "The power of power laws and an interpretation of {Lotkaian} informetric systems as self-similar fractals", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "56", number = "7", pages = "669--675", month = may, year = "2005", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20158", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:27 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "16 Mar 2005", } @Article{Egghe:2005:RBC, author = "L Egghe", title = "Relations between the continuous and the discrete {Lotka} power function", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "56", number = "7", pages = "664--668", month = may, year = "2005", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20157", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:27 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "11 Mar 2005", } @Article{Egghe:2005:ZLC, author = "L. Egghe", title = "{Zipfian} and {Lotkaian} continuous concentration theory", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "56", number = "9", pages = "935--945", month = jul, year = "2005", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20186", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:28 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "21 Apr 2005", } @Article{elSehity:2005:PDA, author = "Tarek el Sehity and Erik Hoelzl and Erich Kirchler", title = "Price developments after a nominal shock: {Benford's Law} and psychological pricing after the euro introduction", journal = j-INT-J-RES-MARK, volume = "22", number = "4", pages = "471--480", month = dec, year = "2005", CODEN = "IJRME6", DOI = "https://doi.org/10.1016/j.ijresmar.2005.09.002", ISSN = "0167-8116 (print), 1873-8001 (electronic)", ISSN-L = "0167-8116", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167811605000522", abstract = "Retail managers use psychological pricing to make the prices of goods appear to be just below a round number. The euro introduction in 2002, with its various exchange rates, distorted existing nominal price patterns while at the same time retaining real prices. We studied consumer prices before and after the introduction of the euro by using Benford's Law as a benchmark for price adjustments. Results indicate the usefulness of this benchmark for detecting irregularities in prices, and a clear trend towards psychological pricing after the nominal shock of the euro introduction. In addition, the tendency towards psychological prices results in different inflation rates in dependence of the price pattern.", acknowledgement = ack-nhfb, fjournal = "International Journal of Research in Marketing", keywords = "Benford's Law; Digital analysis; Price endings; Retail pricing", } @Article{Fairthorne:2005:PDE, author = "Robert A. Fairthorne", title = "Progress in Documentation: Empirical Hyperbolic Distributions ({Bradford--Zipf--Mandelbrot}) for Bibliometric Description and Prediction", journal = j-J-DOC, volume = "61", number = "2", pages = "171--193", month = "????", year = "2005", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/00220410510585179", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 06:27:27 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Reprint of \cite{Fairthorne:1969:PDE}.", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", remark = "According to \cite{Potter:1981:LLR}, this paper is the first to link the distributions of Bradford, Zipf, Mandelbrot, and Lotka.", } @Article{FerreriCancho:2005:CZL, author = "Ramon {Ferrer i Cancho} and Oliver Riordan and B{\'e}la Bollob{\'a}s", title = "The consequences of {Zipf}'s law for syntax and symbolic reference", journal = j-PROC-R-SOC-LOND-SER-B-BIO-SCI, volume = "272", number = "1562", pages = "561--565", day = "7", month = mar, year = "2005", CODEN = "PRLBA4", DOI = "https://doi.org/10.1098/rspb.2004.2957", ISSN = "0962-8452 (print), 1471-2954 (electronic)", ISSN-L = "0962-8452", bibdate = "Tue Nov 15 11:27:26 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rspb.royalsocietypublishing.org/content/272/1562/561.full", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society of London. Series B. Biological sciences", journal-URL = "https://royalsocietypublishing.org/loi/rspb", } @TechReport{Giles:2005:BLN, author = "David E. Giles", title = "{Benford's Law} and Naturally Occurring Prices in Certain {ebaY} Auctions", type = "Econometrics Working Paper", number = "EWP0505", institution = "Department of Economics, University of Victoria", address = "Victoria, BC, Canada", month = may, year = "2005", ISSN = "1485-6441", bibdate = "Thu Feb 15 16:24:39 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://web.uvic.ca/econ/ewp0505.pdf", abstract = "We show that certain the winning bids for certain ebaY auctions obey Benford's Law. One implication of this is that it is unlikely that these bids are subject to collusion among bidders, or ``shilling'' on the part of sellers. Parenthetically, we also show that numbers from the naturally occurring Fibonacci and Lucas sequences also obey Benford's Law.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", } @Article{Harremoes:2005:ZLHa, author = "Peter Harremo{\"e}s and Flemming Topsoe", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", journal = j-PHYSICA-A, volume = "328", number = "3--4", pages = "315--318", day = "1", month = aug, year = "2005", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.endm.2005.07.075", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1571065305051450", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @InCollection{Harremoes:2005:ZLHb, author = "Peter Harremo{\"e}s and Flemming Topsoe", editor = "Rudolf Ahlswede and others", booktitle = "General theory of information transfer and combinatorics.", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", volume = "21", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "315--318", year = "2005", DOI = "https://doi.org/10.1016/j.endm.2005.07.075", bibdate = "Sat Nov 12 11:07:14 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Electronic Notes in Discrete Mathematics", ZMnumber = "1158.91482", abstract = "Zipf's law --- or Estoup-Zipf's law --- is an empirical fact of computational linguistics which relates rank and frequency of words in natural languages. The law suggests modelling by distributions of ``hyperbolic type''. We present a satisfactory general definition and an information-theoretical characterization of the resulting hyperbolic distributions. When applied to linguistics this leads to a property of stability and flexibility, explaining that a language can develop towards higher and higher expressive powers without changing its basic structure.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics) 94A15 (General topics of information theory) 94A17 (Measures of information)", keywords = "entropy loss; hyperbolic distributions; Zipf's law", } @Article{Hill:2005:RDS, author = "Theodore P. Hill and Klaus Sch{\"u}rger", title = "Regularity of digits and significant digits of random variables", journal = j-STOCH-PROC-APPL, volume = "115", number = "10", pages = "1723--1743", month = oct, year = "2005", CODEN = "STOPB7", DOI = "https://doi.org/10.1016/j.spa.2005.05.003", ISSN = "0304-4149 (print), 1879-209X (electronic)", ISSN-L = "0304-4149", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0304414905000657", abstract = "A random variable X is digit-regular (respectively, significant-digit-regular) if the probability that every block of $k$ given consecutive digits (significant digits) appears in the b-adic expansion of $X$ approaches $ b - k$ as the block moves to the right, for all integers $ b > 1$ and $ k \geq 1$. Necessary and sufficient conditions are established, in terms of convergence of Fourier coefficients, and in terms of convergence in distribution modulo 1, for a random variable to be digit-regular (significant-digit-regular), and basic relationships between digit-regularity and various classical classes of probability measures and normal numbers are given. These results provide a theoretical basis for analyses of roundoff errors in numerical algorithms which use floating-point arithmetic, and for detection of fraud in numerical data via using goodness-of-fit of the least significant digits to uniform, complementing recent tests for leading significant digits based on Benford's law.", acknowledgement = ack-nhfb, fjournal = "Stochastic Processes and Their Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03044149", keywords = "Benford's Law; Digit-regular random variable; Floating-point numbers; Law of least significant digits; Nonleading digits; Normal numbers; Significant digits; Significant-digit-regular random variable; Trailing digits", } @InProceedings{Hjorland:2005:BLS, author = "Birger Hj{\o}rland and Jeppe Nicolaisen", editor = "Fabio Crestani and Ian Ruthven", booktitle = "Context: nature, impact, and role: {5th International Conference on Conceptions of Library and Information Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005; proceedings}", title = "{Bradford}'s law of scattering: ambiguities in the concept of ``subject''", volume = "3507", publisher = pub-SV, address = pub-SV:adr, bookpages = "xiii + 250", pages = "96--106", year = "2005", ISBN = "3-540-26178-8", ISBN-13 = "978-3-540-26178-0", LCCN = "Z672.5 .I5616 2005", bibdate = "Fri Nov 25 11:52:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @Article{Ioannidis:2005:WMP, author = "John P. A. Ioannidis", title = "Why Most Published Research Findings Are False", journal = j-PLOS-MED, volume = "2", number = "8", pages = "696--701", month = aug, year = "2005", CODEN = "PMLEAC", DOI = "https://doi.org/10.1371/journal.pmed.0020124", ISSN = "1549-1277 (print), 1549-1676 (electronic)", ISSN-L = "1549-1277", bibdate = "Fri Nov 18 12:42:05 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124", abstract = "There is increasing concern that most current published research findings are false. The probability that a research claim is true may depend on study power and bias, the number of other studies on the same question, and, importantly, the ratio of true to no relationships among the relationships probed in each scientific field. In this framework, a research finding is less likely to be true when the studies conducted in a field are smaller; when effect sizes are smaller; when there is a greater number and lesser preselection of tested relationships; where there is greater flexibility in designs, definitions, outcomes, and analytical modes; when there is greater financial and other interest and prejudice; and when more teams are involved in a scientific field in chase of statistical significance. Simulations show that for most study designs and settings, it is more likely for a research claim to be false than true. Moreover, for many current scientific fields, claimed research findings may often be simply accurate measures of the prevailing bias. In this essay, I discuss the implications of these problems for the conduct and interpretation of research.", acknowledgement = ack-nhfb, articleno = "e124", fjournal = "PLoS Medicine", journal-URL = "http://medicine.plosjournals.org/", remark = "This article does not discuss Benford's Law, but is related to the use of that law in the detection of fraud in research data. Ioannidis discusses the abuse of statistics for limited experimental data, a topic that receives book-length treatment in \cite{Ziliak:2008:CSS}.", } @Article{Jolissaint:2005:LBR, author = "Paul Jolissaint", title = "Loi de {Benford}, relations de r{\'e}currence et suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s Law, recurrence relations, and equidistributed sequences]", journal = j-ELEM-MATH, volume = "60", number = "1", pages = "10--18", year = "2005", CODEN = "????", DOI = "https://doi.org/10.4171/EM/2", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRclass = "11K36 (37A45 60E99)", MRnumber = "2188341 (2006j:11109)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{Kechedzhi:2005:RDW, author = "K. E. Kechedzhi and O. V. Usatenko and V. A. Yampol{\cprime}skii", title = "Rank distributions of words in correlated symbolic systems and the {Zipf} law", journal = j-PHYS-REV-E, volume = "72", number = "4", pages = "046138", day = "28", month = oct, year = "2005", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.72.046138", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", MRclass = "82C31", MRnumber = "2183723 (2006f:82069)", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.72.046138", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "6", } @Article{Kontorovich:2005:BLV, author = "Alex V. Kontorovich and Steven J. Miller", title = "{Benford}'s law, values of {$L$}-functions and the {$ 3 x + 1 $} problem", journal = j-ACTA-ARITHMETICA, volume = "120", number = "3", pages = "269--297", year = "2005", CODEN = "AARIA9", DOI = "https://doi.org/10.4064/aa120-3-4", ISSN = "0065-1036 (print), 1730-6264 (electronic)", ISSN-L = "0065-1036", MRclass = "11K06 (11B37 11M06 37A45)", MRnumber = "2188844 (2007c:11085)", MRreviewer = "J. C. Lagarias", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2005AcAri.120..269K; http://arxiv.org/abs/math/0412003", abstract = "We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The other is a general technique of applying Poisson Summation to the limiting distribution. We show the distribution of values of $L$-functions near the central line and (in some sense) the iterates of the $ 3 x + 1 $ Problem are Benford.", acknowledgement = ack-nhfb, fjournal = "Acta Arithmetica", journal-URL = "https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all", } @Article{Kulikova:2005:CAS, author = "A. A. Kulikova and Yu. V. Prokhorov", title = "Completely Asymmetric Stable Laws and {Benford's Law}", journal = j-THEORY-PROBAB-APPL, volume = "49", number = "1", pages = "163--169", month = mar, year = "2005", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/S0040585X97980944", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Thu Jul 7 19:15:48 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/98094", acknowledgement = ack-nhfb, fjournal = "Theory of probability and its applications", journal-URL = "http://epubs.siam.org/tvp", keywords = "Benford's Law; Zipf's Law", } @Article{Kulikova:2005:HFD, author = "A. A. Kulikova and Yu. V. Prokhorov and V. I. Khokhlov", title = "{H. F. D.} ({$H$}-function distribution) and the {Benford} law. {I}", journal = "Teor. Veroyatn. Primen.", volume = "50", number = "2", pages = "366--371", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1137/S0040585X97981706", ISSN = "0040-361X", ISSN-L = "0040-361X", MRclass = "60E07 (60F05)", MRnumber = "2221718 (2007b:60029)", MRreviewer = "S{\'a}ndor Cs{\"o}rg{\H{o}}", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoriya Veroyatnoste{\u\i} i ee Primeneniya", } @Article{Lagarias:2005:BLF, author = "J. C. Lagarias and K. Soundararajan", title = "{Benford}'s law for the $ 3 x + 1 $ function", journal = "ArXiv Mathematics e-prints", month = sep, year = "2005", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2005math......9175L; http://arxiv.org/abs/math/0509175", acknowledgement = ack-nhfb, eprint = "arXiv:math/0509175", keywords = "Mathematics - Number Theory, Mathematics - Probability", } @Article{Li:2005:ZLP, author = "Yujian Li and Chuangbai Xiao", title = "{Zipf}'s law probably existing in protein sequences", journal = "J. Beijing Univ. Technol.", volume = "31", number = "4", pages = "366--368", year = "2005", CODEN = "????", ISSN = "????", bibdate = "Sat Nov 12 11:10:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1084.92019", abstract = "In order to analyze whether Zipf's law in linguistics exists in protein sequences, this paper uses $ 1.735 \, 7 \times 10^4 $ protein sequences labeled with secondary structures which are selected from the DSSP database. The segments of successive amino acid residues with a same code of secondary structure are defined as words. The results show that the distribution of words emerging frequency follows Zipf's law with the exponent $ 0.981 $.", acknowledgement = ack-nhfb, classmath = "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics to biology): 92D20 (Protein sequences, DNA sequences)", language = "Chinese. English summary", xxremark = "Which journal is this? Beijing gong ye da xue xue bao = Journal of Beijing Polytechnic University (ISSN 0254-0037), or Beijing ke ji da xue xue bao = Journal of University of Science and Technology, Beijing (ISSN 1001-053X), or something different?", } @Article{Lu:2005:CZL, author = "Tim Lu and Christine M. Costello and Peter J. P. Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl and Stefan Schreiber", title = "Can {Zipf}'s law be adapted to normalize microarrays?", journal = j-BMC-BIOINFORMATICS, volume = "6", number = "??", pages = "37--49", month = "????", year = "2005", CODEN = "BBMIC4", DOI = "https://doi.org/10.1186/1471-2105-6-37", ISSN = "1471-2105", ISSN-L = "1471-2105", bibdate = "Sat Feb 16 18:38:50 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1186/1471-2105-6-37; http://www.biomedcentral.com/1471-2105/6/37", acknowledgement = ack-nhfb, fjournal = "BMC Bioinformatics", journal-URL = "http://www.biomedcentral.com/bmcbioinformatics/", } @InProceedings{Lu:2005:DFH, author = "Fletcher Lu and J. Efrim Boritz", title = "Detecting Fraud in Health Insurance Data: Learning to Model Incomplete {Benford's Law} Distributions", crossref = "Gama:2005:MLE", pages = "633--640", year = "2005", DOI = "https://doi.org/10.1007/11564096_63", bibdate = "Tue Nov 15 08:55:45 2011", bibsource = "DBLP; http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, URL = "http://link.springer.com/chapter/10.1007/11564096_63", acknowledgement = ack-nhfb, } @Article{Ma:2005:CBL, author = "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel and J. Wang and T. Keutgen and Z. Majka and M. Murray and L. Qin and P. Smith and R. Alfaro and J. Cibor and M. Cinausero and Y. El Masri and D. Fabris and E. Fioretto and A. Keksis and M. Lunardon and A. Makeev and N. Marie and E. Martin and A. Martinez-Davalos and A. Menchaca-Rocha and G. Nebbia and G. Prete and V. Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis and P. Staszel and M. Veselsky and G. Viesti and E. M. Winchester and S. J. Yennello", title = "Critical behavior in light nuclear systems: Experimental aspects", journal = j-PHYS-REV-C, volume = "71", number = "5", pages = "054606", day = "26", month = may, year = "2005", CODEN = "PRVCAN", DOI = "https://doi.org/10.1103/PhysRevC.71.054606", ISSN = "0556-2813 (print), 1089-490X, 1538-4497", ISSN-L = "0556-2813", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevC.71.054606", acknowledgement = ack-nhfb, fjournal = "Physical Review C (Nuclear Physics)", journal-URL = "http://prc.aps.org/browse", keywords = "Zipf's Law", } @Article{Manaris:2005:ZLM, author = "Bill Manaris and Juan Romero and Penousal Machado and Dwight Krehbiel and Timothy Hirzel and Walter Pharr and Robert B. Davis", title = "{Zipf}'s law, music classification, and aesthetics", journal = j-COMP-MUSIC-J, volume = "29", number = "1", pages = "55--69", month = "Spring", year = "2005", CODEN = "CMUJDY", ISSN = "0148-9267 (print), 1531-5169 (electronic)", ISSN-L = "0148-9267", bibdate = "Sat Feb 16 18:40:14 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html; http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf", acknowledgement = ack-nhfb, fjournal = "Computer Music Journal", keywords = "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law", } @Article{Martinson:2005:SBB, author = "Brian C. Martinson and Melissa S. Anderson and Raymond de Vries", title = "Scientists Behaving Badly", journal = j-NATURE, volume = "435", number = "7043", pages = "737--738", day = "9", month = jun, year = "2005", CODEN = "NATUAS", DOI = "https://doi.org/10.1007/s00221-007-0889-0", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Sat Sep 10 13:14:54 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v435/n7043/pdf/435737a.pdf", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", keywords = "Benford's Law", remark = "No mention of Benford's Law or first digit phenomenon, but nevertheless relevant for applications of Benford's Law to detection of fraud in science.", } @Article{Maslov:2005:GTS, author = "V. P. Maslov", title = "On a general theorem of set theory that leads to the {Gibbs}, {Bose--Einstein}, and {Pareto} distributions and to the {Zipf--Mandelbrot} law for the stock market", journal = j-MAT-ZAMETKI, volume = "78", number = "6", pages = "870--877", year = "2005", CODEN = "????", DOI = "https://doi.org/10.1007/s11006-005-0186-9", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "91B28 (90C29)", MRnumber = "2249037 (2007b:91077)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", journal-URL = "http://link.springer.com/journal/11006", } @Article{Maslov:2005:RZLa, author = "V. P. Maslov", title = "Refining {Zipf}'s law for frequency dictionaries", journal = j-DOKL-AKAD-NAUK, volume = "405", number = "5", pages = "591--594", year = "2005", CODEN = "DANKAS", ISSN = "0869-5652", ISSN-L = "0869-5652", MRclass = "94A15 (60C05)", MRnumber = "2340762", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii Nauk", journal-URL = "http://istina.msu.ru/journals/366838/", } @Article{Maslov:2005:RZLb, author = "V. P. Maslov", title = "Refinement of {Zipf}'s law for frequency dictionaries", journal = j-DOKL-MATH, volume = "72", number = "3", pages = "942--945", year = "2005", CODEN = "????", ISSN = "1064-5624 (print), 1531-8362 (electronic)", ISSN-L = "1064-5624", bibdate = "Sat Nov 12 11:05:14 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1206.82009", acknowledgement = ack-nhfb, classmath = "82B10 (Quantum equilibrium statistical mechanics (general)) 68T50 (Natural language processing) 68Q45 (Formal languages)", fjournal = "Doklady Mathematics", journal-URL = "http://link.springer.com/journal/11472", keywords = "Bose--Einstein statistics", language = "English. Russian original", } @Article{Maslov:2005:ZML, author = "V. P. Maslov", title = "The {Zipf--Mandelbrot} law: quantization and an application to the stock market", journal = j-RUSS-J-MATH-PHYS, volume = "12", number = "4", pages = "483--488", year = "2005", CODEN = "RJMPEL", ISSN = "1061-9208 (print), 1555-6638 (electronic)", ISSN-L = "1061-9208", MRclass = "91B28 (82B99)", MRnumber = "2201312 (2006i:91053)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Russian Journal of Mathematical Physics", } @Article{McAllister:2005:ACE, author = "James W. McAllister", title = "Algorithmic compression of empirical data: reply to {Twardy}, {Gardner}, and {Dowe}", journal = j-STUD-HIST-PHILOS-SCI, volume = "36", number = "2", pages = "403--410", month = jun, year = "2005", CODEN = "SHPSB5", DOI = "https://doi.org/10.1016/j.shpsa.2005.04.005", ISSN = "0039-3681 (print), 1879-2510 (electronic)", ISSN-L = "0039-3681", bibdate = "Mon Nov 7 12:11:58 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/shps-a.bib; http://www.sciencedirect.com/science/journal/00393681", note = "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.", URL = "http://www.sciencedirect.com/science/article/pii/S0039368105000221", acknowledgement = ack-nhfb, fjournal = "Studies in History and Philosophy of Science Part A", journal-URL = "http://www.sciencedirect.com/science/journal/00393681", } @Article{McCowan:2005:AUZ, author = "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F. Hanser", title = "The appropriate use of {Zipf}'s law in animal communication studies", journal = j-ANIM-BEHAV, volume = "69", number = "1", pages = "F1--F7", day = "20", month = jan, year = "2005", CODEN = "ANBEA8", DOI = "https://doi.org/10.1016/j.anbehav.2004.09.002", ISSN = "0003-3472 (print), 1095-8282 (electronic)", ISSN-L = "0003-3472", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S000334720400346X", acknowledgement = ack-nhfb, fjournal = "Animal Behaviour", journal-URL = "http://www.sciencedirect.com/science/journal/00033472", keywords = "Zipf's Law", } @Article{Miller:2005:BLV, author = "Steven J. Miller and A. Kontorovich", title = "{Benford}'s law, values of {$L$}-functions and the $ 3 x + 1 $ problem", journal = j-ACTA-ARITHMETICA, volume = "120", number = "3", pages = "269--297", month = "????", year = "2005", CODEN = "AARIA9", DOI = "https://doi.org/10.4064/aa120-3-4", ISSN = "0065-1036 (print), 1730-6264 (electronic)", ISSN-L = "0065-1036", MRclass = "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65, 46F12)", bibdate = "Tue Feb 26 06:11:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Acta Arithmetica", journal-URL = "https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/all", } @InProceedings{Nagasaka:2005:BLD, author = "Kenji Nagasaka", editor = "G. Barat and H. Daud{\'e} and M. Laurent and P. Liardet and S. Louboutin and A. Thomas", booktitle = "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July 4--8, 2005, Universit{\'e} de Provence and Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS Marseilles, France}", title = "{Benford}'s law with different basis", publisher = "????", address = "????", pages = "1--2", year = "2005", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 18:49:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://atlas-conferences.com/c/a/r/e/47.htm", acknowledgement = ack-nhfb, } @Article{Newman:2005:PLP, author = "M. E. J. Newman", title = "Power laws, {Pareto} distributions and {Zipf}'s law", journal = j-CONTEMP-PHYS, volume = "46", number = "5", pages = "323--351", month = sep, year = "2005", CODEN = "CTPHAF", DOI = "https://doi.org/10.1080/00107510500052444", ISSN = "0010-7514 (print), 1366-5812 (electronic)", ISSN-L = "0010-7514", bibdate = "Thu Feb 18 20:07:22 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/contempphys.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", abstract = "When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, forest fires, solar flares, moon craters and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.", acknowledgement = ack-nhfb, fjournal = "Contemporary Physics", journal-URL = "http://www.tandfonline.com/loi/tcph20", keywords = "Benford's Law; critical phenomena; Legendre beta function; Pareto distribution; percolation; phase transitions; power-law distributions; random walks; Riemann zeta function; scale-free distributions; Yule process; Zipf's Law", remark = "This article is an excellent survey of continuous and discrete distributions that follow a power law, and some that do not. It is well worth reading.", subject = "astrophysics; atomic and nuclear physics; chemical physics; computational physics; condensed matter physics; environmental physics; experimental physics; general physics; particle and high energy physics; plasma physics; space science; theoretical physics", } @Article{Nigrini:2005:ACI, author = "Mark Nigrini", title = "An assessment of the change in the incidence of earnings management around the {Enron--Andersen} episode", journal = "Review of Accounting and Finance", volume = "4", number = "1", pages = "92--110", month = "????", year = "2005", DOI = "https://doi.org/10.1108/eb043420", ISSN = "1475-7702 (print), 1758-7700 (electronic)", ISSN-L = "1475-7702", bibdate = "Fri Mar 22 09:08:37 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.emeraldinsight.com/journals.htm?issn=1475-7702&volume=4&issue=1&articleid=1657234", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Article{Nitsch:2005:ZZ, author = "Volker Nitsch", title = "{Zipf} zipped", journal = j-J-URBAN-ECON, volume = "57", number = "1", pages = "86--100", day = "15", month = jan, year = "2005", CODEN = "JUECDW", DOI = "https://doi.org/10.1016/j.jue.2004.09.002", ISSN = "0094-1190 (print), 1095-9068 (electronic)", ISSN-L = "0094-1190", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0094119004000981", acknowledgement = ack-nhfb, fjournal = "Journal of Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/00941190", keywords = "Zipf's Law", } @Article{Perline:2005:SWF, author = "Richard Perline", title = "Strong, weak and false inverse power laws", journal = j-STAT-SCI, volume = "20", number = "1", pages = "68--88", month = "????", year = "2005", CODEN = "STSCEP", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", bibdate = "Fri Nov 18 12:15:56 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistical Science", journal-URL = "http://projecteuclid.org/all/euclid.ss", keywords = "Benford's Law", } @Book{Posch:2005:ZTP, author = "Peter N. Posch", title = "{Ziffernanalyse in Theorie und Praxis: Testverfahren zur F{\"a}lschungsaufsp{\"u}rung mit Benfords Gesetz}", publisher = "Shaker", address = "Aachen, Germany", pages = "iv + 87 + v", year = "2005", ISBN = "3-8322-4492-1", ISBN-13 = "978-3-8322-4492-7", LCCN = "????", bibdate = "Mon Feb 18 18:01:33 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.gbv.de:20011/gvk", price = "EUR 29.80 (DE)", series = "Berichte aus der Statistik", URL = "http://www.gbv.de/dms/hbz/toc/ht014717371.pdf", acknowledgement = ack-nhfb, } @Article{Rousseau:2005:RFE, author = "Ronald Rousseau", title = "{Robert Fairthorne} and the empirical power laws", journal = j-J-DOC, volume = "61", number = "2", pages = "194--202", month = "????", year = "2005", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/00220410510585188", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 06:42:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", remark = "Review of \cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.", } @Article{Rowlands:2005:EAD, author = "Ian Rowlands", title = "{Emerald} authorship data, {Lotka}'s law and research productivity", journal = j-ASLIB-PROC, volume = "57", number = "1", pages = "5--10", month = "????", year = "2005", CODEN = "ASLPAO", DOI = "https://doi.org/10.1108/00012530510579039", ISSN = "0001-253X (print), 1758-3748 (electronic)", ISSN-L = "0001-253X", bibdate = "Fri Nov 25 07:25:01 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "ASLIB Proceedings", keywords = "brand loyalty; publishing; research results", remark = "This paper applies Lotka's Law to the question of the likelihood of an author remaining with a particular publisher.", } @Article{Schaefer:2005:AIF, author = "Christin Schaefer and J{\"o}rg-Peter Schr{\"a}pler and Klaus-Robert M{\"u}ller and Gert G. Wagner", title = "Automatic Identification of Faked and Fraudulent Interviews in the {German SOEP}", journal = "Journal of Applied Social Science Studies", volume = "125", number = "??", pages = "183--193", month = "", year = "2005", DOI = "", bibdate = "Sat Sep 10 14:35:50 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.diw.de/documents/publikationen/73/diw_01.c.42515.de/dp441.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law; SOEP (German Socio-Economic Panel Study)", remark = "Cannot find online archive of this journal: Web links to it are dead.", } @Article{Shan:2005:GZD, author = "Shi Shan", title = "On the generalized {Zipf} distribution. {Part I}", journal = j-INFO-PROC-MAN, volume = "41", number = "6", pages = "1369--1386", day = "1", month = dec, year = "2005", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/j.ipm.2005.03.003", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S030645730500018X", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", keywords = "Zipf's Law", } @Article{Soo:2005:ZLC, author = "Kwok Tong Soo", title = "{Zipf's Law} for cities: a cross-country investigation", journal = j-REG-SCI-URBAN-ECON, volume = "35", number = "3", pages = "239--263", day = "1", month = may, year = "2005", CODEN = "RSUEDM", DOI = "https://doi.org/10.1016/j.regsciurbeco.2004.04.004", ISSN = "0166-0462 (print), 1879-2308 (electronic)", ISSN-L = "0166-0462", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S016604620400033X", acknowledgement = ack-nhfb, fjournal = "Regional Science and Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/01660462", keywords = "Zipf's Law", } @Article{Stadje:2005:APD, author = "Wolfgang Stadje", title = "Asymptotic properties of digit sequences of random numbers", journal = j-MATH-NACHR, volume = "278", number = "10", pages = "1209--1229", month = "????", year = "2005", CODEN = "MTMNAQ", DOI = "https://doi.org/10.1002/mana.200310303", ISSN = "0025-584X", ISSN-L = "0025-584X", bibdate = "Mon Feb 18 06:36:36 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1073.11053", acknowledgement = ack-nhfb, fjournal = "Mathematische Nachrichten", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616", keywords = "ergodicity; limit theorem; Markov chain; moments; occurrence probability; random digit sequence; stationary digits; transition function", ZMclass = "11K31 (Special sequences); 60G10 (Stationary processes); 60J05 (Discrete-time Markov processes on general state spaces); 60F99 (Limit theorems (probability))", } @TechReport{Taylor:2005:TMT, author = "Jonathan Taylor", title = "Too many ties? {An} empirical analysis of the {Venezuelan} recall referendum counts", type = "Technical report", number = "??", institution = "Department of Statistics, Stanford University", address = "Stanford, CA 94305, USA", year = "2005", bibdate = "Fri Feb 15 18:29:53 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://esdata.info/pdf/Taylor-Ties.pdf; http://www.benfordonline.net/fullreference/577", acknowledgement = ack-nhfb, remark = "Cited in \cite{Pericchi:2011:QAD}, with ``Statist. Sci. To appear 2009''. However, the article is not yet found there in February 2013. This report was issued as a result of the Carter Center's investigation of fairness of 2004 voting in Venezuela. Its conclusion, that there was no demonstrable electoral fraud, has been challenged; see \cite{Pericchi:2011:QAD}.", } @Article{Twardy:2005:EDS, author = "Charles Twardy and Steve Gardner and David L. Dowe", title = "Empirical data sets are algorithmically compressible: reply to {McAllister}?", journal = j-STUD-HIST-PHILOS-SCI, volume = "36", number = "2", pages = "391--402", month = jun, year = "2005", CODEN = "SHPSB5", DOI = "https://doi.org/10.1016/j.shpsa.2005.04.004", ISSN = "0039-3681 (print), 1879-2510 (electronic)", ISSN-L = "0039-3681", bibdate = "Mon Nov 7 12:11:58 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/shps-a.bib; http://www.sciencedirect.com/science/journal/00393681", note = "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.", URL = "http://www.sciencedirect.com/science/article/pii/S003936810500021X", acknowledgement = ack-nhfb, fjournal = "Studies in History and Philosophy of Science Part A", journal-URL = "http://www.sciencedirect.com/science/journal/00393681", } @Article{vanLeijenhorst:2005:FDH, author = "D. C. van Leijenhorst and Th. P. van der Weide", title = "A formal derivation of {Heaps}' law", journal = j-INFO-SCI, volume = "170", number = "2--4", pages = "263--272", year = "2005", CODEN = "ISIJBC", DOI = "https://doi.org/10.1016/j.ins.2004.03.006", ISSN = "0020-0255 (print), 1872-6291 (electronic)", ISSN-L = "0020-0255", MRclass = "60C05", MRnumber = "2120894 (2005h:60024)", bibdate = "Sat Nov 12 10:28:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Word frequencies in text documents can be reasonably described by the Mandelbrot distribution, which has Zipf's law as a special case. Furthermore, the growth of vocabulary size as a function of the text size (its number of words) has been described in Heaps' law. It has been shown that these two experimental laws are related. In this paper we go a step further, and provide a (formal) derivation of Heaps' law from the Mandelbrot distribution. We also provide a specification of the validity area for applying Heaps' law.", acknowledgement = ack-nhfb, ajournal = "Inform. Sci.", fjournal = "Information Sciences. An International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/00200255", } @Book{Wells:2005:PNM, author = "D. G. (David G.) Wells", title = "Prime Numbers: the Most Mysterious Figures in Math", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xv + 272", year = "2005", ISBN = "0-471-46234-9 (hardcover), 0-471-71892-0 (ebook)", ISBN-13 = "978-0-471-46234-7 (hardcover), 978-0-471-71892-5 (e-book)", LCCN = "QA246 .W35 2005", bibdate = "Wed Feb 21 14:25:53 MST 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0616/2004019974-b.html; http://www.loc.gov/catdir/enhancements/fy0616/2004019974-d.html; http://www.loc.gov/catdir/toc/ecip0422/2004019974.html", abstract = "A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd{\H{o}}s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know-and much more that you never suspected-about prime numbers, including: the unproven Riemann hypothesis and the power of the zeta function, the ``Primes is in P'' algorithm, the sieve of Eratosthenes of Cyrene, Fermat and Fibonacci numbers, the Great Internet Mersenne Prime Search, and much, much more.", acknowledgement = ack-nhfb, libnote = "Not yet in my library.", tableofcontents = "Introduction \\ List of Entries \\ abc conjecture \\ abundant number \\ AKS algorithm for primality testing \\ aliquot sequences (sociable chains) \\ almost-primes \\ amicable numbers \\ amicable curiosities \\ Andrica's conjecture \\ arithmetic progressions, of primes \\ Aurifeuillian factorization \\ average prime \\ Bang's theorem \\ Bateman's conjecture \\ Beal's conjecture, and prize \\ Benford's law \\ Bernoulli numbers \\ Bernoulli number curiosities \\ Bertrand's postulate \\ Bonse's inequality \\ Brier numbers \\ Brocard's conjecture \\ Brun's constant \\ Buss's function \\ Carmichael numbers \\ Catalan's conjecture \\ Catalan's Mersenne conjecture \\ Champion numbers \\ Chinese remainder theorem \\ cicadas and prime periods \\ circle, prime \\ circular prime \\ Clay prizes, the \\ compositorial \\ concatenation of primes \\ conjectures \\ consecutive integer sequence \\ consecutive numbers \\ consecutive primes, sums of \\ Conway's prime-producing machine \\ cousin primes \\ Cullen primes \\ Cunningham project \\ Cunningham chains \\ decimals, recurring (periodic) \\ deficient number \\ deletable and truncatable primes \\ Demlo numbers \\ descriptive primes \\ Dickson's conjecture \\ digit properties \\ Diophantus (c.200: died 284) \\ Dirichlet's theorem and primes in arithmetic series \\ distributed computing \\ divisibility tests \\ divisors (factors) \\ economical numbers \\ Electronic Frontier Foundation \\ elliptic curve primality proving \\ emirp \\ Eratosthenes of Cyrene, the sieve of \\ Erd{\H{o}}s, Paul (1913--1996) \\ errors \\ Euclid \\ Unique factorisation \\ $\sqrt{2}$ is irrational \\ Euclid and the infinity of primes \\ Consecutive composite numbers \\ Primes of the form $4 n + 3$ \\ A recursive sequence \\ Euclid and the first perfect number \\ Euclidean algorithm \\ Euler, Leonhard (1707--1783) \\ Euler's convenient numbers \\ The Basel problem \\ Euler's constant \\ Euler and the reciprocals of the primes \\ Euler's phi [totient] function \\ Carmichael's totient function conjecture \\ Curiosities of $\phi(n)$ \\ Euler's quadratic \\ The Lucky Numbers of Euler \\ factorial \\ factors of factorials \\ factorial primes \\ factorial sums \\ factorials, double, triple, \ldots{} \\ factorization, methods of \\ factors of particular forms \\ Fermat's algorithm \\ Legendre's method \\ How difficult is it to factor large numbers? \\ quantum computation \\ Feit--Thompson conjecture \\ Fermat Pierre de (1607--1665) \\ Fermat's Little Theorem \\ Fermat quotient \\ Fermat and primes of the form $x^2 + y^2$ \\ Fermat's conjecture, Fermat numbers and Fermat primes \\ Fermat factorisation, from $F_6$ to $F_{30}$ \\ Generalized Fermat numbers \\ Fermat's Last Theorem \\ The first case of Fermat's Last Theorem: \\ Wall--Sun--Sun primes \\ Fermat--Catalan equation and conjecture \\ Fibonacci numbers \\ divisibility properties \\ Fibonacci curiosities \\ {\'E}douard Lucas and the Fibonacci numbers \\ Fibonacci composite sequences \\ formulae for primes \\ Fortunate numbers and Fortune's conjecture \\ gaps between primes, and composite runs \\ Gauss Johann Carl Friedrich (1777--1855) \\ Gauss and the distribution of primes \\ Gaussian primes \\ Gauss's circle problem \\ Gilbreath conjecture \\ GIMPS = Great Internet Mersenne Primes Search \\ Giuga's conjecture \\ Giuga numbers \\ Goldbach's conjecture \\ good primes \\ graph, prime number \\ Grimm's problem \\ Hardy, G. H. (1877--1947) \\ Hardy--Littlewood conjectures \\ heuristic reasoning \\ Hilbert's 23 problems \\ home prime \\ hypothesis H \\ illegal prime \\ inconsummate number \\ induction jumping champion \\ $k$-tuples conjecture, prime \\ knots, prime and composite \\ Landau, Edmund (1877--1938) \\ left-truncatable prime \\ Legendre A. M. (1752--1833) \\ Legendre's theorem (1808) \\ Lehmer, Derrick Norman (1867--1938) \\ Lehmer, Derrick Henry (1905--1991) \\ Linnik's constant \\ Liouville, Joseph (1809--1882) \\ Littlewood's theorem \\ the prime numbers race \\ Look and Say sequence \\ Lucas, {\'E}douard (1842--1891) \\ the Lucas sequence \\ primality testing \\ Lucas's game of calculation \\ the Lucas--Lehmer test \\ lucky numbers \\ the number of Lucky numbers and primes \\ `random' primes' \\ magic squares \\ Matijasevic and Hilbert's 10th problem \\ Mersenne numbers and Mersenne primes \\ Mersenne numbers \\ hunting for Mersenne primes \\ the coming of electronic computers \\ Mersenne prime conjectures \\ the New Mersenne Conjecture \\ how many Mersenne primes? \\ Eberhart's conjecture \\ factors of Mersenne Numbers \\ Lucas--Lehmer test for Mersenne primes \\ Mertens' theorem \\ Mertens' constant \\ Mill's theorem \\ Wright's theorem \\ mixed bag \\ multiplication, fast \\ Niven Numbers \\ odd numbers as $p + 2 a^2$ \\ Opperman's conjecture \\ palindromic primes \\ pandigital primes \\ Pascal's Triangle and the binomial coefficients \\ Pascal's triangle and Sierpinski's gasket \\ Pascal triangle curiosities \\ patents on prime numbers \\ P{\'e}pin's test for Fermat numbers \\ perfect numbers \\ odd perfect numbers \\ perfect, multiply \\ permutable primes \\ $o$, primes in the decimal expansion of \\ Pocklington's theorem \\ Polignac's conjectures \\ Polignac or obstinate numbers \\ powerful numbers \\ consecutive powerful numbers \\ primality testing \\ probabilistic methods \\ prime number graph \\ prime number theorem and the prime counting function \\ history \\ elementary proof \\ record calculations \\ estimating $p(n)$ \\ calculating $p(n)$ \\ a curiosity \\ prime pretender \\ primitive prime factor \\ primitive roots \\ Artin's conjecture \\ a curiosity \\ primorial \\ primorial primes \\ Proth's Theorem \\ pseudoperfect numbers \\ bases and pseudpoprimes \\ pseudoprimes, strong \\ public key encryption \\ pyramid, prime \\ Pythagorean triangles, prime \\ quadratic residues \\ residual curiosities \\ polynomial congruences \\ quadratic reciprocity, law of \\ Euler's criterion \\ Ramanujan, Srinivasa (1887--1920) \\ Highly Composite Numbers \\ randomness, of primes \\ Von Sternach and a prime random walk \\ record primes \\ some records \\ repunits, prime \\ Rhonda numbers \\ Riemann hypothesis \\ Farey sequence and Riemann's Hypothesis \\ Riemann's hypothesis and $\sigma(n)$, the sum of divisor function \\ squarefree and blue and red numbers \\ the Mertens conjecture \\ Riemann Hypothesis curiosities \\ Riesel number \\ right-truncatable prime \\ RSA algorithm \\ Martin Gardner's challenge \\ RSA Factoring Challenge, The New \\ Ruth--Aaron numbers \\ Scherk's conjecture \\ semi-primes \\ sexy primes \\ Shank's Conjecture \\ Siamese primes \\ Sierpinski numbers \\ Sierpinski strings \\ Sierpinski's quadratic \\ Sierpinski's $\phi(n)$ conjecture \\ Sloane's On-Line Encyclopedia of Integer Sequences \\ Smith numbers \\ Smith Brothers \\ smooth numbers \\ Sophie Germain primes \\ safe primes \\ square-free numbers \\ Stern prime \\ strong law of small numbers \\ triangular numbers \\ trivia \\ twin primes \\ twin curiosities \\ Ulam spiral \\ unitary divisors \\ unitary perfect \\ untouchable numbers \\ weird numbers \\ Wieferich primes \\ Wilson's theorem \\ twin primes \\ Wilson's quotient \\ Wilson primes \\ Wolstenholme's numbers, and theorems \\ more factors of Wolstenholme numbers \\ Woodall primes \\ zeta mysteries: the quantum connection \\ Appendix A: The First 500 Primes \\ Appendix B: Arithmetic Functions \\ Glossary \\ Bibliography \\ Index", } @Article{Aban:2006:PET, author = "Inmaculada B. Aban and Mark M. Meerschaert and Anna K. Panorska", title = "Parameter Estimation for the Truncated {Pareto} Distribution", journal = j-J-AM-STAT-ASSOC, volume = "101", number = "473", pages = "270--277", month = mar, year = "2006", CODEN = "JSTNAL", DOI = "https://doi.org/10.1198/016214505000000411", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Thu Aug 26 11:26:31 MDT 2010", bibsource = "http://www.amstat.org/publications/jasa/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", } @Article{Baskerville:2006:SEM, author = "Kim Baskerville and Maya Paczuski", title = "Subgraph ensembles and motif discovery using an alternative heuristic for graph isomorphism", journal = j-PHYS-REV-E, volume = "74", number = "??", pages = "051903", day = "3", month = nov, year = "2006", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.74.051903", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.74.051903", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Bohachevsky:2006:DBL, author = "Ihor O. Bohachevsky and Mark E. Johnson and Myron L. Stein", title = "A derivation of {Benford}'s law", journal = j-AM-J-MATH-MANAGE-SCI, volume = "26", number = "3--4", pages = "355--370", year = "2006", CODEN = "AMMSDX", ISSN = "0196-6324", ISSN-L = "0196-6324", MRclass = "60E99 (11K36)", MRnumber = "2312400 (2008h:60062)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Journal of Mathematical and Management Sciences", } @Article{Briscoe:2006:MLW, author = "Bob Briscoe and Andrew Odlyzko and Benjamin Tilly", title = "{Metcalfe's Law} is wrong --- communications networks increase in value as they add members --- but by how much?", journal = j-IEEE-SPECTRUM, volume = "43", number = "7", pages = "34--39", month = jul, year = "2006", CODEN = "IEESAM", DOI = "https://doi.org/10.1109/MSPEC.2006.1653003", ISSN = "0018-9235 (print), 1939-9340 (electronic)", ISSN-L = "0018-9235", bibdate = "Sat Jan 18 12:29:46 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeespectrum2000.bib", abstract = "This paper argues that Metcalfe's law, which states that the value of a communications network is proportional to the square of the number of its users, is incorrect. By seeming to assure that the value of a network would increase quadratically - proportionately to the square of the number of its participants - while costs would, at most, grow linearly, Metcalfe's law gave an air of credibility to the mad rush for growth and the neglect of profitability. The paper discusses the fundamental flaw of Metcalfe's law and describes how Zipf's law can be used as basis to justify the $ n \log (n) $ rule-of-thumb valuation of a general communications network of size $n$.", acknowledgement = ack-nhfb, fjournal = "IEEE Spectrum", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6", keywords = "Communication networks; communications network; Computer networks; Costs; Ethernet networks; Internet; Internet telephony; Investments; IP networks; Metcalfe Law; Profitability; profitability; rule-of-thumb valuation; Web pages; Web sites; Zipf law", } @InProceedings{Dallacasa:2006:TBS, author = "F. Dallacasa and Valerio Dallacasa", editor = "????", booktitle = "{5th International Conference: APLIMAT 2006, Slovak University of Technology, Bratislava}", title = "Temporal behaviour of stock data from {Benford}'s law", publisher = "????", address = "????", pages = "425--432", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 17:32:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", price = "US\$", URL = "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf", acknowledgement = ack-nhfb, } @Article{deMarchi:2006:AAS, author = "Scott de Marchi and James Hamilton", title = "Assessing the Accuracy of Self-Reported Data: an Evaluation of the Toxics Release Inventory", journal = j-J-RISK-UNCERT, volume = "32", number = "1", pages = "57--76", month = jan, year = "2006", CODEN = "JRUNEN", DOI = "https://doi.org/10.1007/s10797-006-6666-3", ISSN = "0895-5646 (print), 1573-0476 (electronic)", ISSN-L = "0895-5646", bibdate = "Fri Nov 25 11:25:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Risk and Uncertainty", journal-URL = "http://link.springer.com/journal/11166", } @Article{Dorogovtsev:2006:FON, author = "S. N. Dorogovtsev and J. F. F. Mendes and J. G. Oliveira", title = "Frequency of occurrence of numbers in the {World Wide Web}", journal = j-PHYSICA-A, volume = "360", number = "2", pages = "548--556", month = feb, year = "2006", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2005.06.064", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://arxiv.org/abs/physics/0504185; http://www.sciencedirect.com/science/article/pii/S0378437105006874", abstract = "The distribution of numbers in human documents is determined by a variety of diverse natural and human factors, whose relative significance can be evaluated by studying the numbers frequency of occurrence. Although it has been studied since the 1880's, this subject remains poorly understood. Here, we obtain the detailed statistics of numbers in the World Wide Web, finding that their distribution is a heavy-tailed dependence which splits in a set of power-law ones. In particular, we find that the frequency of numbers associated to western calendar years shows an uneven behavior: 2004 represents a singular critical point, appearing with a strikingly high frequency; as we move away from it, the decreasing frequency allows us to compare the amounts of existing information on the past and on the future. Moreover, while powers of ten occur extremely often, allowing us to obtain statistics up to the huge 10 127, non-round numbers occur in a much more limited range, the variations of their frequencies being dramatically different from standard statistical fluctuations. These findings provide a view of the array of numbers used by humans as a highly non-equilibrium and inhomogeneous system, and shed a new light on an issue that, once fully investigated, could lead to a better understanding of many sociological and psychological phenomena.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Critical point; Fluctuations; Power-law distributions; Search engines; Statistics of natural numbers; The World Wide Web", } @Article{Duranton:2006:SFZ, author = "Gilles Duranton", title = "Some foundations for {Zipf}'s law: Product proliferation and local spillovers", journal = j-REG-SCI-URBAN-ECON, volume = "36", number = "4", pages = "542--563", day = "1", month = jul, year = "2006", CODEN = "RSUEDM", DOI = "https://doi.org/10.1016/j.regsciurbeco.2006.03.008", ISSN = "0166-0462 (print), 1879-2308 (electronic)", ISSN-L = "0166-0462", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0166046206000354", acknowledgement = ack-nhfb, fjournal = "Regional Science and Urban Economics", journal-URL = "http://www.sciencedirect.com/science/journal/01660462", keywords = "Zipf's Law", } @Article{Egghe:2006:DHL, author = "L. Egghe", title = "The dependence of the height of a {Lorenz} curve of a {Zipf} function on the size of the system", journal = j-MATH-COMP-MODELLING, volume = "43", number = "7--8", pages = "870--879", day = "15", month = apr, year = "2006", CODEN = "MCMOEG", DOI = "https://doi.org/10.1016/j.mcm.2005.09.033", ISSN = "0895-7177 (print), 1872-9479 (electronic)", ISSN-L = "0895-7177", MRclass = "94A15 (91B82)", MRnumber = "2218323 (2006k:94033)", MRreviewer = "Ulrich Tamm", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S089571770500508X", acknowledgement = ack-nhfb, fjournal = "Mathematical and Computer Modelling", keywords = "Zipf's Law", } @Article{Gaite:2006:CSZ, author = "Jos{\'e} Gaite", title = "Cut-out sets and the {Zipf} law for fractal voids", journal = j-PHYSICA-D, volume = "223", number = "2", pages = "248--255", day = "15", month = nov, year = "2006", CODEN = "PDNPDT", DOI = "https://doi.org/10.1016/j.physd.2006.09.021", ISSN = "0167-2789 (print), 1872-8022 (electronic)", ISSN-L = "0167-2789", MRclass = "28A80", MRnumber = "2307212", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167278906003848", acknowledgement = ack-nhfb, fjournal = "Physica. D, Nonlinear phenomena", journal-URL = "http://www.sciencedirect.com/science/journal/01672789", keywords = "Zipf's Law", } @Article{Gan:2006:ZLS, author = "Li Gan and Dong Li and Shunfeng Song", title = "Is the {Zipf} law spurious in explaining city-size distributions?", journal = j-ECONOM-LETT, volume = "92", number = "2", pages = "256--262", day = "1", month = aug, year = "2006", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/j.econlet.2006.03.004", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176506000772", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Handurukande:2006:PSB, author = "S. B. Handurukande and A.-M. Kermarrec and F. {Le Fessant} and L. Massouli{\'e} and S. Patarin", title = "Peer sharing behaviour in the {eDonkey} network, and implications for the design of server-less file sharing systems", journal = j-OPER-SYS-REV, volume = "40", number = "4", pages = "359--371", month = oct, year = "2006", CODEN = "OSRED8", DOI = "https://doi.org/10.1145/1218063.1217970", ISSN = "0163-5980 (print), 1943-586X (electronic)", ISSN-L = "0163-5980", bibdate = "Fri Jun 20 17:14:10 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this paper we present an empirical study of a workload gathered by crawling the eDonkey network --- a dominant peer-to-peer file sharing system --- for over 50 days. We first confirm the presence of some known features, in particular the prevalence of free-riding and the Zipf-like distribution of file popularity. We also analyze the evolution of document popularity. We then provide an in-depth analysis of several clustering properties of such workloads. We measure the geographical clustering of peers offering a given file. We find that most files are offered mostly by peers of a single country, although popular files don't have such a clear home country. We then analyze the overlap between contents offered by different peers. We find that peer contents are highly clustered according to several metrics of interest. We propose to leverage this property by allowing peers to search for content without server support, by querying suitably identified semantic neighbours. We find via trace-driven simulations that this approach is generally effective, and is even more effective for rare files. If we further allow peers to query both their semantic neighbours, and in turn their neighbours' neighbours, we attain hit rates as high as over 55\% for neighbour lists of size 20.", acknowledgement = ack-nhfb, fjournal = "ACM SIGOPS Operating Systems Review", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597", keywords = "file sharing; peer-to-peer; simulation; trace", } @InCollection{Harremoes:2006:ZLH, author = "P. Harremo{\"e}s and F. Topsoe", editor = "Rudolf Ahlswede and others", booktitle = "General theory of information transfer and combinatorics", title = "{Zipf}'s law, hyperbolic distributions and entropy loss", volume = "4123", publisher = pub-SV, address = pub-SV:adr, pages = "788--792", year = "2006", DOI = "https://doi.org/10.1007/11889342_50", bibdate = "Sat Nov 12 11:15:28 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, ZMnumber = "1158.91481", abstract = "Zipf's law --- or Estoup-Zipf's law --- is an empirical fact of computational linguistics which relates rank and frequency of words in natural languages. The law suggests modelling by distributions of ``hyperbolic type''. We present a satisfactory general definition and an information-theoretical characterization of the resulting hyperbolic distributions. When applied to linguistics this leads to a property of stability and flexibility, explaining that a language can develop towards higher and higher expressive powers without changing its basic structure.", acknowledgement = ack-nhfb, classmath = "91F20 (Linguistics) 94A15 (General topics of information theory) 94A17 (Measures of information)", keywords = "entropy loss; hyperbolic distributions; Zipf's law", } @Article{Horn:2006:DSA, author = "B. Horn and M. Kreuzer and E. Kochs and G. Schneider", title = "Different States of Anesthesia Can Be Detected by {Benford's Law}", journal = "Journal of Neurosurgical Anesthesiology", volume = "18", number = "4", pages = "328--329", month = oct, year = "2006", ISSN = "0898-4921 (print), 1537-1921 (electronic)", ISSN-L = "0898-4921", bibdate = "Sat Sep 10 12:15:52 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Neurosurgical Anesthesiology", journal-URL = "http://www.edmgr.com/JNA/; http://journals.lww.com/jnsa/pages/default.aspx", keywords = "Benford's Law", } @TechReport{Humenberger:2006:BGV, author = "Hans Humenberger", title = "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on the distribution of the first digit of numbers]", type = "Report", institution = "Institut f{\"u}r Mathematik und Angewandte Statistik, Universit{\"a}t f{\"u}r Bodenkultur", address = "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria", month = aug, year = "2006", bibdate = "Sun Feb 17 09:37:40 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf", acknowledgement = ack-nhfb, language = "German", } @TechReport{Hurlimann:2006:BLB, author = "Werner H{\"u}rlimann", title = "{Benford's Law} from 1881 to 2006: a bibliography", type = "Report", address = "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland", pages = "15", day = "5", month = jul, year = "2006", bibdate = "Fri Mar 30 11:32:30 2007", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/pdf/math.ST/0607168", abstract = "On the occasion of the 125-th anniversary of Newcomb's paper, a bibliography of academic work related to Benford's law from its year of origin 1881 to 2006 has been compiled.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Law of Anomalous Numbers; Zipf's Law", remark = "This bibliography lists 325 references on the title subject, with these (years) and counts: (1881) 1, (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1, (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1, (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2, (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1, (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2, (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3, (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4, (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1, (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6, (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4, (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12, (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29, (2005) 34, (2006) 18.", } @Article{Hurlimann:2006:GBL, author = "Werner H{\"u}rlimann", title = "Generalizing {Benford}'s law using power laws: application to integer sequences", journal = "ArXiv Mathematics e-prints", month = jul, year = "2006", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......7166H", acknowledgement = ack-nhfb, eprint = "arXiv:math/0607166", keywords = "Mathematics - Statistics, Mathematics - Number Theory, 11B73, 11B83, 11K31, 62E15, 62E17", } @Article{Izsak:2006:MLE, author = "F. Izs{\'a}k", title = "Maximum likelihood estimation for constrained parameters of multinomial distributions --- Application to {Zipf--Mandelbrot} models", journal = j-COMPUT-STAT-DATA-ANAL, volume = "51", number = "3", pages = "1575--1583", day = "1", month = dec, year = "2006", CODEN = "CSDADW", DOI = "https://doi.org/10.1016/j.csda.2006.05.008", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", MRnumber = "2307527", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S016794730600154X", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", keywords = "Zipf's Law", } @TechReport{Judge:2006:DPS, author = "George Judge and Laura Schechter", title = "Detecting problems in survey data using {Benford}'s law", type = "Preprint", institution = "University of California at Berkeley and University of Wisconsin at Madison", address = "Berkeley, CA, USA and Madison, WI, USA", pages = "30", day = "1", month = nov, year = "2006", bibdate = "Sat Feb 16 18:12:29 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.aae.wisc.edu/lschechter/benford.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Kossovsky:2006:TBU, author = "Alex Ely Kossovsky", title = "Towards a Better Understanding of the Leading Digits Phenomena", journal = "ArXiv Mathematics e-prints", year = "2006", bibdate = "Mon Nov 21 06:46:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/math/0612627", abstract = "This article on leading digits (Benford's Law) contains the following: (i) An attempt at a comprehensive account on the leading digits phenomena, incorporating many of its existing explanations, proofs, and differing points of view. (ii) The finding that leading digits of random numbers derived from a chain of distributions that are linked via parameter selection are logarithmic in the limit as the number of sequences approaches infinity, and that empirically only around 5 or 6 sequences of such a distribution chain are needed to obtain results that are close enough to the logarithmic (i.e., rapid convergence). (iii) An outright exact logarithmic behavior for a 2-sequence chain whenever parametrical density is exactly logarithmic. (iv) An account on the existence of singularities in exponential growth rates with regards to the leading digits distributions of their series. (v) An account on several distributions that are intrinsically logarithmic or approximately so. (vi) A conceptual justification of Flehinger's iterated averaging scheme --- an algorithm that was presented without any clear motivation. (vii) A note on the close relationship of Flehinger's scheme and the chain of distribution to Hill's super distribution. (viii) A conceptual argument justifying the scale invariance principle --- a principle invoked in derivations of Benford's law. (ix) A note on the intimate connection between one-sided tail to the right in density distributions and logarithmic leading digit behavior.", acknowledgement = ack-nhfb, remark = "On 18 February 2013, the archive has 17 revisions of this article.", xxjournal = "CoRR", } @Article{Kristiansen:2006:BTZ, author = "K. de Lange Kristiansen and G. Helgesen and A. T. Skjeltorp", title = "Braid theory and {Zipf--Mandelbrot} relation used in microparticle dynamics", journal = j-EUR-PHYS-J-B, volume = "51", number = "3", pages = "363--371", month = jun, year = "2006", CODEN = "EPJBFY", DOI = "https://doi.org/10.1140/epjb/e2006-00241-7", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Sat Sep 8 18:31:14 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", } @Book{Kuipers:2006:UDS, author = "Lauwerens Kuipers and Harald Niederreiter", title = "Uniform distribution of sequences", publisher = pub-DOVER, address = pub-DOVER:adr, pages = "xviii + 390", year = "2006", ISBN = "0-486-45019-8 (paperback)", ISBN-13 = "978-0-486-45019-3 (paperback)", LCCN = "QA292 .K84 2006", bibdate = "Sat Nov 12 15:42:53 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html; http://www.loc.gov/catdir/toc/fy0612/2005056064.html", acknowledgement = ack-nhfb, remark = "Originally published in \cite{Kuipers:1974:UDS}.", subject = "Sequences (Mathematics); Uniform distribution (Probability theory)", } @Article{Kulikova:2006:HFD, author = "A. A. Kulikova and Yu. V. Prokhorov and V. I. Khokhlov", title = "{H.F.D.} ({$H$}-function Distribution) and {Benford's Law}. {I}", journal = j-THEORY-PROBAB-APPL, volume = "50", number = "2", pages = "311--315", month = jan, year = "2006", CODEN = "TPRBAU", DOI = "https://doi.org/10.1137/S0040585X97981706", ISSN = "0040-585X (print), 1095-7219 (electronic)", ISSN-L = "0040-585X", bibdate = "Wed May 19 18:14:51 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1", acknowledgement = ack-nhfb, fjournal = "Theory of probability and its applications", journal-URL = "http://epubs.siam.org/tvp", } @Article{Lagarias:2006:BLF, author = "Jeffrey C. Lagarias and K. Soundararajan", title = "{Benford}'s law for the $ 3 x + 1 $ function", journal = j-J-LOND-MATH-SOC-2, volume = "74", number = "2", pages = "289--303", year = "2006", CODEN = "JLMSAK", DOI = "https://doi.org/10.1112/S0024610706023131", ISSN = "0024-6107 (print), 1469-7750 (electronic)", ISSN-L = "0024-6107", MRclass = "37A45", MRnumber = "2269630 (2007h:37007)", MRreviewer = "Radhakrishnan Nair", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the London Mathematical Society. Second Series", journal-URL = "http://jlms.oxfordjournals.org/content/by/year", } @Article{Leinicke:2006:FFN, author = "Linda M. Leinicke and Joyce A. Ostrosky and W. Max Rexroad", title = "Fighting fraud by the numbers: Digital analysis primer", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2006", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:13:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294967620", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", keywords = "Benford's Law", } @Article{Leydesdorff:2006:CPL, author = "Loet Leydesdorff and Stephen Bensman", title = "Classification and power laws: the logarithmic transformation", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "57", number = "11", pages = "1470--1486", month = sep, year = "2006", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20467", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Sat Feb 16 18:31:04 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", keywords = "Benford's Law", } @Article{Lim:2006:BRB, author = "Nena Lim", title = "Book Review: {{\booktitle{The new forensics: investigating corporate fraud and the theft of intellectual property}}, J. Anastasi. John Wiley \& Sons, New Jersey (2003)}", journal = "Digital Investigation", volume = "3", number = "4", pages = "245--246", year = "2006", DOI = "https://doi.org/10.1016/j.diin.2006.10.002", ISSN = "1742-2876 (print), 1873-202X (electronic)", ISSN-L = "1742-2876", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S174228760600106X", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InCollection{Lu:2006:AFD, author = "Fletcher Lu and J. Efrim Boritz and Dominic Covvey", booktitle = "Advances in artificial intelligence", title = "Adaptive fraud detection using {Benford}'s law", volume = "4013", publisher = pub-SV, address = pub-SV:adr, pages = "347--358", year = "2006", DOI = "https://doi.org/10.1007/11766247_30", MRnumber = "2280590", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @InProceedings{Lu:2006:BCF, author = "F. Lu and J. E. Boritz", editor = "????", booktitle = "{Uncertainty in Artificial Intelligence: Proceedings of the 22nd Conference}", title = "Building a case for fraud using {Benford}'s law with reinforcement learning", publisher = "????", address = "????", pages = "??--??", year = "2006", bibdate = "Sat Feb 16 18:34:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InProceedings{Manaris:2006:IES, author = "Bill Manaris and Luca Pellicoro and George Pothering and Harland Hodges", editor = "????", booktitle = "{2006 IASTED International Conference on Artificial Intelligence and Applications (AIA 2006), February 13--16, 2006, Innsbruck, Austria}", title = "Investigating {Esperanto}'s statistical proportions relative to other languages using neural networks and {Zipf}'s law", publisher = "Acta Press", address = "????", pages = "1--7", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 18:41:37 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf", acknowledgement = ack-nhfb, } @Article{Maslov:2006:BGA, author = "V. P. Maslov", title = "{Bose} gas of anharmonic oscillators and a refinement of {Zipf}'s law", journal = j-TEORET-MATH-FIZ, volume = "148", number = "3", pages = "495--496", year = "2006", CODEN = "TMFZAL", DOI = "https://doi.org/10.1007/s11232-006-0117-2", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B10", MRnumber = "2283664", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", journal-URL = "http://link.springer.com/journal/11232", } @Article{Maslov:2006:NAD, author = "V. P. Maslov", title = "Negative asymptotic dimension, a new condensate, and their relation to the quantized {Zipf} law", journal = j-MAT-ZAMETKI, volume = "80", number = "6", pages = "856--863", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1007/s11006-006-0203-7", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "82B10 (20F69 53C23 81S10 91F20)", MRnumber = "2311613 (2008e:82005)", MRreviewer = "Artur E. Ruuge", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", journal-URL = "http://link.springer.com/journal/11006", } @Article{Maslov:2006:RZM, author = "V. P. Maslov", title = "A refinement of the {Zipf--Mandelbrot} law and lacunarity in an ideal gas", journal = j-TEORET-MATH-FIZ, volume = "147", number = "3", pages = "511--512", year = "2006", CODEN = "TMFZAL", DOI = "https://doi.org/10.1007/s11232-006-0083-8", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B10", MRnumber = "2254729 (2007d:82007)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", journal-URL = "http://link.springer.com/journal/11232", } @Article{Maslov:2006:ZLR, author = "V. P. Maslov and T. V. Maslova", title = "On {Zipf}'s law and rank distributions in linguistics and semiotics", journal = j-MAT-ZAMETKI, volume = "80", number = "5", pages = "718--732", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1007/s11006-006-0189-1", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "60C05 (62-07 62P99)", MRnumber = "2311586 (2008g:60027)", MRreviewer = "Konstantin E. Feldman", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "Zbl 1134.62086", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", journal-URL = "http://link.springer.com/journal/11006", } @Article{Maslova:2006:ZLM, author = "T. V. Maslova", title = "{Zipf}'s law and {Maslov}'s formula as applied to semiotic systems", journal = j-DOKL-MATH, volume = "74", number = "3", pages = "917--920", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1134/S1064562406060330", ISSN = "1064-5624 (print), 1531-8362 (electronic)", ISSN-L = "1064-5624", bibdate = "Sat Nov 12 11:13:35 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "pre05824774", acknowledgement = ack-nhfb, classmath = "62E20 (Asymptotic distribution theory in statistics) 82B03 (Foundations of equilibrium statistical mechanics)", fjournal = "Doklady Mathematics", journal-URL = "http://link.springer.com/journal/11472", language = "English. Russian original", } @Article{Maslova:2006:ZLV, author = "T. V. Maslova", title = "On the {Zipf} law and the {V. P. Maslov} formula for semiotic systems", journal = j-DOKL-AKAD-NAUK, volume = "411", number = "6", pages = "754--757", year = "2006", CODEN = "DANKAS", ISSN = "0869-5652", ISSN-L = "0869-5652", MRclass = "62E20 (82B03)", MRnumber = "2451374", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii Nauk", journal-URL = "http://istina.msu.ru/journals/366838/", } @InProceedings{Mebane:2006:DAE, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2006 Annual Meeting of the Midwest Political Science Association, April 20--23, Palmer House, Chicago}", title = "Detecting Attempted Election Theft: Vote Counts, Voting Machines and {Benford's Law}", publisher = "????", address = "????", pages = "i + 50", day = "19", month = apr, year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:14:14 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/mw06.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2006:EFS, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{Election Fraud Conference, Salt Lake City, Utah, September 29--30, 2006}", title = "Election Forensics: The Second-digit {Benford's Law} Test and Recent {American Presidential} Elections", publisher = "????", address = "????", pages = "??--??", year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Feb 15 18:22:27 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www-personal.umich.edu/~wmebane/fraud06.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2006:EFV, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2006 Summer Meeting of the Political Methodology Society, UC-Davis, July 20--22, 2006}", title = "Election Forensics: Vote Counts and {Benford's Law}", publisher = "????", address = "????", pages = "ii + 48", day = "18", month = jul, year = "2006", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:01:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm06.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law; Second Digit Benford Law (2BL)", } @Article{Mellor:2006:GKZ, author = "Andy Mellor", title = "Book Review: {G. K. Zipf, \booktitle The Psycho-biology of Language (1935) MIT Press, Cambridge, MA}", journal = j-SYSTEM, volume = "34", number = "3", pages = "455--457", day = "20", month = sep, year = "2006", CODEN = "????", DOI = "https://doi.org/10.1016/j.system.2006.07.004", ISSN = "0346-251X (print), 1879-3282 (electronic)", ISSN-L = "0346-251X", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0346251X06000674", acknowledgement = ack-nhfb, fjournal = "System", journal-URL = "http://www.sciencedirect.com/science/journal/0346251X", keywords = "Zipf's Law", } @Article{Metwally:2006:IES, author = "Ahmed Metwally and Divyakant Agrawal and Amr {El Abbadi}", title = "An integrated efficient solution for computing frequent and top-$k$ elements in data streams", journal = j-TODS, volume = "31", number = "3", pages = "1095--1133", month = sep, year = "2006", CODEN = "ATDSD3", DOI = "https://doi.org/10.1145/1166074.1166084", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Tue Oct 17 05:41:01 MDT 2006", bibsource = "http://www.acm.org/pubs/contents/journals/tods/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See comments in \cite{Liu:2010:CIE}.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Database Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", } @Book{Miller:2006:IMN, author = "Steven J. Miller and Ramin Takloo-Bighash", title = "An Invitation to Modern Number Theory", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xx + 503", year = "2006", ISBN = "0-691-12060-9 (hardcover)", ISBN-13 = "978-0-691-12060-7 (hardcover)", LCCN = "QA241 .M5344 2006", bibdate = "Fri Mar 22 08:57:57 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Number theory", tableofcontents = "Part 1. Basic Number Theory \\ 1. Mod p Arithmetic, Group Theory and Cryptography \\ 2. Arithmetic Functions \\ 3. Zeta and L-Functions \\ 4. Solutions to Diophantine Equations \\ Part 2. Continued Fractions and Approximations \\ 5. Algebraic and Transcendental Numbers \\ 6. The Proof of Roth's Theorem \\ 7. Introduction to Continued Fractions \\ Part 3. Probabilistic Methods and Equidistribution \\ 8. Introduction to Probability \\ 9. Applications of Probability: Benford's Law and Hypothesis Testing \\ 10. Distribution of Digits of Continued Fractions \\ 11. Introduction to Fourier Analysis \\ 12. f n k g and Poissonian Behavior \\ Part 4. The Circle Method \\ 13. Introduction to the Circle Method \\ 14. Circle Method: Heuristics for Germain Primes \\ Part 5. Random Matrix Theory and L-Functions \\ 15. From Nuclear Physics to L-Functions \\ 16. Random Matrix Theory: Eigenvalue Densities \\ 17. Random Matrix Theory: Spacings between Adjacent Eigenvalues \\ 18. The Explicit Formula and Density Conjectures \\ Appendix A. Analysis Review \\ Appendix B. Linear Algebra Review \\ Appendix C. Hints and Remarks on the Exercises \\ Appendix D. Concluding Remarks", } @Article{Miller:2006:MCL, author = "Steven J. Miller and M. J. Nigrini", title = "The {Modulo 1 Central Limit Theorem} and {Benford's Law} for Products", journal = "International Journal of Algebra", volume = "3", number = "3", pages = "119--130", month = jul, year = "2006", CODEN = "????", ISSN = "1312-8868 (print), 1314-7595 (electronic)", ISSN-L = "1312-8868", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......7686M; http://arxiv.org/abs/math/0607686", abstract = "We derive a necessary and sufficient condition for the sum of $M$ independent continuous random variables modulo $1$ to converge to the uniform distribution in $ L^1 ([0, 1]) $, and discuss generalizations to discrete random variables. A consequence is that if $ X_1, \ldots {}, X_M $ are independent continuous random variables with densities $ f_1, \ldots {}, f_M $, for any base $B$ as $ M \to \infty $ for many choices of the densities the distribution of the digits of $ X_1 * \cdots {} * X_M $ converges to Benford's law base $B$. The rate of convergence can be quantified in terms of the Fourier coefficients of the densities, and provides an explanation for the prevalence of Benford behavior in many diverse systems.", acknowledgement = ack-nhfb, eprint = "arXiv:math/0607686", journal-URL = "http://www.m-hikari.com/ija/index.html", keywords = "Mathematics - Probability, Mathematics - Classical Analysis and ODEs, 60F05, 60F25, 11K06 (Primary), 42A10, 42A61, 62E15 (Secondary)", } @Article{Miller:2006:OSB, author = "Steven J. Miller and M. J. Nigrini", title = "Order Statistics and {Benford's Law}", journal = "ArXiv Mathematics e-prints", month = jan, year = "2006", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006math......1344M", acknowledgement = ack-nhfb, eprint = "arXiv:math/0601344", keywords = "Mathematics - Probability, Mathematics - Number Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16 (Secondary)", } @Article{Moret:2006:NBL, author = "M. A. Moret and V. de Senna and M. G. Pereira and G. F. Zebende", title = "{Newcomb--Benford} Law in Astrophysical Sources", journal = j-INT-J-MOD-PHYS-C, volume = "17", number = "11", pages = "1597--1604", month = "????", year = "2006", CODEN = "IJMPEO", DOI = "https://doi.org/10.1142/S0129183106010054", ISSN = "0129-1831 (print), 1793-6586 (electronic)", ISSN-L = "0129-1831", bibdate = "Mon Nov 14 17:37:59 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M", acknowledgement = ack-nhfb, fjournal = "International Journal of Modern Physics C [Physics and Computers]", journal-URL = "http://www.worldscientific.com/loi/ijmpc", } @TechReport{Morrow:2006:BLF, author = "John Morrow", title = "{Benford's Law}, Families of Distributions and a Test Basis", type = "Report", institution = "University of Wisconsin--Madison", address = "Madison, WI, USA", month = "????", year = "2006", bibdate = "Tue Nov 22 20:44:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Revised draft of 9 October 2010.", URL = "http://www.johnmorrow.info/projects/benford/benfordMain.pdf", acknowledgement = ack-nhfb, lastaccess = "22 November 2011", } @Article{Moura:2006:ZLB, author = "Newton J. {Moura, Jr.} and Marcelo B. Ribeiro", title = "{Zipf} law for {Brazilian} cities", journal = j-J-THEOR-BIOL, volume = "219", number = "4", pages = "441--448", day = "15", month = jul, year = "2006", CODEN = "JTBIAP", DOI = "https://doi.org/10.1016/j.physa.2005.11.038", ISSN = "0022-5193 (print), 1095-8541 (electronic)", ISSN-L = "0022-5193", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437105012422", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Biology", journal-URL = "http://www.sciencedirect.com/science/journal/00225193", keywords = "Zipf's Law", } @TechReport{Nigrini:2006:BLA, author = "M. J. Nigrini and Steven J. Miller", title = "{Benford}'s law applied to hydrology data --- results and relevance to other geophysical data", type = "Preprint", institution = "????", address = "????", month = "????", year = "2006", bibdate = "Sat Feb 16 18:58:34 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Ogasawara:2006:ZLH, author = "Osamu Ogasawara and Shoko Kawamoto and Kousaku Okubo", title = "{Zipf}'s law and human transcriptomes: an explanation with an evolutionary model", journal = j-C-R-BIOL, volume = "326", number = "10--11", pages = "1097--1101", day = "1", month = jul, year = "2006", CODEN = "CRBOCM", DOI = "https://doi.org/10.1016/j.crvi.2003.09.031", ISSN = "1631-0691 (print), 1768-3238 (electronic)", ISSN-L = "1631-0691", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1631069103002294", acknowledgement = ack-nhfb, fjournal = "Comptes Rendus Biologies", journal-URL = "http://sciencedirect.com/science/journal/16310691", keywords = "Zipf's Law", } @Article{Pocheau:2006:SDL, author = "A. Pocheau", title = "The significant digit law: a paradigm of statistical scale symmetries", journal = j-EUR-PHYS-J-B, volume = "49", number = "4", pages = "491--511", month = feb, year = "2006", CODEN = "EPJBFY", DOI = "https://doi.org/10.1140/epjb/e2006-00084-2", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Sat Feb 16 15:06:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1140/epjb/e2006-00084-2", acknowledgement = ack-nhfb, fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", } @Article{Posch:2006:ADP, author = "Peter N. Posch and Welf A. Kreiner", title = "Analysing digits for portfolio formation and index tracking", journal = j-J-ASSET-MANAGE, volume = "7", number = "1", pages = "69--80", month = may, year = "2006", CODEN = "????", DOI = "https://doi.org/10.1057/palgrave.jam.2240203", ISSN = "1470-8272 (print), 1479-179X (electronic)", ISSN-L = "1470-8272", bibdate = "Fri Nov 25 11:19:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "A general methodology is proposed for using digit distributions as an approach to examining arbitrary datasets. With the Newcomb--Benford law as a starting point, a more general framework for digital analysis is developed. A new measure is proposed based on this framework, namely the Digital-Fit Factor (DFF). The use of index comparison on the S\&P500 and the Dow Jones Industrial Average is demonstrated. The DFF is then used to construct portfolios and measure their performance compared with that of the index. The average returns using the measure exceed the index composition by 6--14 percentage points per year by being more stable at the same time. Furthermore, these measures require only a very small proportion of the available information and are thus very efficient.", acknowledgement = ack-nhfb, fjournal = "Journal of Asset Management", keywords = "Benford's Law", } @Article{Ree:2006:PLD, author = "Suhan Ree", title = "Power-law distributions from additive preferential redistributions", journal = j-PHYS-REV-E, volume = "73", number = "??", pages = "026115", day = "15", month = feb, year = "2006", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.73.026115", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.73.026115", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @InProceedings{Sanches:2006:IRU, author = "Jo{\~a}o M. Sanches and Jorge S. Marques", booktitle = "{2006 IEEE International Conference on Image Processing, Atlanta, Georgia, 8--11 October 2006}", title = "Image Reconstruction using the {Benford Law}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "2029--2032", year = "2006", DOI = "https://doi.org/10.1109/ICIP.2006.312845", ISBN = "1-4244-0480-0", ISBN-13 = "978-1-4244-0480-3", ISSN = "1522-4880", bibdate = "Tue Nov 15 09:03:24 2011", bibsource = "DBLP; http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Tt has been claimed that the first digit of real signals follows a logarithmic distribution, called Benford law. This paper shows that this distribution is a natural prior for the gradient of several types of medical images (MRI, CT, ultrasound) and proposes a reconstruction algorithm based on the Benford law which does not require any parameter tuning. Experimental results are presented to illustrate the performance of the reconstruction algorithm", acknowledgement = ack-nhfb, } @Article{Saville:2006:UBL, author = "Adrian D. Saville", title = "Using {Benford's} Law to detect data error and fraud: An examination of companies listed on the {Johannesburg Stock Exchange}", journal = "South African Journal of Economic and Management Sciences", volume = "9", number = "3", pages = "341--354", month = "????", year = "2006", CODEN = "????", ISSN = "1015-8812 (print), 2222-3436 (electronic)", ISSN-L = "1015-8812", bibdate = "Fri Mar 22 09:12:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, journal-URL = "http://sajems.org/index.php/sajems/issue/archive", keywords = "Benford's Law", remark = "No issues online before volume 10, number 1, 2007.", } @Article{Schneider:2006:RAS, author = "Reto U. Schneider", title = "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber hundert Jahren stiess ein Astronom auf ein merkw{\"u}rdiges statistisches Gesetz, das heute Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The} puzzle of the worn pages: More than a hundred years ago an astronomer came across a strange statistical law that will now expose tax cheats]", journal = "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher Zeitung}", volume = "??", number = "1/06", month = "????", year = "2006", bibdate = "Fri Nov 18 12:18:17 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html; http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx", acknowledgement = ack-nhfb, language = "German", } @Article{Schuette:2006:TFZ, author = "Paul Schuette and Marcus C. Spruill", title = "Tail fit and the {Zipf--Pareto} law", journal = "Extremes", volume = "9", number = "3--4", pages = "243--261", year = "2006", CODEN = "????", DOI = "https://doi.org/10.1007/s10687-007-0030-6", ISSN = "1386-1999", ISSN-L = "1386-1999", MRnumber = "2367837", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Extremes. Statistical Theory and Applications in Science, Engineering and Economics", xxyear = "2007", } @Article{Sugimoto:2006:AFP, author = "Toyoaki Sugimoto and Naoto Miyoshi", title = "On the asymptotics of fault probability in least-recently-used caching with {Zipf}-type request distribution", journal = j-RAND-STRUCT, volume = "29", number = "3", pages = "296--323", year = "2006", CODEN = "RSALFD", DOI = "https://doi.org/10.1002/rsa.20098", ISSN = "1042-9832 (print), 1098-2418 (electronic)", ISSN-L = "1042-9832", MRclass = "68N25 (60C05 62E20 62P30 68P05 68U35)", MRnumber = "2254493 (2008h:68028)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Random Structures and Algorithms", keywords = "distributional tail asymptotics; least-recently-used caching; move-to-front algorithm; negative association; Zipf-type distribution", } @MastersThesis{TorresNunez:2006:NBL, author = "David A. {Torres N{\'u}{\~n}ez}", title = "{Newcomb--Benford's Law}: Applications to Electoral Processes, Bioinformatics, and the Stock Index", type = "{M.S.} thesis", school = "Center for Bioststatistics and Bioinformatics, University of Puerto Rico, R{\'\i}o Piedras Campus", address = "PO Box 23355, San Juan, PR 00931-3355", month = may, year = "2006", bibdate = "Fri Feb 15 18:34:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, advisor = "Luis R{\'a}ul Pericchi Guerra", } @Article{VandeWalle:2006:ZGK, author = "J. {Van de Walle} and K. Willems", title = "{Zipf, George Kingsley (1902--1950)}", journal = j-J-ECON-DYN-CONTROL, volume = "31", number = "7", pages = "756--757", day = "15", month = jul, year = "2006", CODEN = "JEDCDH", DOI = "https://doi.org/10.1016/B0-08-044854-2/04726-X", ISSN = "0165-1889 (print), 1879-1743 (electronic)", ISSN-L = "0165-1889", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/B008044854204726X", acknowledgement = ack-nhfb, fjournal = "Journal of Economic Dynamics and Control", keywords = "Zipf's Law", } @Article{Wilkinson:2006:RPC, author = "Leland Wilkinson", title = "Revising the {Pareto} Chart", journal = j-AMER-STAT, volume = "60", number = "4", pages = "332--334", month = nov, year = "2006", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/000313006X152243", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Thu Aug 26 21:48:27 MDT 2010", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Ackermann:2007:DMB, author = "Heiner Ackermann and Alantha Newman and Heiko R{\"o}glin and Berthold V{\"o}cking", title = "Decision-making based on approximate and smoothed {Pareto} curves", journal = j-THEOR-COMP-SCI, volume = "378", number = "3", pages = "253--270", day = "9", month = jun, year = "2007", CODEN = "TCSCDI", ISSN = "0304-3975 (print), 1879-2294 (electronic)", ISSN-L = "0304-3975", bibdate = "Tue Mar 29 08:55:49 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/03043975", acknowledgement = ack-nhfb, fjournal = "Theoretical Computer Science", journal-URL = "http://www.sciencedirect.com/science/journal/03043975", } @Article{Amin:2007:TVA, author = "Zeinab H. Amin", title = "Tests for the Validity of the Assumption that the Underlying Distribution of Life is {Pareto}", journal = j-J-APPL-STAT, volume = "34", number = "2", pages = "195--201", year = "2007", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Wed Aug 25 11:41:54 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Misc{Anonymous:2007:ZL, author = "Anonymous", key = "Zipf's Law", title = "{Zipf}'s law", year = "2007", bibdate = "Sat Jan 26 12:46:16 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/datacompression.bib", URL = "http://en.wikipedia.org/wiki/Zipf's_law", acknowledgement = ack-ds, lastaccess = "27 January 2013", rawdata = "Zipf's Law (2007) |http://en.wikipedia.org/wiki/Zipf's_law|", } @Article{Bakulina:2007:AZL, author = "M. P. Bakulina", title = "Application of {Zipf}'s law for text compression", journal = "Diskretn. Anal. Issled. Oper. Ser. 2", volume = "14", number = "2", pages = "3--13", year = "2007", CODEN = "????", ISSN = "1560-9901", ISSN-L = "1560-9901", MRclass = "94A15", MRnumber = "2542308 (2010i:94076)", MRreviewer = "I. Vajda", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}. Seriya 2", } @Article{Baskerville:2007:GAS, author = "Kim Baskerville and Peter Grassberger and Maya Paczuski", title = "Graph animals, subgraph sampling, and motif search in large networks", journal = j-PHYS-REV-E, volume = "76", number = "??", pages = "036107", day = "11", month = sep, year = "2007", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.76.036107", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036107", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Beeli:2007:FCG, author = "Gian Beeli and Michaela Esslen and Lutz J{\"a}ncke", title = "Frequency Correlates in Grapheme-Color Synaesthesia", journal = "Psychological Science", volume = "18", number = "9", pages = "788--792", year = "2007", DOI = "https://doi.org/10.1111/j.1467-9280.2007.01980.x", bibdate = "Sat Sep 10 10:35:44 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pss.sagepub.com/content/18/9/788.abstract", abstract = "Individuals with synaesthesia experience certain stimuli in more than one sensory modality. Most common is the linkage of letters and digits (graphemes) to colors. Whereas synaesthesia might be partly genetically determined, the linkages to specific colors are assumed to be learned. We present a systematic statistical analysis of synaesthetic color perception based on subjects' reproduction of individual colors for each grapheme, instead of simple verbal categorizations. The statistical analysis revealed that the color perceptions, measured with the HSL (hue, saturation, and luminance) scale, varied systematically among the different digits and letters. The frequencies of the digits and letters (in the German language) partly explained these systematic variations. However, digit frequency was more strongly related to color perception in the synaesthetes than was letter frequency. The results for digit and letter frequency indicate that experience with graphemes may shape synaesthetic color perception.", acknowledgement = ack-nhfb, eprint = "http://pss.sagepub.com/content/18/9/788.full.pdf+html", keywords = "Benford's Law", } @Article{Benguigui:2007:DMC, author = "Lucien Benguigui and Efrat Blumenfeld-Lieberthal", title = "A dynamic model for city size distribution beyond {Zipf}'s law", journal = j-PHYSICA-A, volume = "384", number = "2", pages = "613--627", day = "15", month = oct, year = "2007", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2007.05.059", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437107006061", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Berger:2007:DMN, author = "A. Berger and S. Siegmund", title = "On the distribution of mantissae in nonautonomous difference equations", journal = j-J-DIFFERENCE-EQU-APPL, volume = "13", number = "8--9", pages = "829--845", month = "????", year = "2007", CODEN = "JDEAEA", DOI = "https://doi.org/10.1080/10236190701388039", ISSN = "1023-6198 (print), 1563-5120 (electronic)", ISSN-L = "1023-6198", MRclass = "37A45 (37B55 39A11)", MRnumber = "2343033 (2008j:37010)", MRreviewer = "Reinhard Winkler", bibdate = "Tue Feb 19 09:37:52 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Second Memorial Issue in Honour of Bernd Aulbach.", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Difference Equations and Applications", journal-URL = "http://www.informaworld.com/1023-6198", } @Article{Berger:2007:NMO, author = "Arno Berger and Theodore P. Hill", title = "{Newton}'s Method Obeys {Benford}'s Law", journal = j-AMER-MATH-MONTHLY, volume = "114", number = "7", pages = "588--601", month = aug # "\slash " # sep, year = "2007", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "65G50 (37N30)", MRnumber = "2341322 (2008h:65016)", MRreviewer = "Uwe Sch{\"a}fer", bibdate = "Mon Jan 30 12:00:29 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i27642270; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/27642274", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Bernik:2007:BLA, author = "V. I. Bernik and N. I. Kalosha", title = "{Benford}'s law and the approximation of logarithms of natural numbers by rational numbers", journal = "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser. F{\=\i}z.-Mat. Navuk", volume = "??", number = "3", pages = "68--73, 127", year = "2007", CODEN = "????", ISSN = "0002-3574", ISSN-L = "0002-3574", MRclass = "11J83 (11A63 11K36)", MRnumber = "2398318 (2008j:11084)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Vests{\=\i} Natsyyanal\cprime na{\u\i} Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya Natsional\cprime no{\u\i} Akademii Nauk Belarusi. Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series", } @Article{Brown:2007:UZL, author = "R. J. C. Brown", title = "The use of {Zipf}'s law in the screening of analytical data: a step beyond {Benford}", journal = j-ANALYST, volume = "132", number = "4", pages = "344", year = "2007", CODEN = "ANALAO", DOI = "https://doi.org/10.1039/b618255k", ISSN = "0003-2654 (print), 1364-5528 (electronic)", ISSN-L = "0003-2654", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2007Ana...132..344B", abstract = "This study shows for the first time the effectiveness of Zipf's law in screening analytical data sets for outliers, data formatting and data transcription errors, particularly when the data sets are small. In the case of pollutant concentrations in ambient air, the multivariate nature of the measurement, and the relationship between the measured values of these multivariant quantities are the characteristics that allow a Zipf's law approach to data screening to be successful. Furthermore, it has been shown that Zipf's law has advantages over other novel data screening techniques, such as Benford's law, in terms of sensitivity and scope", acknowledgement = ack-nhfb, fjournal = "The Analyst", journal-URL = "http://pubs.rsc.org/en/journals/journalissues/an", } @Article{Chacko:2007:EPB, author = "Manoj Chacko and P. Yageen Thomas", title = "Estimation of a Parameter of Bivariate {Pareto} Distribution by Ranked Set Sampling", journal = j-J-APPL-STAT, volume = "34", number = "6", pages = "703--714", year = "2007", CODEN = "????", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", bibdate = "Wed Aug 25 11:41:54 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Cho:2007:BBL, author = "Wendy K. Tam Cho and Brian J. Gaines", title = "Breaking the ({Benford}) law: statistical fraud detection in campaign finance", journal = j-AMER-STAT, volume = "61", number = "3", pages = "218--223", month = aug, year = "2007", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/000313007X223496", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2393725", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496; http://www.tandfonline.com/doi/abs/10.1198/000313007X223496", abstract = "Benford's law is seeing increasing use as a diagnostic tool for isolating pockets of large datasets with irregularities that deserve closer inspection. Popular and academic accounts of campaign finance are rife with tales of corruption, but the complete dataset of transactions for federal campaigns is enormous. Performing a systematic sweep is extremely arduous; hence, these data are a natural candidate for initial screening by comparison to Benford's distributions.", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Clauset:2007:FST, author = "Aaron Clauset and Maxwell Young and Kristian Skrede Gleditsch", title = "On the Frequency of Severe Terrorist Events", journal = j-J-CONFL-RESOLUT, volume = "51", number = "1", pages = "58--87", month = feb, year = "2007", CODEN = "JCFRAL", DOI = "https://doi.org/10.1177/0022002706296157", ISSN = "0022-0027 (print), 1552-8766 (electronic)", ISSN-L = "0022-0027", bibdate = "Thu Nov 24 14:07:17 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jcr.sagepub.com; http://jcr.sagepub.com/content/51/1/58.abstract; http://www.jstor.org/journals/00220027.html", abstract = "In the spirit of Lewis Richardson's original study of the statistics of deadly conflicts, we study the frequency and severity of terrorist attacks worldwide since 1968. We show that these events are uniformly characterized by the phenomenon of ``scale invariance,'' that is, the frequency scales as an inverse power of the severity, $ P(x) \approx x{- \alpha } $. We find that this property is a robust feature of terrorism, persisting when we control for economic development of the target country, the type of weapon used, and even for short time scales. Further, we show that the center of the distribution oscillates slightly with a period of roughly 13 years, that there exist significant temporal correlations in the frequency of severe events, and that current models of event incidence cannot account for these variations or the scale invariance property of global terrorism. Finally, we describe a simple toy model for the generation of these statistics and briefly discuss its implications.", acknowledgement = ack-nhfb, fjournal = "Journal of Conflict Resolution", } @Article{Clauset:2007:PLDa, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-law distributions in empirical data", journal = "ArXiv Physics e-prints", day = "7", month = jun, year = "2007", bibdate = "Thu Feb 28 08:52:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "arXiv:0706.1062.", URL = "http://arxiv.org/abs/0706.1062v1", acknowledgement = ack-nhfb, pagecount = "27", } @Article{Clauset:2007:PLDb, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-law distributions in empirical data", journal = "ArXiv Physics e-prints", day = "2", month = feb, year = "2009", DOI = "https://doi.org/10.1137/070710111", bibdate = "Thu Feb 28 08:52:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "arXiv:0706.1062.", URL = "http://arxiv.org/abs/0706.1062v1", acknowledgement = ack-nhfb, pagecount = "43", } @Article{Decker:2007:GPC, author = "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E. Moses", title = "Global Patterns of City Size Distributions and Their Fundamental Drivers", journal = j-PLOS-ONE, volume = "2", number = "9", pages = "e934", month = sep, year = "2007", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0000934", ISSN = "1932-6203", bibdate = "Wed Feb 27 06:29:22 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000934", abstract = "Urban areas and their voracious appetites are increasingly dominating the flows of energy and materials around the globe. Understanding the size distribution and dynamics of urban areas is vital if we are to manage their growth and mitigate their negative impacts on global ecosystems. For over 50 years, city size distributions have been assumed to universally follow a power function, and many theories have been put forth to explain what has become known as Zipf's law (the instance where the exponent of the power function equals unity). Most previous studies, however, only include the largest cities that comprise the tail of the distribution. Here we show that national, regional and continental city size distributions, whether based on census data or inferred from cluster areas of remotely-sensed nighttime lights, are in fact lognormally distributed through the majority of cities and only approach power functions for the largest cities in the distribution tails. To explore generating processes, we use a simple model incorporating only two basic human dynamics, migration and reproduction, that nonetheless generates distributions very similar to those found empirically. Our results suggest that macroscopic patterns of human settlements may be far more constrained by fundamental ecological principles than more fine-scale socioeconomic factors.", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", keywords = "Zipf's Law", pagecount = "6", } @Article{Diekmann:2007:FDU, author = "Andreas Diekmann", title = "Not the First Digit! {Using} {Benford's Law} to Detect Fraudulent Scientific Data", journal = j-J-APPL-STAT, volume = "34", number = "3--4", pages = "321--329", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1080/02664760601004940", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", MRnumber = "2380543", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.tandf.co.uk/journals/routledge/02664763.html", URL = "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940", abstract = "Digits in statistical data produced by natural or social processes are often distributed in a manner described by `Benford's law'. Recently, a test against this distribution was used to identify fraudulent accounting data. This test is based on the supposition that first, second, third, and other digits in real data follow the Benford distribution while the digits in fabricated data do not. Is it possible to apply Benford tests to detect fabricated or falsified scientific data as well as fraudulent financial data? We approached this question in two ways. First, we examined the use of the Benford distribution as a standard by checking the frequencies of the nine possible first and ten possible second digits in published statistical estimates. Second, we conducted experiments in which subjects were asked to fabricate statistical estimates (regression coefficients). The digits in these experimental data were scrutinized for possible deviations from the Benford distribution. There were two main findings. First, both digits of the published regression coefficients were approximately Benford distributed or at least followed a pattern of monotonic decline. Second, the experimental results yielded new insights into the strengths and weaknesses of Benford tests. Surprisingly, first digits of faked data also exhibited a pattern of monotonic decline, while second, third, and fourth digits were distributed less in accordance with Benford's law. At least in the case of regression coefficients, there were indications that checks for digit-preference anomalies should focus less on the first (i.e., leftmost) and more on later digits.", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", keywords = "Benford's Law; data fabrication; digital analysis; distribution of digits from regression coefficients; first digit law; Zipf's Law", } @Article{Dumbgen:2007:EBA, author = "L. D{\"u}mbgen and C. Leuenberger", title = "Explicit bounds for the approximation error in {Benford}'s law", journal = "ArXiv e-prints", month = may, year = "2007", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0705.4488", keywords = "Mathematics - Probability, 60E15, 60F99", primaryclass = "math.PR", } @Article{Egghe:2007:UHL, author = "Leo Egghe", title = "Untangling {Herdan's Law} and {Heaps' Law}: Mathematical and informetric arguments", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "58", number = "5", pages = "702--709", month = mar, year = "2007", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20524", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:40 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", keywords = "Heaps' law in information retrieval; Herdan's law in linguistics", onlinedate = "2 Feb 2007", } @InProceedings{Fu:2007:GBL, author = "D. Fu and Y. Q. Shi and W. Su", editor = "Edward J. {Delp III} and Ping Wah Wong", booktitle = "{Society of Photo-Optical Instrumentation Engineers (SPIE)} Conference Series", title = "A generalized {Benford}'s law for {JPEG} coefficients and its applications in image forensics", volume = "6505", publisher = pub-SPIE, address = pub-SPIE:adr, month = feb, year = "2007", DOI = "https://doi.org/10.1117/12.704723", ISSN = "0277-786X (print), 1996-756X (electronic)", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series", URL = "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F", acknowledgement = ack-nhfb, } @InProceedings{Gava:2007:IQF, author = "Alexandre Majola Gava and Luiz {Roque de Souza Vitiello, Jr.}", booktitle = "{EnANPAD 2007: XXXI Encontro da ANPAD. Rio de Janeiro / RJ-22 a 26 de setembro de 2007}", title = "Inflation, Quarterly Financial Statements and Fraud: {Benford's Law} and the {Brazilian} Case", publisher = "????", address = "????", pages = "1--13", year = "2007", bibdate = "Thu Oct 13 07:36:53 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.anpad.org.br/diversos/trabalhos/EnANPAD/enanpad_2007/CONT/2007_CONA819.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Giles:2007:BLN, author = "D. E. Giles", title = "{Benford's Law} and naturally occurring prices in certain {eBay} auctions", journal = j-APPL-ECON-LETT, volume = "14", number = "3", pages = "157--161", year = "2007", CODEN = "????", DOI = "https://doi.org/10.1080/13504850500425667", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Wed Nov 16 09:49:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/toc/rael20/current", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", journal-URL = "http://www.tandfonline.com/loi/rael20", keywords = "Benford's Law; Fibonacci sequences; Lucas sequences", } @Article{Grendar:2007:ENP, author = "Marian Grendar and George Judge and Laura Schechter", title = "An empirical non-parametric likelihood family of data-based {Benford}-like distributions", journal = j-PHYSICA-A, volume = "380", number = "0", pages = "429--438", day = "1", month = jul, year = "2007", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2007.02.062", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://adsabs.harvard.edu/abs/2007PhyA..380..429G; http://www.sciencedirect.com/science/article/pii/S0378437107001963", abstract = "A mathematical expression known as Benford's law provides an example of an unexpected relationship among randomly selected sequences of first significant digits (FSDs). Newcomb [Note on the frequency of use of the different digits in natural numbers, Am. J. Math. 4 (1881) 39 40], and later Benford [The law of anomalous numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551 572], conjectured that {FSDs} would exhibit a weakly monotonic decreasing distribution and proposed a frequency proportional to the logarithmic rule. Unfortunately, the Benford {FSD} function does not hold for a wide range of scale-invariant multiplicative data. To confront this problem we use information-theoretic methods to develop a data-based family of alternative Benford-like exponential distributions that provide null hypotheses for testing purposes. Two data sets are used to illustrate the performance of generalized Benford-like distributions.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Empirical likelihood; First significant digit phenomenon; Information-theoretic method; Minimum-divergence distance measure; Relative frequencies", } @Article{Guo:2007:DIM, author = "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao and Xiaodong Zhang", title = "Does {Internet} media traffic really follow {Zipf}-like distribution?", journal = j-SIGMETRICS, volume = "35", number = "1", pages = "359--360", month = jun, year = "2007", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/1254882.1254929", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Fri Jun 27 09:42:48 MDT 2008", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "It is commonly agreed that Web traffic follows the Zipf-like distribution, which is an analytical foundation for improving Web access performance by client-server based proxy caching systems on the Internet. However, some recent studies have observed non-Zipf-like distributions of Internet media traffic in different content delivery systems. Due to the variety of media delivery systems and the diversity of media content, existing studies on media traffic are largely workload specific, and the observed access patterns are often different from or even conflict with each other. For Web media systems, study [3] reports that the access pattern of streaming media is Zipf-like in a university campus network, while study [2] finds that it is not Zipf-like in an enterprise media server.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "media; stretched exponential; Zipf-like", } @Article{Gupta:2007:IMS, author = "Arjun K. Gupta and Saralees Nadarajah", title = "Information matrices for some bivariate {Pareto} distributions", journal = j-APPL-MATH-COMP, volume = "184", number = "2", pages = "1069--1079", day = "15", month = jan, year = "2007", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Sat Jul 12 09:03:01 MDT 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @Article{Hand:2007:DDD, author = "David Hand", title = "Deception and Dishonesty with Data: Fraud in Science", journal = j-SIGNIF, volume = "4", number = "1", pages = "22--25", month = mar, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1111/j.1740-9713.2007.00215.x", ISSN = "1740-9705 (print), 1740-9713 (electronic)", ISSN-L = "1740-9705", bibdate = "Thu Nov 17 19:17:58 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/significance.bib", acknowledgement = ack-nhfb, ajournal = "Signif.", fjournal = "Significance", journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713", onlinedate = "02 March 2007", } @Article{Hasumi:2007:ITS, author = "Tomohiro Hasumi", title = "Interoccurrence time statistics in the two-dimensional {Burridge--Knopoff} earthquake model", journal = j-PHYS-REV-E, volume = "76", number = "??", pages = "026117", day = "29", month = aug, year = "2007", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.76.026117", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.026117", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf--Mandelbrot law", } @TechReport{Hungerbuhler:2007:BGF, author = "Norbert H{\"u}ngerb{\"u}hler", title = "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie die Mathematik Steuers{\"u}ndern das F{\"u}rchten lehrt} [{Benford's Law} on leading digits. Mathematics teaches tax evaders to fear]", type = "Report", institution = "EducETH", address = "Z{\"u}rich, Switzerland", pages = "24", day = "2", month = mar, year = "2007", bibdate = "Fri Nov 18 12:02:21 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf", acknowledgement = ack-nhfb, language = "German", lastaccess = "18 November 2011", remark = "This report has several nice figures, including photographs of Newcomb, Benford, and worn pages of log tables, and an amazing plot of the agreement of 200,125,088 mathematical constants with Benford's Law.", } @Article{Kumar:2007:DDD, author = "Kuldeep Kumar and Sukanto Bhattacharya", title = "Detecting the dubious digits: {Benford}'s law in forensic accounting", journal = j-SIGNIF, volume = "4", number = "2", pages = "81--83", month = jun, year = "2007", CODEN = "????", DOI = "https://doi.org/10.1111/j.1740-9713.2007.00234.x", ISSN = "1740-9705 (print), 1740-9713 (electronic)", ISSN-L = "1740-9705", MRnumber = "2380610", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/significance.bib", acknowledgement = ack-nhfb, ajournal = "Signif.", fjournal = "Significance", journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713", onlinedate = "07 June 2007", } @Article{Loetscher:2007:ENS, author = "T. Loetscher and P. Brugger", title = "Exploring Number Space by Random Digit Generation", journal = "Experimental Brain Research", volume = "180", number = "4", pages = "655--665", month = jul, year = "2007", CODEN = "EXBRAP", DOI = "https://doi.org/10.1007/s00221-007-0889-0", ISSN = "0014-4819 (print), 1432-1106 (electronic)", ISSN-L = "0014-4819", bibdate = "Sat Sep 10 13:10:08 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s00221-007-0889-0", acknowledgement = ack-nhfb, ajournal = "Exp. Brain Res.", journal-URL = "http://link.springer.com/journal/221", keywords = "Benford's Law", } @InProceedings{Lu:2007:UFD, author = "Fletcher Lu", booktitle = "{Knowledge Discovery in Databases: PKDD 2007}", title = "Uncovering Fraud in Direct Marketing Data with a Fraud Auditing Case Builder", publisher = pub-SV, address = pub-SV:adr, pages = "540--547", year = "2007", DOI = "https://doi.org/10.1007/978-3-540-74976-9_56", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/chapter/10.1007/978-3-540-74976-9_56", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Mansury:2007:EZL, author = "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s", title = "The emergence of {Zipf's Law} in a system of cities: an agent-based simulation approach", journal = j-J-ECON-DYN-CONTROL, volume = "31", number = "7", pages = "2438--2460", day = "15", month = jul, year = "2007", CODEN = "JEDCDH", DOI = "https://doi.org/10.1016/j.jedc.2006.08.002", ISSN = "0165-1889 (print), 1879-1743 (electronic)", ISSN-L = "0165-1889", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165188906001527", ZMnumber = "1163.91504", abstract = "This paper develops a spatial agent-based model to generate a system of cities that exhibits the statistical properties of the Zipf's Law. The numerical results suggest that the combination of bounded rationality and maximum heterogeneity of agents can produce a generic power-law relationship in the size distribution of cities, but does not always generate the Zipf's Law. We found sufficient conditions on the probability distribution of spatial reach to generate the Zipf's Law associated with unit power coefficient. Our model also indicates that the Zipf's Law breaks down unless the extent of agglomeration economies overwhelms the negative disagglomerating forces.", acknowledgement = ack-nhfb, classmath = "91B72 (Spatial models)", fjournal = "Journal of Economic Dynamics and Control", keywords = "complex systems; power laws; spatial agent based models; Zipf's Law", } @Article{Maslov:2007:PTZ, author = "V. P. Maslov", title = "Phase transitions of the zeroth kind and the quantization of the {Zipf} law", journal = j-TEORET-MATH-FIZ, volume = "150", number = "1", pages = "118--142", year = "2007", CODEN = "TMFZAL", DOI = "https://doi.org/10.1007/s11232-007-0008-1", ISSN = "0564-6162", ISSN-L = "0564-6162", MRclass = "82B26 (82B03)", MRnumber = "2325869 (2008g:82037)", MRreviewer = "N. N. Ganikhodjaev", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i Matematicheskaya Fizika", journal-URL = "http://link.springer.com/journal/11232", } @InProceedings{Mebane:2007:SD, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2007 Summer Meeting of the Political Methodology Society, Pennsylvania State University, July 18--21, 2007}", title = "Statistics for Digits", publisher = "????", address = "????", pages = "1--21", day = "2", month = jul, year = "2007", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:03:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm07.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Morris:2007:MRT, author = "Steven A. Morris and Michel L. Goldstein", title = "Manifestation of research teams in journal literature: a growth model of papers, authors, collaboration, coauthorship, weak ties, and {Lotka's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "58", number = "12", pages = "1764--1782", month = oct, year = "2007", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.20661", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:37 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "24 Aug 2007", } @Article{Nadarajah:2007:CPG, author = "Saralees Nadarajah and Samuel Kotz", title = "On the convolution of {Pareto} and gamma distributions", journal = j-COMP-NET-AMSTERDAM, volume = "51", number = "12", pages = "3650--3654", day = "22", month = aug, year = "2007", CODEN = "????", ISSN = "1389-1286 (print), 1872-7069 (electronic)", ISSN-L = "1389-1286", bibdate = "Sat Apr 2 08:42:20 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/13891286", acknowledgement = ack-nhfb, fjournal = "Computer Networks", journal-URL = "http://www.sciencedirect.com/science/journal/13891286", } @Article{Nicolaisen:2007:PPB, author = "Jeppe Nicolaisen and Birger Hj{\o}rland", title = "Practical potentials of {Bradford}'s law: a critical examination of the received view", journal = j-J-DOC, volume = "63", number = "3", pages = "359--377", month = "????", year = "2007", CODEN = "JDOCAS", DOI = "https://doi.org/10.1108/00220410710743298", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 11:58:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{Nigrini:2007:BLA, author = "Mark J. Nigrini and Steven J. Miller", title = "{Benford's Law} Applied to Hydrology Data --- Results and Relevance to Other Geophysical Data", journal = j-MATH-GEOL, volume = "39", number = "5", pages = "469--490", month = jul, year = "2007", CODEN = "MATGED", DOI = "https://doi.org/10.1007/s11004-007-9109-5", ISSN = "0882-8121 (print), 1573-8868 (electronic)", ISSN-L = "0882-8121", bibdate = "Sun Feb 17 13:35:42 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11004-007-9109-5; http://www.springerlink.com/content/m2274ng70435u3x6/", acknowledgement = ack-nhfb, fjournal = "Mathematical Geology", } @Article{Nye:2007:PEN, author = "J. Nye and C. Moul", title = "The Political Economy of Numbers: On the Application of {Benford's Law} to International Macroeconomic Statistics", journal = "{B. E.} Journal of Macroeconomics", volume = "7", number = "1", pages = "??--??", month = "????", year = "2007", CODEN = "????", DOI = "https://doi.org/10.2202/1935-1690.1449", ISSN = "1935-1690", ISSN-L = "1935-1690", bibdate = "Tue Nov 22 20:48:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.bepress.com/bejm/vol7/iss1/art17", acknowledgement = ack-nhfb, articleno = "17", fjournal = "Berkeley Electronic Press Journal of Macroeconomics", } @Article{Oteo:2007:DPE, author = "J. A. Oteo and J. Ros", title = "Double precision errors in the logistic map: Statistical study and dynamical interpretation", journal = j-PHYS-REV-E, volume = "76", pages = "036214", month = sep, year = "2007", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.76.036214", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:35:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.76.036214", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", issue = "3", journal-URL = "http://pre.aps.org/browse", pagecount = "8", remark = "From the abstract: ``a comparison with Benford?s law for the distribution of the leading digit of compilation of numbers is discussed.''", } @Article{Paech:2007:ZLN, author = "Kerstin Paech and Wolfgang Bauer and Scott Pratt", title = "{Zipf}'s law in nuclear multifragmentation and percolation theory", journal = j-PHYS-REV-C, volume = "76", number = "??", pages = "054603", day = "15", month = nov, year = "2007", CODEN = "PRVCAN", DOI = "https://doi.org/10.1103/PhysRevC.76.054603", ISSN = "0556-2813 (print), 1089-490X, 1538-4497", ISSN-L = "0556-2813", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevC.76.054603", acknowledgement = ack-nhfb, fjournal = "Physical Review C (Nuclear Physics)", journal-URL = "http://prc.aps.org/browse", keywords = "Zipf's Law", } @InProceedings{Perez-Gonzalez:2007:GBL, author = "F. P{\'e}rez-Gonz{\'a}lez and G. L. Heileman and C. T. Abdallah", booktitle = "2007 European Control Conference (ECC)", title = "A generalization of {Benford's Law} and its application to images", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "3613--3619", month = jul, year = "2007", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Approximation methods; Benford's law; Benford's law generalization; Convolution; DCT; discrete cosine transform domain; discrete cosine transforms; Discrete cosine transforms; first significant digit; forensics; Fourier expansion; Fourier series; hidden message; Histograms; image forensics; Image forensics; image forensics; modular logarithmic domain; probability; probability density function; Random variables; watermarking", } @InProceedings{Perin:2007:CNA, author = "Stephen P{\'e}rin", booktitle = "Constructal Theory of Social Dynamics", title = "The Constructal Nature of the Air Traffic System", publisher = pub-SV, address = pub-SV:adr, pages = "119--145", year = "2007", DOI = "https://doi.org/10.1007/978-0-387-47681-0_6", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/chapter/10.1007/978-0-387-47681-0_6", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Simons:2007:SIP, author = "John L. Simons", title = "A simple (inductive) proof for the non-existence of 2-cycles of the $ 3 x + 1 $ problem", journal = j-J-NUMBER-THEORY, volume = "123", number = "1", pages = "10--17", month = mar, year = "2007", CODEN = "JNUTA9", DOI = "https://doi.org/10.1016/j.jnt.2006.05.011", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0022314X06001223", acknowledgement = ack-nhfb, fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", keywords = "Benford's Law", } @Book{Tijms:2007:UPC, author = "H. C. Tijms", title = "Understanding probability: chance rules in everyday life", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Second", pages = "x + 442", year = "2007", ISBN = "0-511-34626-3 (e-book), 0-511-35003-1 (e-book), 0-521-70172-4 (paperback)", ISBN-13 = "978-0-511-34626-2 (e-book), 978-0-511-35003-0 (e-book), 978-0-521-70172-3 (paperback)", LCCN = "QA273 .T48 2007", bibdate = "Mon Feb 18 06:48:08 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Probabilities; Mathematical analysis; Chance; Mathematics; Probability and Statistics; General; Waarschijnlijkheidstheorie; Wahrscheinlichkeitsverteilung", tableofcontents = "Probability questions \\ The law of large numbers and simulation \\ Probabilities in everyday life \\ Rare events and lotteries \\ Probability and statistics \\ Chance trees and Bayes' rule \\ Foundations of probability theory \\ Conditional probability and Bayes \\ Basic rules for discrete random variables \\ Continuous random variables \\ Jointly distributed random variables \\ Multivariate normal distribution \\ Conditional distributions \\ Generating functions \\ Markov chains", } @Article{Torres:2007:HDN, author = "J. Torres and S. Fern{\'a}ndez and A. Gamero and A. Sola", title = "How do numbers begin? (the first digit law)", journal = j-EUR-J-PHYS, volume = "28", number = "3", pages = "L17--L25", month = may, year = "2007", CODEN = "EJPHD4", DOI = "https://doi.org/10.1088/0143-0807/28/3/N04", ISSN = "0143-0807 (print), 1361-6404 (electronic)", ISSN-L = "0143-0807", bibdate = "Fri Feb 15 18:37:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://iopscience.iop.org/0143-0807/28/3/N04", acknowledgement = ack-nhfb, fjournal = "European Journal of Physics", journal-URL = "http://iopscience.iop.org/0143-0807/", keywords = "Benford's Law; Frank Benford; Simon Newcomb", remark-1 = "From page L19: ``He [Newcomb] founded the American Astronomical Society, and was its first president; he was a successful scientist.''.", remark-2 = "From page L19: ``His [Newcomb's] discovery went unnoticed by the scientific community, in spite of the fact that Newcomb was already a famous scientist at the time. He continued working in physical and mathematical astronomy, receiving honours for his career --- a crater of Mars takes his name --- but he was also responsible for a famous funny mistake: he tried to demonstrate that an object heavier than air could not fly, just months before the Wright brothers' first one-man aeroplane flew in 1903. Far from retracting, Newcomb said that an aeroplane for two or more people could not fly, so aeroplanes would not be worthwhile pursuing [3, 4]. He died in 1909, without even remembering the matter of the first significant digit law.''", remark-3 = "From page L19: ``Frank Benford, a physicist working at General Electric (who was the inventor of the electric light pointer), \ldots{}''.", } @Article{Wells:2007:QPV, author = "K. Wells and J. Chiverton and M. Partridge and M. Barry and H. Kadhem and B. Ott", title = "Quantifying the Partial Volume Effect in {PET} Using {Benford's Law}", journal = j-IEEE-TRANS-NUCL-SCI, volume = "54", number = "5", pages = "1616--1625", month = oct, year = "2007", CODEN = "IRNSAM", DOI = "https://doi.org/10.1109/TNS.2007.903182", ISSN = "0018-9499 (print), 1558-1578 (electronic)", ISSN-L = "0018-9499", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Nuclear Science", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23", } @Article{Yeh:2007:SMD, author = "Hsiaw-Chan Yeh", title = "Some multivariate discrete time series models for dependent multivariate {Zipf} counts", journal = "Bulletin of the Institute of Mathematics. Academia Sinica. New Series", volume = "2", number = "1", pages = "29--53", year = "2007", CODEN = "????", ISSN = "0304-9825", ISSN-L = "0304-9825", MRclass = "62M10 (62H20)", MRnumber = "2294107", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Bull. Inst. Math. Acad. Sin. (N.S.)", fjournal = "Bulletin of the Institute of Mathematics. Academia Sinica. New Series", } @Article{Aerts:2008:CDD, author = "Walter Aerts and Geert {Van Campenhout} and Tom {Van Caneghem}", title = "Clustering in dividends: Do managers rely on cognitive reference points?", journal = "Journal of Economic Psychology", volume = "29", number = "3", pages = "276--284", year = "2008", DOI = "https://doi.org/10.1016/j.joep.2007.10.003", ISSN = "0167-4870 (print), 1872-7719 (electronic)", ISSN-L = "0167-4870", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167487007000864", abstract = "Prior studies (see e.g. [Rosch, E. (1975). Cognitive reference points. Cognitive Psychology, {\bf 7}, 532--547]) indicate that multiples of ten serve as cognitive reference points with a view to perceiving and evaluating numbers. In order to explore whether managers set dividends per share (henceforth DPS) at or just above a cognitive reference point, we perform a digital analysis on {US} firms' {DPS} for the period 1995--2004. That is, based on the theory of cognitive reference points, {DPS} of \$2.00 will be viewed as being abnormally larger than {DPS} of \$1.99, whereas the actual difference only amounts to a marginal \$0.01. Results presented in this paper indicate that managers fall back on cognitive reference points when they set DPS, which shows in significantly more (fewer) zeroes (large digits) in the second-from-the-left position of {DPS} than would normally be expected. Overall, results presented in this paper tally with prior findings on odd-ending prices and price clustering documented in related disciplines.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Cognitive psychology; Management", } @Article{Aono:2008:ISO, author = "June Y. Aono and Liming Guan", title = "The impact of {Sarbanes--Oxley} act on cosmetic earnings management", journal = "Research in Accounting Regulation", volume = "20", number = "0", pages = "205--215", month = oct, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1016/S1052-0457(07)00212-3", ISSN = "1052-0457 (print), 2467-9895 (electronic)", ISSN-L = "1052-0457", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S1052045707002123", abstract = "This study examines the mitigating effect of Sarbanes--Oxley Act on cosmetic earnings management, referred by Kinnunen and Koskela (2003) as earnings manipulative behavior to round earnings such that they result in an upward bias. This behavior reports income numbers to achieve key cognitive reference points represented by $ N \times $ 10k. Using Benford's Law, our analysis compares the distribution of second digits in reported annual net income for publicly listed {US} companies between a 2-year periods before and after the year 2002 when Sarbanes--Oxley Act went into effect. Our empirical results suggest that, in the 2-year period prior to the Act, there was evidence of cosmetic earnings management. However, such behavior in manipulating net income has noticeably decreased in the period after the Act. This finding is consistent with the notion that Sarbanes--Oxley Act has a deterring impact on corporate America's manipulative behavior to report earnings that achieve certain key reference points.", acknowledgement = ack-nhfb, fjournal = "Research in Accounting Regulation", keywords = "Benford's Law", } @Article{Batty:2008:PSS, author = "Michael Batty", title = "Perspective: The Size, Scale, and Shape of Cities", journal = j-SCIENCE, volume = "318", number = "5864", pages = "769--771", day = "8", month = feb, year = "2008", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.1151419", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Wed Feb 27 06:02:28 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/319/5864/769.abstract", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "200 tallest buildings in world; US cities of one million (or more) population; Zipf's law", } @Article{Berger:2008:SDI, author = "Arno Berger and Theodore P. Hill and Kent E. Morrison", title = "Scale-Distortion Inequalities for Mantissas of Finite Data Sets", journal = j-J-THEOR-PROBAB, volume = "21", number = "1", pages = "97--117", month = mar, year = "2008", CODEN = "JTPREO", DOI = "https://doi.org/10.1007/s10959-007-0112-z", ISSN = "0894-9840 (print), 1572-9230 (electronic)", ISSN-L = "0894-9840", bibdate = "Thu Aug 28 19:04:16 MDT 2014", bibsource = "http://link.springer.com/journal/10959; http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0894-9840&volume=21&issue=1; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib", URL = "http://link.springer.com/article/10.1007/s10959-007-0112-z", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Probability", journal-URL = "http://link.springer.com/journal/10959", } @Article{Bhattacharya:2008:FAB, author = "S. Bhattacharya and K. Kumar", title = "Forensic Accounting and {Benford's Law} [In the Spotlight]", journal = j-IEEE-SIGNAL-PROCESS-MAG, volume = "25", number = "2", pages = "152--150", month = mar, year = "2008", CODEN = "ISPRE6", DOI = "https://doi.org/10.1109/MSP.2007.914724", ISSN = "1053-5888 (print), 1558-0792 (electronic)", ISSN-L = "1053-5888", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008ISPM...25..152B", acknowledgement = ack-nhfb, fjournal = "IEEE signal processing magazine", } @Article{Brown:2008:CSP, author = "Philip Brown and Jason Mitchell", title = "Culture and stock price clustering: Evidence from {The Peoples' Republic of China}", journal = "Pacific-Basin Finance Journal", volume = "16", number = "1 2", pages = "95--120", year = "2008", DOI = "https://doi.org/10.1016/j.pacfin.2007.04.005", ISSN = "0927-538X (print), 1879-0585 (electronic)", ISSN-L = "0927-538X", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Behavioral Finance in Asia", URL = "http://www.sciencedirect.com/science/article/pii/S0927538X0700025X", abstract = "Price clustering is the tendency of prices to be observed more frequently at some numbers than others. It results from human bias and from haziness or imprecise beliefs about underlying value. To many Chinese, the number 8 is attractive because it is considered lucky, while 4 is unlucky and to be avoided. We conduct a tightly controlled experiment to determine whether a culturally heuristic number preference exists, by studying trading on the Shanghai and Shenzhen stock exchanges, which historically have been relatively segmented along cultural lines. Our results are extremely clear. For much of our sample period (1994 2002), the prices of A-shares (mostly held by Chinese organisations or individuals) traded on the Shanghai stock exchange were more than twice as likely to end in 8, than 4. Similarly, for A-shares traded on the Shenzhen stock exchange a preference for 8 was found. Preference for 8 on both exchanges was initially very strong, but has weakened somewhat over time. It is observed in opening, high and low as well as closing prices, reinforcing its pervasiveness. Overall, the cultural preference manifest in the prices of A-shares is widespread in both markets and its presence is accentuated once other factors that influence price clustering are taken into account. The preference for 8 was much weaker for B-shares, which largely have been held by foreigners.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Feng shui; Number preferences; Shanghai and Shenzhen stock exchanges; Stock price clustering", } @Article{Chakravorty:2008:TAE, author = "Douglas N. Hales and V. Sridharan and Abirami Radhakrishnan and Satya S. Chakravorty and Samia M. Siha", title = "Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods", journal = j-EUR-J-OPER-RES, volume = "189", number = "3", pages = "583--593", day = "16", month = sep, year = "2008", CODEN = "EJORDT", DOI = "https://doi.org/10.1016/j.ejor.2006.09.092", ISSN = "0377-2217 (print), 1872-6860 (electronic)", ISSN-L = "0377-2217", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702", acknowledgement = ack-nhfb, fjournal = "European Journal of Operational Research", journal-URL = "http://www.sciencedirect.com/science/journal/03772217", keywords = "Benford's Law", xxauthor = "S. Chakravorty and Samia M. Siha", } @Article{Costas:2008:NCC, author = "Eduardo Costas and Victoria L{\'o}pez-Rodas and F. Javier Toro and Antonio Flores-Moya", title = "The number of cells in colonies of the cyanobacterium {{\em Microcystis aeruginosa\/}} satisfies {Benford}'s law", journal = j-AQUAT-BOT, volume = "89", number = "3", pages = "341--343", month = oct, year = "2008", CODEN = "AQBODS", DOI = "https://doi.org/10.1016/j.aquabot.2008.03.011", ISSN = "0304-3770 (print), 1879-1522 (electronic)", ISSN-L = "0304-3770", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0304377008000533", abstract = "Nowadays, numerous power- or scaling-laws are encountered in many fields of biology: an example is Benford's law. According to this law, the first significant digit of any given series of numbers is figure 1 more often than figure 2, which in turn appears more often than 3, and so on. Here we show that number of cells per colony in the cyanobacterium Microcystis aeruginosa (F. T. K{\"u}tzing), randomly isolated from different reservoirs and lakes from Andalusia (S Spain), was very variable (with figures differing up to five orders of magnitude). However, the distribution of the number of cells per colony satisfies Benford's law. This situation could be much more general in colonial cyanobacteria.", acknowledgement = ack-nhfb, fjournal = "Aquatic Botany", keywords = "Benford's Law; Colony; Microcystis aeruginosa", } @Article{Depken:2008:BZB, author = "Craig A. {Depken II}", title = "{Benford}, {Zipf} and the blogosphere", journal = j-APPL-ECON-LETT, volume = "15", number = "9", pages = "689--692", month = "????", year = "2008", DOI = "https://doi.org/10.1080/13504850600735270", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Sat Jan 07 09:18:33 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", journal-URL = "http://www.tandfonline.com/loi/rael20", onlinedate = "04 Jul 2008", } @Article{Dumbgen:2008:EBA, author = "Lutz D{\"u}mbgen and Christoph Leuenberger", title = "Explicit bounds for the approximation error in {Benford}'s law", journal = j-ELECTRON-COMMUN-PROBAB, volume = "13", pages = "99--112", year = "2008", CODEN = "????", ISSN = "1083-589X", ISSN-L = "1083-589X", MRclass = "60E15 (60F99)", MRnumber = "2386066 (2009b:60056)", MRreviewer = "Pieter C. Allaart", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://arxiv.org/abs/0705.4488; http://weber.math.washington.edu/~ejpecp/ECP/index.php", abstract = "Benford's law states that for many random variables $ X > 0 $ its leading digit $ D = D(X) $ satisfies approximately the equation $ P(D = d) = \log_{10}(1 + 1 / d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon follows from another, maybe more intuitive fact, applied to $ Y \coloneq \log_{10}(X) $: For many real random variables $Y$, the remainder $ U \coloneq Y - \floor (Y) $ is approximately uniformly distributed on $ [0, 1) $. The present paper provides new explicit bounds for the latter approximation in terms of the total variation of the density of $Y$ or some derivative of it. These bounds are an interesting alternative to traditional Fourier methods which yield mostly qualitative results. As a by-product we obtain explicit bounds for the approximation error in Benford's law.", acknowledgement = ack-nhfb, fjournal = "Electronic Communications in Probability", journal-URL = "http://ecp.ejpecp.org/", } @Article{Gauvrit:2008:PLB, author = "Nicolas Gauvrit and Jean-Paul Delahaye", title = "Pourquoi la loi de {Benford} n'est pas myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is not mysterious]", journal = "Math{\'e}matiques et Sciences Humaines = Mathematics and Social Sciences", volume = "46", number = "182", pages = "7--15", year = "2008", CODEN = "????", ISSN = "0987-6936 (print), 1950-6821 (electronic)", ISSN-L = "0987-6936", MRclass = "62A01 (91E10)", MRnumber = "2433183 (2009f:62008)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf", acknowledgement = ack-nhfb, ajournal = "Math. Sci. Hum. Math. Soc. Sci.", fjournal = "Math{\'e}matiques et Sciences Humaines= Mathematics and Social Sciences", language = "French", } @Article{Grandison:2008:BPK, author = "S. Grandison and R. J. Morris", title = "Biological Pathway Kinetic Rate Constants Are Scale-Invariant", journal = j-BIOINFORMATICS, volume = "24", number = "6", pages = "741--743", month = "????", year = "2008", DOI = "https://doi.org/10.1093/bioinformatics/btn041", ISSN = "1367-4803 (print), 1367-4811 (electronic)", ISSN-L = "1367-4803", bibdate = "Sat Sep 10 11:56:57 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ncbi.nlm.nih.gov/pubmed/18238786", acknowledgement = ack-nhfb, fjournal = "Bioinformatics", journal-URL = "http://bioinformatics.oxfordjournals.org/", keywords = "Benford's Law", } @Article{Hales:2008:TAE, author = "Douglas N. Hales and V. Sridharan and Abirami Radhakrishnan and Satya S. Chakravorty and Samia M. Siha", title = "Testing the accuracy of employee-reported data: An inexpensive alternative approach to traditional methods", journal = j-EUR-J-OPER-RES, volume = "189", number = "3", pages = "583--593", year = "2008", CODEN = "EJORDT", DOI = "https://doi.org/10.1016/j.ejor.2006.09.092", ISSN = "0377-2217 (print), 1872-6860 (electronic)", ISSN-L = "0377-2217", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377221706011702", abstract = "Although Information Technology (IT) solutions improve the collection and validation of operational data, Operations Managers must often rely on self-reported data from workers to make decisions. The problem with this data is that they are subject to intentional manipulation, thus reducing their suitability for decision-making. A method of identifying manipulated data, digital analysis, addresses this problem at low cost. In this paper, we demonstrate how one uses this method in real-world companies to validate self-reported data from line workers. The results of our study suggest that digital analysis estimates the accuracy of employee reported data in operations management, within limited contexts. These findings lead to improved operating performance by providing a tool for practitioners to exclude inaccurate information.", acknowledgement = ack-nhfb, fjournal = "European Journal of Operational Research", journal-URL = "http://www.sciencedirect.com/science/journal/03772217", keywords = "Benford's Law; Digital analysis; Fraud detection; Operations management; Plastics industry", } @Article{Hayes:2008:LED, author = "S. J. Hayes", title = "Letter to the {Editor}: Does Terminal Digit Preference Occur in Pathology?", journal = j-J-CLIN-PATHOL, volume = "61", number = "8", pages = "975--976", month = "????", year = "2008", CODEN = "JCPAAK", DOI = "https://doi.org/10.1136/jcp.2008.057851", ISSN = "0021-9746 (print), 1472-4146 (electronic)", ISSN-L = "0021-9746", bibdate = "Sat Sep 10 12:01:29 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jcp.bmj.com/content/61/8/975.2", acknowledgement = ack-nhfb, fjournal = "Journal of Clinical Pathology", journal-URL = "http://jcp.bmj.com/content/by/year", keywords = "Benford's Law", } @Article{Hayes:2008:TDP, author = "S. J. Hayes", title = "Terminal Digit Preference Occurs in Pathology Reporting Irrespective of Patient Management Implication", journal = j-J-CLIN-PATHOL, volume = "61", number = "9", pages = "1071--1072", month = "????", year = "2008", CODEN = "JCPAAK", DOI = "https://doi.org/10.1136/jcp.2008.059543", ISSN = "0021-9746 (print), 1472-4146 (electronic)", ISSN-L = "0021-9746", bibdate = "Sat Sep 10 12:05:19 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jcp.bmj.com/content/61/9/1071.extract", acknowledgement = ack-nhfb, fjournal = "Journal of Clinical Pathology", journal-URL = "http://jcp.bmj.com/content/by/year", keywords = "Benford's Law", } @Article{Hefeeda:2008:TMP, author = "Mohamed Hefeeda and Osama Saleh", title = "Traffic modeling and proportional partial caching for peer-to-peer systems", journal = j-IEEE-TRANS-NETWORKING, volume = "16", number = "6", pages = "1447--1460", month = dec, year = "2008", CODEN = "IEANEP", DOI = "https://doi.org/10.1109/TNET.2008.918081", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Fri Mar 6 16:31:04 MST 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", abstract = "Peer-to-peer (P2P) file sharing systems generate a major portion of the Internet traffic, and this portion is expected to increase in the future. We explore the potential of deploying proxy caches in different Autonomous Systems (ASes) with the goal of reducing the cost incurred by Internet service providers and alleviating the load on the Internet backbone. We conduct an eight-month measurement study to analyze the P2P traffic characteristics that are relevant to caching, such as object popularity, popularity dynamics, and object size. Our study shows that the popularity of P2P objects can be modeled by a Mandelbrot-Zipf distribution, and that several workloads exist in P2P traffic. Guided by our findings, we develop a novel caching algorithm for P2P traffic that is based on object segmentation, and proportional partial admission and eviction of objects. Our trace-based simulations show that with a relatively small cache size, a byte hit rate of up to 35\% can be achieved by our algorithm, which is close to the byte hit rate achieved by an off-line optimal algorithm with complete knowledge of future requests. Our results also show that our algorithm achieves a byte hit rate that is at least 40\% more, and at most triple, the byte hit rate of the common web caching algorithms. Furthermore, our algorithm is robust in face of aborted downloads, which is a common case in P2P systems.", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771", keywords = "internet measurement; network protocols; peer-to-peer systems; traffic analysis; traffic modeling", } @Article{Huang:2008:IZL, author = "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and Jing-Shiuan Hua", title = "An investigation of {Zipf's Law} for fraud detection {(DSS\# 06-10-1826R(2))}", journal = j-DEC-SUPP-SYS, volume = "46", number = "1", pages = "70--83", month = dec, year = "2008", CODEN = "DSSYDK", DOI = "https://doi.org/10.1016/j.dss.2008.05.003", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167923608001073", abstract = "Fraud risk is higher than ever before. Unfortunately, many auditors lack the expertise to deal with the related risks. The objectives of this research are to develop an innovative fraud detection mechanism on the basis of Zipf's Law. The purpose of this technique is to assist auditors in reviewing the overwhelming volumes of datasets and identifying any potential fraud records. The authors conducted Quasi-experiment research on the KDDCUP'99 benchmark intrusion detection dataset to verify the performance of the proposed mechanism. The simulation experimental results demonstrate that Zipf Analysis can assist auditors to locate the source of suspicion and further enhance the resulting audit processes.", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law; Fraud detection; Misclassification cost matrix; Quasi-experiment research; Zipf's Law", } @Article{Humenberger:2008:EBB, author = "H. Humenberger", title = "{Eine elementarmathematische Begr{\"u}ndung des Benford-Gesetzes}. ({German}) [{An} elementary mathematical derivation of the {Benford Law}]", journal = "Der Mathematikunterricht", volume = "54", number = "??", pages = "24--34", month = "????", year = "2008", CODEN = "????", ISSN = "0025-5807", ISSN-L = "0025-5807", bibdate = "Fri Nov 18 11:59:44 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Ipeirotis:2008:CAH, author = "Panagiotis G. Ipeirotis and Luis Gravano", title = "Classification-aware hidden-web text database selection", journal = j-TOIS, volume = "26", number = "2", pages = "6:1--6:??", month = mar, year = "2008", CODEN = "ATISET", DOI = "https://doi.org/10.1145/1344411.1344412", ISSN = "1046-8188", ISSN-L = "0734-2047", bibdate = "Thu Jun 12 16:52:34 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/tois/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Many valuable text databases on the web have noncrawlable contents that are ``hidden'' behind search interfaces. Metasearchers are helpful tools for searching over multiple such ``hidden-web'' text databases at once through a unified query interface. An important step in the metasearching process is database selection, or determining which databases are the most relevant for a given user query. The state-of-the-art database selection techniques rely on statistical summaries of the database contents, generally including the database vocabulary and associated word frequencies. Unfortunately, hidden-web text databases typically do not export such summaries, so previous research has developed algorithms for constructing approximate content summaries from document samples extracted from the databases via querying. We present a novel ``focused-probing'' sampling algorithm that detects the topics covered in a database and adaptively extracts documents that are representative of the topic coverage of the database. Our algorithm is the first to construct content summaries that include the frequencies of the words in the database. Unfortunately, Zipf's law practically guarantees that for any relatively large database, content summaries built from moderately sized document samples will fail to cover many low-frequency words; in turn, incomplete content summaries might negatively affect the database selection process, especially for short queries with infrequent words. To enhance the sparse document samples and improve the database selection decisions, we exploit the fact that topically similar databases tend to have similar vocabularies, so samples extracted from databases with a similar topical focus can complement each other. We have developed two database selection algorithms that exploit this observation. The first algorithm proceeds hierarchically and selects the best categories for a query, and then sends the query to the appropriate databases in the chosen categories. The second algorithm uses ``shrinkage,'' a statistical technique for improving parameter estimation in the face of sparse data, to enhance the database content summaries with category-specific words. We describe how to modify existing database selection algorithms to adaptively decide (at runtime) whether shrinkage is beneficial for a query. A thorough evaluation over a variety of databases, including 315 real web databases as well as TREC data, suggests that the proposed sampling methods generate high-quality content summaries and that the database selection algorithms produce significantly more relevant database selection decisions and overall search results than existing algorithms.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "ACM Transactions on Information Systems (TOIS)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J779", keywords = "database selection; Distributed information retrieval; web search", } @Article{Jager:2008:DAD, author = "Hendrik Jager and Pierre Liardet", title = "Distributions arithm{\'e}tiques des d{\'e}nominateurs de convergents de fractions continues. ({French}) [Arithmetic distributions of the denominators of continued fractions]", journal = "Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, Indagationes mathematicae", volume = "91", number = "2", pages = "181--197", day = "20", month = jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1016/S1385-7258(88)80026-X", ISSN = "1385-7258 (print), 1878-5972 (electronic)", ISSN-L = "1385-7258", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S138572588880026X", acknowledgement = ack-nhfb, fjournal = "Indagationes Mathematicae (Proceedings)", keywords = "Benford's Law", language = "French", xxjournal = "Indagationes Mathematicae (Proceedings)", } @Article{Jang:2008:CDH, author = "Dennis Jang and Jung Uk Kang and Alex Kruckman and Jun Kudo and Steven J. Miller", title = "Chains of Distributions, Hierarchical {Bayesian} Models and {Benford's Law}", journal = "arxiv.org", pages = "1--15", day = "27", month = may, year = "2008", CODEN = "????", ISSN = "????", bibdate = "Thu Oct 13 07:41:45 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J; http://arxiv.org/abs/0805.4226", abstract = "Kossovsky recently conjectured that the distribution of leading digits of a chain of probability distributions converges to Benford's law as the length of the chain grows. We prove his conjecture in many cases, and provide an interpretation in terms of products of independent random variables and a central limit theorem. An interesting consequence is that in hierarchical Bayesian models priors tend to satisfy Benford's Law as the number of levels of the hierarchy increases, which allows us to develop some simple tests (based on Benford's law) to test proposed models. We give explicit formulas for the error terms as sums of Mellin transforms, which converges extremely rapidly as the number of terms in the chain grows. We may interpret our results as showing that certain Markov chain Monte Carlo processes are rapidly mixing to Benford's law.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0805.4226", keywords = "Mathematics - Probability, Mathematics - Statistics Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)", pagecount = "15", primaryclass = "math.PR", } @Article{Jelenkovic:2008:CMS, author = "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang", title = "Characterizing the miss sequence of the {LRU} cache", journal = j-SIGMETRICS, volume = "36", number = "2", pages = "119--121", month = sep, year = "2008", CODEN = "PEREDN", DOI = "https://doi.org/10.1145/1453175.1453203", ISSN = "0163-5999 (print), 1557-9484 (electronic)", ISSN-L = "0163-5999", bibdate = "Wed Aug 25 07:31:09 MDT 2010", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib", abstract = "Renewed interest in caching systems stems from their wide-spread use for reducing the document download latency over the Internet. Since caches are usually organized in a hierarchical manner, it is important to study the performance properties of tandem caches. The first step in understanding this problem is to characterize the miss stream from one single cache since it represents the input to the next level cache. In this regard, we discover that the miss stream from one single cache is approximated well by the superposition of a number of asymptotically independent renewal processes. Interestingly, when this weakly correlated miss sequence is fed into another cache, this barely observable correlation can lead to measurably different caching performance when compared to the independent reference model. This result is likely to enable the development of a rigorous analysis of the tandem cache performance.", acknowledgement = ack-nhfb, fjournal = "ACM SIGMETRICS Performance Evaluation Review", journal-URL = "http://portal.acm.org/toc.cfm?id=J618", keywords = "average-case analysis; cache fault probability; hierarchical caching; least-recently-used caching; web caching; Zipf's law", } @Article{Kafri:2008:SIS, author = "Oded Kafri", title = "Sociological Inequality and the {Second Law}", journal = "ArXiv e-prints", year = "2008", bibdate = "Mon Nov 21 06:41:29 2011", bibsource = "http://dblp.uni-trier.de; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/0805.3206", abstract = "There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power law distribution function yields an uneven distribution of particles in boxes. It is shown that the obtained distribution fits well to sociological phenomena, such as the distribution of votes in polls and the distribution of wealth and Benford's law.", acknowledgement = ack-nhfb, } @InProceedings{Krakar:2008:ABL, author = "Zdravko Krakar and Mario {\v{Z}}gela", editor = "Boris Aurer and Miroslav Ba{\'c}a", booktitle = "Proceedings of the 19th Central European Conference on Information and Intelligent Systems (CECIS 2008)", title = "Application of {Benford's Law} in Payment System Auditing", publisher = "Fakultet organizacije i informatike", address = "Vara{\v{z}}din, Croatia", pages = "187--193", year = "2008", bibdate = "Sun Nov 13 11:14:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InProceedings{Krakar:2008:EBL, author = "Zdravko Krakar and Mario {\v{Z}}gela", editor = "Mario Plenkovi{\'c}", booktitle = "Society and Technology 2008", title = "Evaluation of {Benford's Law}: application in stock prices and stock turnover", publisher = "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo", address = "Zagreb, Croatia", pages = "57--71", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sun Nov 13 11:18:37 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, remark = "International Federation of Communication Studies, Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u Zagrebu.", } @Article{Linville:2008:PFN, author = "Mark Linville", title = "The Problem of False Negative Results in the Use of Digit Analysis", journal = "Journal of Applied Business Research", volume = "24", number = "1", pages = "17--25", month = "First Quarter", year = "2008", DOI = "https://doi.org/10.19030/jabr.v24i1.1363", ISSN = "0892-7626 (print), 2157-8834 (electronic)", ISSN-L = "0892-7626", bibdate = "Thu Oct 13 07:34:30 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.cluteinstitute.com/ojs/index.php/JABR/article/view/1363", acknowledgement = ack-nhfb, ajournal = "J. Appl. Bus. Res.", journal-URL = "http://journals.cluteonline.com/index.php/JABR", keywords = "Benford's Law", } @Article{Liu:2008:MNS, author = "Cheng-Shi Liu", title = "Maximal non-symmetric entropy leads naturally to {Zipf}'s law", journal = j-FRACTALS, volume = "16", number = "1", pages = "99--101", year = "2008", CODEN = "FRACEG", DOI = "https://doi.org/10.1142/S0218348X08003788", ISSN = "0218-348X", ISSN-L = "0218-348X", MRclass = "94A17 (94A15)", MRnumber = "2399875 (2009c:94027)", MRreviewer = "Yasuichi Horibe", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Fractals. Complex Geometry, Patterns, and Scaling in Nature and Society", journal-URL = "http://www.worldscientific.com/loi/fractals", } @Article{Lolbert:2008:NEG, author = "Tam{\'a}s Lolbert", title = "On the non-existence of a general {Benford}'s law", journal = j-MATH-SOC-SCI, volume = "55", number = "2", pages = "103--106", month = mar, year = "2008", CODEN = "MSOSDD", DOI = "https://doi.org/10.1016/j.mathsocsci.2007.09.001", ISSN = "0165-4896 (print), 1879-3118 (electronic)", ISSN-L = "0165-4896", MRclass = "60A10 (60E10)", MRnumber = "2391902", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165489607000935", abstract = "Benford's law states that in randomly collected numbers certain digits are more often leading digits than others. More formally: the general law states that the mantissae follow the logarithmic distribution in any base. Benford's law was recognized by many mathematicians so that several possible explanations have been derived, but several questions are still open. Applications are widespread, for example an auditing technique (the so-called digital analysis), which is employed around the world by internal revenue services to detect tax fraud, is based on this phenomenon.\par In this paper it will be shown that there exists no probability measure that would obey Benford's law for any base, but if the set of possible bases does not exceed a given upper limit, most real-life distributions obey, or can be transformed to obey Benford's law.", acknowledgement = ack-nhfb, fjournal = "Mathematical Social Sciences", journal-URL = "http://www.sciencedirect.com/science/journal/01654896", keywords = "Benford's Law; Characteristic function; Mantissa; Numeral base", } @Article{Luque:2008:FDF, author = "Bartolo Luque and Lucas Lacasa", title = "The first digit frequencies of primes and {Riemann} zeta zeros tend to uniformity following a size-dependent generalized {Benford}'s law", journal = "ArXiv e-prints", month = nov, year = "2008", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See published paper \cite {Luque:2009:FDF}.", URL = "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L; http://arxiv.org/abs/0811.3302", abstract = "Prime numbers seem to distribute among the natural numbers with no other law than that of chance, however its global distribution presents a quite remarkable smoothness. Such interplay between randomness and regularity has motivated scientists of all ages to search for local and global patterns in this distribution that eventually could shed light into the ultimate nature of primes. In this work we show that a generalization of the well known first-digit Benford's law, which addresses the rate of appearance of a given leading digit $d$ in data sets, describes with astonishing precision the statistical distribution of leading digits in the prime numbers sequence. Moreover, a reciprocal version of this pattern also takes place in the sequence of the nontrivial Riemann zeta zeros. We prove that the prime number theorem is, in the last analysis, the responsible of these patterns. Some new relations concerning the prime numbers distribution are also deduced, including a new approximation to the counting function $ \pi (n) $. Furthermore, some relations concerning the statistical conformance to this generalized Benford's law are derived. Some applications are finally discussed.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0811.3302", keywords = "Mathematics - Number Theory, Mathematics - Probability, Mathematics - Statistics", pagecount = "20", primaryclass = "math.NT", } @Article{Maillart:2008:ETZ, author = "T. Maillart and D. Sornette and S. Spaeth and G. von Krogh", title = "Empirical Tests of {Zipf's Law} Mechanism in Open Source {Linux} Distribution", journal = j-PHYS-REV-LET, volume = "101", number = "21", pages = "218701", day = "19", month = nov, year = "2008", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.101.218701", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/linux.bib; https://www.math.utah.edu/pub/tex/bib/unix.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", pagecount = "4", } @Article{Manin:2008:ZLA, author = "Dmitrii Y. Manin", title = "{Zipf's Law} and Avoidance of Excessive Synonymy", journal = j-COGN-SCI, volume = "32", number = "7", pages = "1075--1098", year = "2008", CODEN = "COGSD5", DOI = "https://doi.org/10.1080/03640210802020003", ISSN = "0364-0213 (print), 1551-6709 (electronic)", ISSN-L = "0364-0213", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Cognitive Science", keywords = "Semantics; Synonymy; Word frequency; Word meaning; Zipf's law", } @Article{Mayr:2008:EBE, author = "Philipp Mayr", title = "An evaluation of {Bradfordizing} Effects", journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE, volume = "2", number = "2", pages = "21--27", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1080/09737766.2008.10700850", ISSN = "0973-7766 (print), 2168-930X (electronic)", ISSN-L = "0973-7766", bibdate = "Thu Sep 10 17:47:02 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib", acknowledgement = ack-nhfb, fjournal = "Collnet Journal of Scientometrics and Information Management", journal-URL = "http://www.tandfonline.com/loi/tsim20", } @InProceedings{Mebane:2008:EFO, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{The American Electoral Process conference, Center for the Study of Democratic Politics, Princeton University, May 1--3, 2008}", title = "Election Forensics: Outlier and Digit Tests in {America} and {Russia}", publisher = "????", address = "????", pages = "i + 26", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:08:23 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/aep2008.pdf", acknowledgement = ack-nhfb, } @InProceedings{Mebane:2008:EFSa, author = "Walter R. {Mebane, Jr.}", editor = "R. Michael Alvarez and Thad E. Hall and Susan D. Hyde", booktitle = "{The Art and Science of Studying Election Fraud: Detection, Prevention, and Consequences}", title = "Election Forensics: The Second-digit {Benford's Law} Test and Recent {American Presidential} Elections", publisher = "Brookings Institution", address = "Washington, DC, USA", pages = "ii + 30", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Sat Feb 16 12:04:22 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Preprint dated 3 November 2006.", URL = "http://www.umich.edu/~wmebane/fraud06.pdf", acknowledgement = ack-nhfb, remark = "An earlier version of this paper was presented at the Election Fraud Conference, Salt Lake City, Utah, September 29--30, 2006.", } @InCollection{Mebane:2008:EFSb, author = "Walter R. {Mebane, Jr.}", title = "Election forensics: the second-digit {Benford's Law} test and recent {American} presidential elections", crossref = "Alvarez:2008:EFD", pages = "??--??", year = "2008", bibdate = "Sat Sep 10 14:25:52 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Miller:2008:MCL, author = "Steven J. Miller and Mark J. Nigrini", title = "The modulo $1$ central limit theorem and {Benford's Law} for products", journal = "International Journal of Algebra", volume = "2", number = "3", pages = "119--130", year = "2008", CODEN = "????", ISSN = "1312-8868 (print), 1314-7595 (electronic)", ISSN-L = "1312-8868", MRclass = "60F05 (11K06 42A10)", MRnumber = "2417189 (2009e:60053)", MRreviewer = "Gutti J. Babu", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.m-hikari.com/ija/ija-password-2008/ija-password1-4-2008/millerIJA1-4-2008.pdf", acknowledgement = ack-nhfb, ajournal = "Int. J. Algebra", fjournal = "International Journal of Algebra", journal-URL = "http://www.m-hikari.com/ija/index.html", } @Article{Miller:2008:OSB, author = "Steven J. Miller and Mark J. Nigrini", title = "Order statistics and {Benford}'s law", journal = j-INT-J-MATH-MATH-SCI, pages = "382948:1--382948:19", year = "2008", CODEN = "????", DOI = "https://doi.org/10.1155/2008/382948", ISSN = "0161-1712 (print), 1687-0425 (electronic)", ISSN-L = "0161-1712", MRclass = "62G30 (62E10)", MRnumber = "2461421 (2010c:62168)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Article ID 382948.", URL = "http://arxiv.org/abs/math/0601344; https://www.hindawi.com/journals/ijmms/2008/382948/", abstract = "Fix a base $B$ and let zeta have the standard exponential distribution; the distribution of digits of zeta base $B$ is known to be very close to Benford's Law. If there exists a $C$ such that the distribution of digits of $C$ times the elements of some set is the same as that of zeta, we say that set exhibits shifted exponential behavior base $B$ (with a shift of $ \log_B C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be independent identically distributed random variables. If the $ X_i $'s are drawn from the uniform distribution on $ [0, L] $, then as $ N \to \infty $ the distribution of the digits of the differences between adjacent order statistics converges to shifted exponential behavior (with a shift of $ \log_B L / N \bmod 1 $ ). By differentiating the cumulative distribution function of the logarithms modulo 1, applying Poisson Summation and then integrating the resulting expression, we derive rapidly converging explicit formulas measuring the deviations from Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$ independent random variables from any compactly supported distribution with uniformly bounded first and second derivatives and a second order Taylor series expansion at each point. The distribution of digits of any $ N^\delta $ consecutive differences {\em and\/} all $ N - 1 $ normalized differences of the order statistics exhibit shifted exponential behavior. We derive conditions on the probability density which determine whether or not the distribution of the digits of all the un-normalized differences converges to Benford's Law, shifted exponential behavior, or oscillates between the two, and show that the Pareto distribution leads to oscillating behavior.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", journal-URL = "https://www.hindawi.com/journals/ijmms/", keywords = "Benford's Law", pagecount = "19", } @Article{Mitchell:2008:TST, author = "James G. Mitchell and Laurent Seuront", title = "Towards a seascape topology {II}: {Zipf} analysis of one-dimensional patterns", journal = j-J-MAR-SYST, volume = "69", number = "3--4", pages = "328--338", month = feb, year = "2008", CODEN = "JMASE5", DOI = "https://doi.org/10.1016/j.jmarsys.2006.03.026", ISSN = "0924-7963 (print), 1879-1573 (electronic)", ISSN-L = "0924-7963", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000632", acknowledgement = ack-nhfb, fjournal = "Journal of Marine Systems", keywords = "Zipf's Law", } @Article{Mizuno:2008:PLE, author = "Takayuki Mizuno and Masahiro Toriyama and Takao Terano and Misako Takayasu", title = "{Pareto} law of the expenditure of a person in convenience stores", journal = j-PHYSICA-A, volume = "387", number = "15", pages = "3931--3935", year = "2008", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2008.01.059", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "91B82", MRnumber = "2586890", bibdate = "Mon Feb 18 17:05:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Ni:2008:BLH, author = "D. Ni and Z. Ren", title = "{Benford}'s law and half-lives of unstable nuclei", journal = j-EUR-PHYS-J-A, volume = "38", pages = "251--255", month = dec, year = "2008", CODEN = "EPJAFV", DOI = "https://doi.org/10.1140/epja/i2008-10680-8", ISSN = "1434-6001 (print), 1434-601X (electronic)", ISSN-L = "1434-6001", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008EPJA...38..251N", acknowledgement = ack-nhfb, fjournal = "European Physical Journal A: Hadrons and Nuclei", journal-URL = "http://www.springerlink.com/content/1434-6001", } @Article{Pain:2008:BLC, author = "Jean-Christophe Pain", title = "{Benford}'s law and complex atomic spectra", journal = j-PHYS-REV-E, volume = "77", number = "1", pages = "012102:1--012102:3", month = jan, year = "2008", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.77.012102", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P; http://pre.aps.org/abstract/PRE/v77/i1/e012102", abstract = "We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This indicates that atomic processes result from the superposition of uncorrelated probability laws and that the occurrence of digits reflects the constraints induced by the selection rules. Furthermore, Benford's law can be a useful test of theoretical spectroscopic models. Its applicability to the statistics of electric-dipolar lines can be understood in the framework of random matrix theory and is consistent with the Porter-Thomas law.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eid = "012102", eprint = "0801.0946", fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Probability theory, Oscillator strengths, lifetimes, transition moments, Other topics in the theory of the electronic structure of atoms and molecules", pagecount = "3", primaryclass = "quant-ph", } @Article{Petek:2008:PNH, author = "Marija Petek", title = "Personal name headings in {COBIB}: Testing {Lotka}'s Law", journal = j-SCIENTOMETRICS, volume = "75", number = "1", pages = "175--188", month = apr, year = "2008", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-007-1829-2", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:03 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib", URL = "http://link.springer.com/article/10.1007/s11192-007-1829-2", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Ravikumar:2008:BND, author = "Bala Ravikumar", title = "The {Benford--Newcomb} Distribution and Unambiguous Context-Free Languages", journal = j-INT-J-FOUND-COMP-SCI, volume = "19", number = "3", pages = "717--727", month = jun, year = "2008", CODEN = "IFCSEN", DOI = "https://doi.org/10.1142/S0129054108005905", ISSN = "0129-0541 (print), 1793-6373 (electronic)", ISSN-L = "0129-0541", MRclass = "68Q42 (68Q25 68Q45)", MRnumber = "2417964 (2009h:68068)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Foundations of Computer Science (IJFCS)", journal-URL = "http://www.worldscientific.com/loi/ijfcs", } @Article{Ristic:2008:GSP, author = "Miroslav M. Risti{\'c}", title = "A generalized semi-{Pareto} minification process", journal = j-STAT-PAPERS, volume = "49", number = "2", pages = "343--351", month = apr, year = "2008", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-006-0017-4", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:27 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-006-0017-4", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Schurger:2008:EBS, author = "Klaus Sch{\"u}rger", title = "Extensions of {Black--Scholes} processes and {Benford's Law}", journal = j-STOCH-PROC-APPL, volume = "118", number = "7", pages = "1219--1243", month = jul, year = "2008", CODEN = "STOPB7", DOI = "https://doi.org/10.1016/j.spa.2007.07.017", ISSN = "0304-4149 (print), 1879-209X (electronic)", ISSN-L = "0304-4149", MRclass = "60F10 (60G44 91B02 91B28)", MRnumber = "2428715 (2009g:60037)", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0304414907001391", abstract = "Let $Z$ be a stochastic process of the form $ Z (t) = Z (0) \exp (\mu t + X (t) - \langle X \rangle_t / 2) $ where $ Z (0) > 0 $, $ \mu $ are constants, and $X$ is a continuous local martingale having a deterministic quadratic variation $ \langle X \rangle $ such that $ \langle X \rangle_t \to \infty $ as $ t \to \infty $. We show that the mantissa (base $b$) of $ Z (t)$ (denoted by $ M (b) (Z (t))$) converges weakly to Benford's Law as $ t \to \infty $. Supposing that $X$ satisfies a certain growth condition, we obtain large deviation results for certain functionals (including occupation time) of ($ M^{(b)} (Z(t))$). Similar results are obtained in the discrete-time case. The latter are used to construct a non-parametric test for nonnegative processes ( $ Z (t)$ ) (based on the observation of significant digits of ( $ Z (n)$ ) ) of the null hypothesis $ H_0 (\sigma_0)$ which says that $Z$ is a general Black--Scholes process having a volatility $ \sigma \geq \sigma_0 ( > 0)$. Finally it is shown that the mantissa of Brownian motion is not even weakly convergent.", acknowledgement = ack-nhfb, fjournal = "Stochastic Processes and Their Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03044149", keywords = "Azuma's inequality; Benford's Law; Black Scholes processes; Brownian motion; Exponential local martingales; Large deviations; Leading digits; Non-parametric hypothesis testing for processes; Occupation time; Poisson's summation formula; Significant digits; Strong theorems; Weak theorems", } @Article{Semboloni:2008:HCS, author = "F. Semboloni", title = "Hierarchy, cities size distribution and {Zipf}'s law", journal = j-EUR-PHYS-J-B, volume = "63", number = "3", pages = "295--301", year = "2008", CODEN = "EPJBFY", DOI = "https://doi.org/10.1140/epjb/e2008-00203-1", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", MRclass = "91D10 (82B99 91D25)", MRnumber = "2421552 (2009f:91111)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "Zbl 1189.91174", acknowledgement = ack-nhfb, fjournal = "The European Physical Journal B. Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", } @Article{Seuront:2008:TST, author = "Laurent Seuront and James G. Mitchell", title = "Towards a seascape typology. {I}. {Zipf} versus {Pareto} laws", journal = j-J-MAR-SYST, volume = "69", number = "3--4", pages = "310--327", month = feb, year = "2008", CODEN = "JMASE5", DOI = "https://doi.org/10.1016/j.jmarsys.2006.03.025", ISSN = "0924-7963 (print), 1879-1573 (electronic)", ISSN-L = "0924-7963", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0924796307000620", acknowledgement = ack-nhfb, fjournal = "Journal of Marine Systems", keywords = "Zipf's Law", } @Article{Shaki:2008:RSN, author = "Samuel Shaki and Martin H. Fischer", title = "Reading space into numbers --- a cross-linguistic comparison of the {SNARC} effect", journal = j-COGNITION, volume = "108", number = "2", pages = "590--599", month = aug, year = "2008", CODEN = "CGTNAU", DOI = "https://doi.org/10.1016/j.cognition.2008.04.001", ISSN = "0010-0277 (print), 1873-7838 (electronic)", ISSN-L = "0010-0277", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0010027708000978", abstract = "Small numbers are spontaneously associated with left space and larger numbers with right space (the {SNARC} effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian Hebrew readers show a {SNARC} effect after reading Cyrillic script (from left-to-right) that is significantly reduced after reading Hebrew script (from right-to-left). In contrast, they have similar {SNARC} effects after listening to texts in either language. These results support the view that spatially directional scanning habits contribute to the spatial association of numbers but also emphasize its flexibility.", acknowledgement = ack-nhfb, fjournal = "Cognition", keywords = "Benford's Law; Mental number line; Reading direction; Spatial Numerical Association of Response Codes (SNARC); {SNARC}", } @Article{Volchenkov:2008:SUC, author = "D. Volchenkov and Ph. Blanchard", title = "Scaling and universality in city space syntax: Between {Zipf} and {Matthew}", journal = j-PHYSICA-A, volume = "387", number = "10", pages = "2353--2364", day = "1", month = apr, year = "2008", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2007.11.049", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437107012630", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Vuko:2008:UBL, author = "Tina Vuko", title = "Using {Benford's Law} to Detect Earnings Management Practice: the Case of Listed Companies in {Croatia}", journal = "Global Business \& Economics Anthology", volume = "1", number = "??", pages = "69--74", month = "????", year = "2008", CODEN = "????", ISSN = "1553-1333", ISSN-L = "1553-1333", bibdate = "Sun Nov 13 11:10:55 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Watrin:2008:BLI, author = "C. Watrin and R. Struffert and R. Ullmann", title = "{Benford's Law}: An Instrument for Selecting Tax Audit Targets?", journal = "Review of Managerial Science", volume = "2", number = "3", pages = "219--237", month = nov, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1007/s11846-008-0019-9", ISSN = "1863-6683 (print), 1863-6691 (electronic)", ISSN-L = "1863-6683", bibdate = "Tue Nov 22 20:58:51 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11846-008-0019-9", acknowledgement = ack-nhfb, } @Article{Wu:2008:IEP, author = "Shu-Fei Wu", title = "Interval estimation for a {Pareto} distribution based on a doubly type {II} censored sample", journal = j-COMPUT-STAT-DATA-ANAL, volume = "52", number = "7", pages = "3779--3788", day = "15", month = mar, year = "2008", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:42:27 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947308000030", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Book{Ziliak:2008:CSS, author = "Stephen Thomas Ziliak and Deirdre N. McCloskey", title = "The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives", publisher = "University of Michigan Press", address = "Ann Arbor, MI, USA", pages = "xxiii + 321", year = "2008", ISBN = "0-472-07007-X (cloth), 0-472-05007-9 (paperback)", ISBN-13 = "978-0-472-07007-7 (cloth), 978-0-472-05007-9 (paperback)", LCCN = "HB137 .Z55 2008", bibdate = "Tue Dec 9 15:55:11 MST 2008", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", series = "Economics, cognition, and society", URL = "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html", acknowledgement = ack-nhfb, remark = "This book has important comments on the battles among Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl Pearson, supplementing the discussion of those conflicts in \cite{McGrayne:2011:TWH}.", subject = "economics; statistical methods; statistics; social aspects; statistical hypothesis testing", } @Article{Ainsworth:2009:QSR, author = "Richard Thompson Ainsworth and Urs Hengartner", title = "{Quebec's Sales Recording Module (SRM)}: Fighting the {Zapper}, {Phantomware}, and Tax Fraud with technology", journal = "Canadian Tax Journal", volume = "57", number = "4", pages = "715--761", month = "????", year = "2009", CODEN = "????", ISSN = "0068-9823", ISSN-L = "0068-9823", bibdate = "Fri Mar 22 08:37:54 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf", acknowledgement = ack-mjn # "\slash " # ack-nhfb, journal-URL = "https://www.ctf.ca/ctfweb", keywords = "Benford's Law", } @TechReport{Alexander:2009:RUB, author = "James C. Alexander", title = "Remarks on the use of {Benford's Law}", type = "Working paper", institution = "Department of Mathematics and Cognitive Science, Case Western Reserve University", address = "Cleveland, OH, USA", day = "23", month = nov, year = "2009", bibdate = "Fri Mar 22 08:40:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147", acknowledgement = ack-mjn # "\slash " # ack-nhfb, } @InProceedings{Altamirano:2009:GTU, author = "Carlo Altamirano and Alberto Robledo", editor = "J. Zhou", booktitle = "Complex Sciences", title = "Generalized Thermodynamics Underlying the Laws of {Zipf} and {Benford}", volume = "5", publisher = pub-SV, address = pub-SV:adr, pages = "2232--??", year = "2009", DOI = "https://doi.org/10.1007/978-3-642-02469-6_100", ISBN = "3-642-02468-8", ISBN-13 = "978-3-642-02468-9", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A", acknowledgement = ack-nhfb, } @Article{Anderson:2009:CRC, author = "Thomas Anderson", title = "Conference reviewing considered harmful", journal = j-OPER-SYS-REV, volume = "43", number = "2", pages = "108--116", month = apr, year = "2009", CODEN = "OSRED8", DOI = "https://doi.org/10.1145/1531793.1531815", ISSN = "0163-5980 (print), 1943-586X (electronic)", ISSN-L = "0163-5980", bibdate = "Thu Apr 23 19:43:22 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "This paper develops a model of computer systems research to help prospective authors understand the often obscure workings of conference program committees. We present data to show that the variability between reviewers is often the dominant factor as to whether a paper is accepted. We argue that paper merit is likely to be Zipf distributed, making it inherently difficult for program committees to distinguish between most papers. We use game theory to show that with noisy reviews and Zipf merit, authors have an incentive to submit papers too early and too often. These factors make conference reviewing, and systems research as a whole, less efficient and less effective. We describe some recent changes in conference design to address these issues, and we suggest some further potential improvements.", acknowledgement = ack-nhfb, fjournal = "ACM SIGOPS Operating Systems Review", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J597", } @TechReport{Ansari:2009:PAV, author = "Ali Ansari", title = "Preliminary Analysis of the Voting Figures in {Iran}'s 2009 {Presidential} Election", type = "Report", number = "MENAP PP 2009/01", institution = "Chatham House and the Institute of Iranian Studies, University of St Andrews", address = "St Andrews, UK", day = "21", month = jun, year = "2009", bibdate = "Sat Sep 10 10:42:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.chathamhouse.org/sites/files/chathamhouse/public/Research/Middle%20East/iranelection0609.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Battersby:2009:SAH, author = "Stephen Battersby", title = "Statistical analyses hint at fraud in {Iranian} election", journal = j-NEW-SCIENTIST, volume = "202", number = "2714", pages = "10--??", day = "24", month = jun, year = "2009", CODEN = "NWSCAL", DOI = "https://doi.org/10.1016/S0262-4079(09)61682-1", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0262407909616821", abstract = "Mathematicians add their own concerns to claims that vote may have been rigged", acknowledgement = ack-nhfb, fjournal = "The New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law", xxISSN = "0262-4079, 0028-6664", } @TechReport{Bauer:2009:DDF, author = "J. Bauer and J. Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford's Law} on Regression Tables", type = "Report", number = "??", institution = "Institute of Sociology, LMU Munich", address = "Munich, Germany", month = "????", year = "2009", bibdate = "Fri Nov 18 11:46:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Beber:2009:DD, author = "B. Beber and A. Scacco", title = "The Devil Is in the Digits", journal = j-WASHINGTON-POST, volume = "??", number = "??", pages = "??--??", day = "20", month = jun, year = "2009", ISSN = "0190-8286", bibdate = "Sat Sep 10 10:28:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Washington Post", journal-URL = "http://www.washingtonpost.com/", keywords = "Benford's Law", remark = "Not found in online newspaper archives.", } @TechReport{Berger:2009:BOB, author = "A. Berger and T. P. Hill", title = "{Benford} Online Bibliography", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", year = "2009", bibdate = "Sat Nov 12 16:48:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.benfordonline.net", acknowledgement = ack-nhfb, remark = "According to \cite{Berger:2011:BLS}, the authors' online bibliography contains more than 600 references.", } @InProceedings{Berinde:2009:SOH, author = "Radu Berinde and Graham Cormode and Piotr Indyk and Martin J. Strauss", title = "Space-optimal heavy hitters with strong error bounds", crossref = "Paredaens:2009:PTE", pages = "157--166", year = "2009", DOI = "https://doi.org/10.1145/1559795.1559819", bibdate = "Thu Jul 2 14:05:34 MDT 2009", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "The problem of finding heavy hitters and approximating the frequencies of items is at the heart of many problems in data stream analysis. It has been observed that several proposed solutions to this problem can outperform their worst-case guarantees on real data. This leads to the question of whether some stronger bounds can be guaranteed. We answer this in the positive by showing that a class of `counter-based algorithms' (including the popular and very space-efficient FREQUENT and SPACESAVING algorithms) provide much stronger approximation guarantees than previously known. Specifically, we show that errors in the approximation of individual elements do not depend on the frequencies of the most frequent elements, but only on the frequency of the remaining `tail.' This shows that counter-based methods are the most space-efficient (in fact, space-optimal) algorithms having this strong error bound.\par This tail guarantee allows these algorithms to solve the `sparse recovery' problem. Here, the goal is to recover a faithful representation of the vector of frequencies, $f$. We prove that using space $ O(k) $, the algorithms construct an approximation $ f* $ to the frequency vector $f$ so that the L1 error $ ||f - f*||_1 $ is close to the best possible error $ \hbox {min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over all vectors with at most $k$ non-zero entries. This improves the previously best known space bound of about $ O(k \log n) $ for streams without element deletions (where $n$ is the size of the domain from which stream elements are drawn). Other consequences of the tail guarantees are results for skewed (Zipfian) data, and guarantees for accuracy of merging multiple summarized streams.", acknowledgement = ack-nhfb, keywords = "frequency estimation; heavy hitters; streaming algorithms", } @Article{Blasius:2009:ZLP, author = "Bernd Blasius and Ralf T{\"o}njes", title = "{Zipf's Law} in the Popularity Distribution of Chess Openings", journal = j-PHYS-REV-LET, volume = "103", number = "21", pages = "218701", day = "16", month = nov, year = "2009", CODEN = "PRLTAO", DOI = "https://doi.org/10.1103/PhysRevLett.103.218701", ISSN = "0031-9007 (print), 1079-7114 (electronic), 1092-0145", ISSN-L = "0031-9007", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701", acknowledgement = ack-nhfb, fjournal = "Physical Review Letters", journal-URL = "http://prl.aps.org/browse", keywords = "Zipf's Law", pagecount = "4", } @Article{Bradley:2009:WBL, author = "Jonathan R. Bradley and David L. Farnsworth", title = "What Is {Benford's Law}?", journal = "Teaching Statistics", volume = "31", number = "1", pages = "2--6", month = jan, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1111/j.1467-9639.2009.00347.x", ISSN = "0141-982X (print), 1467-9639 (electronic)", ISSN-L = "0141-982X", bibdate = "Mon Nov 14 17:09:33 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Class activity; First significant digit; Goodness of fit; Teaching", onlinedate = "6 Jan 2009", } @InProceedings{Burns:2009:SSR, author = "B. D. Burns", editor = "N. Taatgen and H. van Rijn", booktitle = "{Proceedings of the Thirty-First Annual Conference of the Cognitive Science Society, Cognitive Science Society, Austin, TX}", title = "Sensitivity to Statistical Regularities: People (Largely) Follow {Benford's Law}", publisher = "????", address = "????", pages = "2872--2877", year = "2009", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Nov 18 11:57:33 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Chakravorty:2009:TBL, author = "S. Chakravorty and V. Sridharan", title = "Testing {Benford's Law} for improving supply chain decision-making: a field experiment", journal = j-DRUG-DISCOVERY-TODAY, volume = "122", number = "2", pages = "606--618", month = dec, year = "2009", CODEN = "DDTOFS", DOI = "https://doi.org/10.1016/j.ijpe.2009.06.017", ISSN = "1359-6446 (print), 1878-5832 (electronic)", ISSN-L = "1359-6446", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163", acknowledgement = ack-nhfb, fjournal = "Drug Discovery Today", keywords = "Benford's Law", } @InProceedings{Chen:2009:DDM, author = "Wen Chen and Yun Q. Shi", booktitle = "{Digital Watermarking}", title = "Detection of Double {MPEG} Compression Based on First Digit Statistics", publisher = pub-SV, address = pub-SV:adr, pages = "16--30", year = "2009", DOI = "https://doi.org/10.1007/978-3-642-04438-0_2", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/chapter/10.1007/978-3-642-04438-0_2", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Chou:2009:BLN, author = "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and Zuozheng Wang and Huan Zheng", title = "{Benford's Law} and Number Selection in Fixed-Odds Numbers Game", journal = j-J-GAMBL-STUD, volume = "25", number = "4", pages = "503--521", month = dec, year = "2009", CODEN = "JGSTEM", DOI = "https://doi.org/10.1007/s10899-009-9145-9", ISSN = "1050-5350 (print), 1573-3602 (electronic)", ISSN-L = "1050-5350", bibdate = "Sat Feb 16 15:35:14 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s10899-009-9145-9", acknowledgement = ack-nhfb, fjournal = "Journal of Gambling Studies", } @Article{Chuang:2009:FPS, author = "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen", title = "Feature-preserved sampling over streaming data", journal = j-TKDD, volume = "2", number = "4", pages = "15:1--15:??", month = jan, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1460797.1460798", ISSN = "1556-4681 (print), 1556-472X (electronic)", ISSN-L = "1556-4681", bibdate = "Fri Apr 24 17:59:51 MDT 2009", bibsource = "http://www.acm.org/pubs/contents/journals/tkdd/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "In this article, we explore a novel sampling model, called {\em feature preserved sampling\/} ({\em FPS\/}) that sequentially generates a high-quality sample over sliding windows. The sampling quality we consider refers to the degree of consistency between the sample proportion and the population proportion of each attribute value in a window. Due to the time-variant nature of real-world datasets, users are more likely to be interested in the most recent data. However, previous works have not been able to generate a high-quality sample over sliding windows that precisely preserves up-to-date population characteristics. Motivated by this shortcoming, we have developed the {\em FPS\/} algorithm, which has several advantages: (1) it sequentially generates a sample from a time-variant data source over sliding windows; (2) the execution time of {\em FPS\/} is linear with respect to the database size; (3) the {\em relative\/} proportional differences between the sample proportions and population proportions of most distinct attribute values are guaranteed to be below a specified error threshold, $ \epsilon $, while the {\em relative\/} proportion differences of the remaining attribute values are as close to $ \epsilon $ as possible, which ensures that the generated sample is of high quality; (4) the sample rate is close to the user specified rate so that a high quality sampling result can be obtained without increasing the sample size; (5) by a thorough analytical and empirical study, we prove that {\em FPS\/} has acceptable space overheads, especially when the attribute values have Zipfian distributions, and {\em FPS\/} can also excellently preserve the population proportion of multivariate features in the sample; and (6) {\em FPS\/} can be applied to infinite streams and finite datasets equally, and the generated samples can be used for various applications. Our experiments on both real and synthetic data validate that {\em FPS\/} can effectively obtain a high quality sample of the desired size. In addition, while using the sample generated by {\em FPS\/} in various mining applications, a significant improvement in efficiency can be achieved without compromising the model's precision.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Knowledge Discovery from Data (TKDD)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1054", keywords = "sampling; Streaming mining", } @Article{Clauset:2009:PLDc, author = "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J. Newman", title = "Power-Law Distributions in Empirical Data", journal = j-SIAM-REVIEW, volume = "51", number = "4", pages = "661--703", month = "????", year = "2009", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/070710111", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Mon May 17 17:56:49 MDT 2010", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Dlugosz:2009:VLD, author = "Stephan Dlugosz and Ulrich M{\"u}ller-Funk", title = "The value of the last digit: statistical fraud detection with digit analysis", journal = "Advances in Data Analysis and Classification", volume = "3", number = "3", pages = "281--290", month = dec, year = "2009", DOI = "https://doi.org/10.1007/s11634-009-0048-5", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11634-009-0048-5", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/11634", keywords = "Benford's Law", } @Article{Docampo:2009:BLA, author = "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio Flores-Moya", title = "{Benford}'s law applied to aerobiological data and its potential as a quality control tool", journal = j-AEROBIOLOGIA, volume = "25", number = "4", pages = "275--283", month = dec, year = "2009", CODEN = "AROBFT", DOI = "https://doi.org/10.1007/s10453-009-9132-8", ISSN = "0393-5965 (print), 1573-3025 (electronic)", ISSN-L = "0393-5965", bibdate = "Fri Nov 25 10:47:33 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132", acknowledgement = ack-nhfb, fjournal = "Aerobiologia", } @Article{Dorfleitner:2009:PBE, author = "Gregor Dorfleitner and Christian Klein", title = "Psychological barriers in {European} stock markets: Where are they?", journal = j-GLOB-FINANCE-J, volume = "19", number = "3", pages = "268--285", month = oct, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1016/j.gfj.2008.09.001", ISSN = "1044-0283 (print), 1873-5665 (electronic)", ISSN-L = "1044-0283", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S1044028308000549", abstract = "We examine four European stock indices and the prices of eight major German stocks for indications of psychological barriers. The frequency, (expected) returns, intraday volatility and trading volume of these assets are studied contingent on whether the prices lie within a certain range around round numbers. Our results indicate that psychological barriers do not exist on a consistent basis. It seems that some barriers have disappeared after these anomalies have been published. This discovery is consistent with current literature findings about disappearing stock market anomalies.", acknowledgement = ack-nhfb, fjournal = "Global Finance Journal", keywords = "Benford's Law; Disappearing anomalies; M-values; Psychological barriers", } @Article{Egghe:2009:PRP, author = "Leo Egghe", title = "Performance and its relation with productivity in {Lotkaian} systems", journal = j-SCIENTOMETRICS, volume = "81", number = "2", pages = "567--585", month = nov, year = "2009", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-008-2226-1", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib", URL = "http://link.springer.com/article/10.1007/s11192-008-2226-1", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Fewster:2009:SEB, author = "Rachel M. Fewster", title = "A Simple Explanation of {Benford's Law}", journal = j-AMER-STAT, volume = "63", number = "1", pages = "26--32", month = feb, year = "2009", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/tast.2009.0005", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2655700", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat2000.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Gauvrit:2009:LBG, author = "Nicolas Gauvrit and Jean-Paul Delahaye", title = "Loi de {Benford} g{\'e}n{\'e}rale. ({French}) [{General} {Benford}'s law]", journal = "Math. Sci. Hum. Math. Soc. Sci.", volume = "??", number = "186", pages = "5--15", year = "2009", CODEN = "????", ISSN = "0987-6936 (print), 1950-6821 (electronic)", ISSN-L = "0987-6936", MRclass = "62E10 (11A63 37A45)", MRnumber = "2562062 (2010i:62029)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://msh.revues.org/document11034.html", acknowledgement = ack-nhfb, fjournal = "Math{\'e}matiques et Sciences Humaines. Mathematics and Social Sciences", language = "French", } @Article{Gauvrit:2009:SRI, author = "N. Gauvrit and J.-P. Delahaye", title = "Scatter and regularity imply {Benford}'s law \ldots{} and more", journal = "ArXiv e-prints", month = oct, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G; http://arxiv.org/abs/0910.1359", abstract = "A random variable (r.v.) $X$ is said to follow Benford's law if $ \log (X) $ is uniform $ \bmod 1 $. Many experimental data sets prove to follow an approximate version of it, and so do many mathematical series and continuous random variables. This phenomenon received some interest, and several explanations have been put forward. Most of them focus on specific data, depending on strong assumptions, often linked with the log function. Some authors hinted --- implicitly --- that the two most important characteristics of a random variable when it comes to Benford are regularity and scatter. In a first part, we prove two theorems, making up a formal version of this intuition: scattered and regular r.v.'s do approximately follow Benford's law. The proofs only need simple mathematical tools, making the analysis easy. Previous explanations thus become corollaries of a more general and simpler one. These results suggest that Benford's law does not depend on properties linked with the log function. We thus propose and test a general version of the Benford's law. The success of these tests may be viewed as an a posteriori validation of the analysis formulated in the first part.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0910.1359", keywords = "Mathematics - Probability, Statistics - Methodology, G.3", primaryclass = "math.PR", } @Article{Gisin:2009:EEV, author = "Vladimir Gisin and Andrey Markov and Igor Vinukov", title = "Estimation of extreme values of returns using the {Zipf--Mandelbrot} flow", journal = j-INT-J-PURE-APPL-MATH, volume = "50", number = "2", pages = "245--250", year = "2009", CODEN = "????", ISSN = "1311-8080 (print), 1314-3395 (electronic)", ISSN-L = "1314-3395", MRclass = "60G70 (91B28 91B84)", MRnumber = "2488836", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Pure and Applied Mathematics", journal-URL = "http://ijpam.eu/", } @TechReport{Gonzales-Garcia:2009:BLM, author = "J. Gonzales-Garcia and G. Pastor", title = "{Benford's Law} and Macroeconomic Data Quality", type = "Working Paper", institution = "International Monetary Fund", address = "Washington, DC, USA", year = "2009", bibdate = "Tue Nov 22 18:53:16 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437", acknowledgement = ack-nhfb, } @Article{Graham:2009:SFD, author = "Scott D. J. Graham and John Hasseldine and David Paton", title = "Statistical fraud detection in a commercial lobster fishery", journal = "New Zealand Journal of Marine and Freshwater Research", volume = "43", number = "1", pages = "457--463", year = "2009", DOI = "https://doi.org/10.1080/00288330909510014", bibdate = "Sat Sep 10 11:38:12 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Abstract In this study we introduce the first step towards a statistical model for the reliability of fisheries data. We applied Benford's Law to catch data from the Atlantic Canadian lobster ({\em Homarus americanus}) fishery's lobster fishery areas (LFAs) 33 and 34 and compared our results to those using observations from the grey zone (a highly regulated lobster fishery shared by Canada and United States) and a fishery with a different regulatory regime (snow crab, {\em Chionoecetes opilio}). Non conformity with Benford's Law is often considered as an indicator of human manipulation of accounting data. We found that observations from the grey zone conformed to the distribution predicted by Benford's Law, whereas observations from snow crab and both lobster fishery areas did not conform.", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Gunnel:2009:DBL, author = "S. G{\"u}nnel and K.-H. T{\"o}dter", title = "Does {Benford's Law} Hold in Economic Research and Forecasting?", journal = j-EMPIRICA, volume = "36", number = "3", pages = "273--292", month = aug, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1007/s10663-008-9084-1", ISSN = "0340-8744 (print), 1573-6911 (electronic)", ISSN-L = "0340-8744", bibdate = "Thu Nov 17 19:16:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/content/100261/", abstract = "First and higher order digits in data sets of natural and socio-economic processes often follow a distribution called Benford's law. This phenomenon has been used in business and scientific applications, especially in fraud detection for financial data. In this paper, we analyse whether Benford's law holds in economic research and forecasting. First, we examine the distribution of regression coefficients and standard errors in research papers, published in Empirica and Applied Economics Letters. Second, we analyse forecasts of GDP growth and CPI inflation in Germany, published in Consensus Forecasts. There are two main findings: The relative frequencies of the first and second digits in economic research are broadly consistent with Benford's law. In sharp contrast, the second digits of Consensus Forecasts exhibit a massive excess of zeros and fives, raising doubts on their information content.", acknowledgement = ack-nhfb, fjournal = "Empirica", } @Article{Hales:2009:TBL, author = "Douglas N. Hales and Satya S. Chakravorty and V. Sridharan", title = "Testing {Benford's Law} for improving supply chain decision-making: A field experiment", journal = j-INT-J-PROD-ECON, volume = "122", number = "2", pages = "606--618", month = dec, year = "2009", CODEN = "JPCEYE", DOI = "https://doi.org/10.1016/j.ijpe.2009.06.017", ISSN = "0925-5273 (print), 1873-7579 (electronic)", ISSN-L = "0925-5273", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0925527309002163", abstract = "Supply chain managers must often trust data reported from suppliers to make decisions about sourcing and product reliability due to the costs or complexity of implementing traditional monitoring systems. Without some form of monitoring, these types of data are vulnerable to manipulation, thus making their suitability for decision-making ambiguous and creating an opportunity for supplier opportunism. Recent practitioner literature suggests one solution to this problem they refer to as trust-but-verify. The purpose of this empirical study is to scientifically examine the feasibility and cost of implementing one trust-but-verify method in a real-world supply chain using a principle called Benford's Law. The results of this two-year study suggest that the technique is feasible and cost effective in identifying supply chain data that have been intentionally manipulated. This finding can allow supply chain managers to segregate suspect data from decision-making until they can be validated and thus mitigate supplier opportunism.", acknowledgement = ack-nhfb, ajournal = "Int. j. prod. econ.", fjournal = "International Journal of Production Economics", keywords = "Benford's Law; Digital analysis; Operations management; Supplier opportunism; Supply chain management", } @Article{Hartshorn:2009:BRB, author = "Kevin Hartshorn", title = "Book Review: {{\booktitle{The fabulous Fibonacci numbers}} by Alfred Posamentier and Ingmar Lehmann}", journal = j-J-MATH-ARTS, volume = "3", number = "2", pages = "113--116", month = "????", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1080/17513470902897569", ISSN = "1751-3472 (print), 1751-3480 (electronic)", ISSN-L = "1751-3480", bibdate = "Sat Jan 07 09:43:47 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematics and the Arts", journal-URL = "http://www.tandfonline.com/loi/tmaa20", onlinedate = "05 Jun 2009", } @Article{Hayes:2009:CBL, author = "S. J. Hayes", title = "Correspondence: {Benford's Law} in Relation to Terminal Digit Preference", journal = j-J-CLIN-PATHOL, volume = "62", number = "6", pages = "574--575", month = "????", year = "2009", CODEN = "JCPAAK", ISSN = "0021-9746 (print), 1472-4146 (electronic)", ISSN-L = "0021-9746", bibdate = "Sat Sep 10 12:07:02 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jcp.bmj.com/content/62/6/575.2.extract", acknowledgement = ack-nhfb, fjournal = "Journal of Clinical Pathology", journal-URL = "http://jcp.bmj.com/content/by/year", keywords = "Benford's Law", } @Article{Hernando:2009:ZLF, author = "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas and C. Vesperinas and A. Plastino", title = "{Zipf}'s law from a {Fisher} variational-principle", journal = j-PHYS-LET-A, volume = "374", number = "1", pages = "18--21", day = "14", month = dec, year = "2009", CODEN = "PYLAAG", DOI = "https://doi.org/10.1016/j.physleta.2009.10.027", ISSN = "0375-9601 (print), 1873-2429 (electronic)", ISSN-L = "0375-9601", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0375960109012894", acknowledgement = ack-nhfb, fjournal = "Physics Letters A", journal-URL = "http://www.sciencedirect.com/science/journal/03759601", keywords = "Zipf's Law", } @InCollection{Horgan:2009:BL, author = "Jane M. Horgan", title = "{Benford's Law}", crossref = "Horgan:2009:PRI", chapter = "9.4", pages = "142--144", year = "2009", bibdate = "Mon Feb 18 18:46:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Hurlimann:2009:GBL, author = "Werner H{\"u}rlimann", title = "Generalizing {Benford}'s law using power laws: application to integer sequences", journal = j-INT-J-MATH-MATH-SCI, pages = "10", year = "2009", CODEN = "????", ISSN = "0161-1712 (print), 1687-0425 (electronic)", ISSN-L = "0161-1712", MRclass = "60E05 (11B83 62E15)", MRnumber = "2533550 (2010h:60043)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Article ID 970284.", URL = "http://arxiv.org/abs/math/0607166", abstract = "A simple method to derive parametric analytical extensions of Benford's law for first digits of numerical data is proposed. Two generalized Benford distributions are considered, namely the two-sided power Benford distribution and the new Pareto Benford distribution. The fitting capabilities of these generalized Benford distributions are illustrated and compared at some interesting and important integer sequences.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", journal-URL = "https://www.hindawi.com/journals/ijmms/", } @Article{Jang:2009:CDH, author = "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and Steven J. Miller", title = "Chains of distributions, hierarchical {Bayesian} models and {Benford's Law}", journal = "Journal of Algebra, Number Theory: Advances and Applications", volume = "1", number = "1", pages = "37--60", month = mar, year = "2009", CODEN = "????", ISSN = "0972-5555", ISSN-L = "0972-5555", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0805.4226", keywords = "Mathematics - Probability, Mathematics - Statistics Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)", primaryclass = "math.PR", } @Article{Janvresse:2009:BL, author = "Elise Janvresse and Thierry de la Rue", title = "{Benford}'s law", journal = "Butl. Soc. Catalana Mat.", volume = "24", number = "1", pages = "5--12", year = "2009", CODEN = "????", ISSN = "0214-316X", ISSN-L = "0214-316X", MRclass = "62-01", MRnumber = "2567485", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Translated by Frederic Utzet", acknowledgement = ack-nhfb, fjournal = "Butllet{\'\i}n de la Societat Catalana de Matem{\`a}tiques", } @Article{Jin:2009:AUR, author = "Jang C. Jin", title = "{Asian} University Rankings in International and Development Economics: An Application of {Zipf's Law}", journal = j-REV-INT-ECON, volume = "17", number = "1", pages = "137--143", year = "2009", DOI = "https://doi.org/10.1111/j.1467-9396.2008.00790.x", ISSN = "0965-7576 (print), 1467-9396 (electronic)", ISSN-L = "0965-7576", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Review of International Economics", } @Article{Jin:2009:PME, author = "Jang C. Jin", title = "Publications in mathematical economics and econometrics: ranking of {Asian} universities and an application of {Zipf's Law}", journal = "{Asian-Pacific} Economic Literature", volume = "23", number = "2", pages = "116--122", year = "2009", DOI = "https://doi.org/10.1111/j.1467-8411.2009.01233.x", ISSN = "0818-9935 (print), 1467-8411 (electronic)", ISSN-L = "0818-9935", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411", } @Article{Jolissaint:2009:LBR, author = "Paul Jolissaint", title = "Loi de {Benford}, relations de r{\'e}currence et suites {\'e}quidistribu{\'e}es. {II}. ({French}) [{Benford}'s Law, recurrence relations, and equidistributed sequences. {II}]", journal = j-ELEM-MATH, volume = "64", number = "1", pages = "21--36", year = "2009", CODEN = "????", DOI = "https://doi.org/10.4171/EM/112", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRclass = "62E10 (11A63 37A45)", MRnumber = "2471593 (2010f:62032)", MRreviewer = "Denys Pommeret", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{Judge:2009:DPS, author = "G. Judge and L. Schechter", title = "Detecting Problems in Survey Data using {Benford's Law}", journal = j-J-HUM-RESOUR, volume = "44", number = "1", pages = "1--24", month = "Winter", year = "2009", CODEN = "JHREA9", DOI = "https://doi.org/10.3368/jhr.44.1.1", ISSN = "0022-166X (print), 1548-8004 (electronic)", ISSN-L = "0022-166X", bibdate = "Tue Nov 22 18:55:52 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://jhr.uwpress.org/content/44/1/1.abstract; http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm", acknowledgement = ack-nhfb, fjournal = "Journal of Human Resources", } @Article{Kafri:2009:DNE, author = "Oded Kafri", title = "The Distributions in Nature and Entropy Principle", journal = "ArXiv e-prints", day = "28", month = jul, year = "2009", bibdate = "Mon Nov 21 07:26:11 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/0907.4852", abstract = "The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a ``bell-like'' distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is low, and the second one when the ratio is high. The obtained long tail distribution yields correctly the empirical Zipf law, Pareto's 20:80 rule and Benford's law. Therefore, it is concluded that the long tail and the ``bell-like'' distributions are outcomes of the tendency of statistical systems to maximize entropy.", acknowledgement = ack-nhfb, pagecount = "19", } @Article{Kafri:2009:EPD, author = "Oded Kafri", title = "Entropy Principle in Direct Derivation of {Benford's Law}", journal = "ArXiv e-prints", month = jan, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K; http://arxiv.org/abs/0901.3047", abstract = "The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although it attracts considerable attention, there is no a priori probabilistic criterion when a data set should or should not obey the law. Here a general criterion is suggested, namely that any file of digits in the Shannon limit (namely, having maximum entropy) has a Benford's law distribution of digits.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0901.3047", keywords = "Computer Science - Discrete Mathematics, Physics - Data Analysis, Statistics and Probability", primaryclass = "cs.DM", } @Article{Kim:2009:ITA, author = "Hyo-Jeong Kim and Michael Mannino and Robert J. Nieschwietz", title = "Information technology acceptance in the internal audit profession: Impact of technology features and complexity", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "10", number = "4", pages = "214--228", year = "2009", CODEN = "IJAIA7", DOI = "https://doi.org/10.1016/j.accinf.2009.09.001", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Ninth International Research Symposium on Accounting Information Systems (IRSAIS)", URL = "http://www.sciencedirect.com/science/article/pii/S1467089509000360", abstract = "Although various information technologies have been studied using the technology acceptance model (TAM), the study of acceptance of specific technology features for professional groups employing information technologies such as internal auditors (IA) has been limited. To address this gap, we extended the {TAM} for technology acceptance among {IA} professionals and tested the model using a sample of internal auditors provided by the Institute of Internal Auditors (IIA). System usage, perceived usefulness, and perceived ease of use were tested with technology features and complexity. Through the comparison of {TAM} variables, we found that technology features were accepted by internal auditors in different ways. The basic features such as database queries, ratio analysis, and audit sampling were more accepted by internal auditors while the advanced features such as digital analysis, regression/ANOVA, and classification are less accepted by internal auditors. As feature complexity increases, perceived ease of use decreased so that system usage decreased. Through the path analysis between {TAM} variables, the results indicated that path magnitudes were significantly changed by technology features and complexity. Perceived usefulness had more influence on feature acceptance when basic features were used, and perceived ease of use had more impact on feature acceptance when advanced features were used.", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law; Information technology adoption; Internal auditing; System acceptance; {IS} features", } @Article{Krakar:2009:ABL, author = "Mario {\v{Z}}gela and Zdravko Krakar", title = "Application of {Benford's Law} in Payment System Auditing", journal = j-J-INFO-ORG-SCI, volume = "33", number = "1", pages = "39--51", month = "????", year = "2009", CODEN = "????", ISSN = "1846-3312 (print), 1846-9418 (electronic)", ISSN-L = "1846-3312", bibdate = "Sun Nov 13 11:12:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf; http://jios.foi.hr/index.php/jios/article/view/108/66; http://jios.foi.hr/index.php/jios/issue/view/13", acknowledgement = ack-nhfb, fjournal = "Journal of Informational and Organizational Sciences", journal-URL = "http://jios.foi.hr/index.php/jios/index", xxjournal = "Journal of Information Ethics and Organisational Science (wrong!)", } @Article{Krishna:2009:DBD, author = "Hare Krishna and Pramendra Singh Pundir", title = "Discrete {Burr} and discrete {Pareto} distributions", journal = j-STAT-METHODOL, volume = "6", number = "2", pages = "177--188", month = mar, year = "2009", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:36 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S157231270800052X", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @MastersThesis{Krygier:2009:PRB, author = "J. Krygier", title = "Psychological Relevance of {Benford's Law}: Sensitivity to Statistical Regularities and Implications for Theories of Number Representation", type = "Honours thesis", school = "University of Sydney", address = "Sydney, NSW, Australia", year = "2009", bibdate = "Sat Sep 10 12:48:34 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Lansey:2009:ISR, author = "Jonathan C. Lansey and Bruce Bukiet", title = "{Internet} Search Result Probabilities: {Heaps' Law} and Word Associativity", journal = j-J-QUANT-LINGUISTICS, volume = "16", number = "1", pages = "40--66", month = "????", year = "2009", CODEN = "????", DOI = "https://doi.org/10.1080/09296170802514153", ISSN = "0929-6174 (print), 1744-5035 (electronic)", ISSN-L = "0929-6174", bibdate = "Sat Jan 07 09:36:17 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153", abstract = "We study the number of internet search results returned from multi-word queries based on the number of results returned when each word is searched for individually. We derive a model to describe search result values for multi-word queries using the total number of pages indexed by Google and by applying the Zipf power law to the words per page distribution on the internet and Heaps' law for unique word counts. Based on data from 351 word pairs each with exactly one hit when searched for together, and a Zipf law coefficient determined in other studies, we approximate the Heaps' law coefficient for the indexed worldwide web (about 8 billion pages) to be $ \beta = 0.52 $. Previous studies used under 20,000 pages. We demonstrate through examples how the model can be used to analyse automatically the relatedness of word pairs assigning each a value we call ``strength of associativity''. We demonstrate the validity of our method with word triplets and through two experiments conducted 8 months apart. We then use our model to compare the index sizes of competing search giants Yahoo and Google.", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Linguistics", keywords = "Benford's Law; Heaps' Law; Zipf's Law", onlinedate = "25 Feb 2009", remark = "From page 65: ``We mention that tests we have conducted show that internet searches for random numbers return approximately log-normally distributed results and sorting by first digits yields results that follow Benford's law (1938).''", } @Article{Li:2009:PDD, author = "Weihai Li and Yuan Yuan and Nenghai Yu", title = "Passive detection of doctored {JPEG} image via block artifact grid extraction", journal = j-SIG-PROC, volume = "89", number = "9", pages = "1821--1829", year = "2009", CODEN = "SPRODR", DOI = "https://doi.org/10.1016/j.sigpro.2009.03.025", ISSN = "0165-1684 (print), 1872-7557 (electronic)", ISSN-L = "0165-1684", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165168409001315", abstract = "It has been noticed that the block artifact grids (BAG), caused by the blocking processing during {JPEG} compression, are usually mismatched when interpolating or concealing objects by copy paste operations. In this paper, the {BAGs} are extracted blindly with a new extraction algorithm, and then abnormal {BAGs} can be detected with a marking procedure. Then the phenomenon of grid mismatch or grid blank can be taken as a trail of such forensics. Experimental results show that our method can mark these trails efficiently.", acknowledgement = ack-nhfb, fjournal = "Signal Processing", journal-URL = "http://www.sciencedirect.com/science/journal/01651684", keywords = "Benford's Law; Block artifact grid; Doctored image forensic; Grid mismatch; {JPEG} compression", } @Article{Lipovetsky:2009:PLD, author = "Stan Lipovetsky", title = "{Pareto} $ 80 / 20 $ law: derivation via random partitioning", journal = j-INT-J-MATH-EDU-SCI-TECH, volume = "40", number = "2", pages = "271--277", month = "????", year = "2009", CODEN = "IJMEBM", DOI = "https://doi.org/10.1080/00207390802213609", ISSN = "0020-739X (print), 1464-5211 (electronic)", ISSN-L = "0020-739X", bibdate = "Sat Jan 07 09:22:31 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609", abstract = "The Pareto 80/20 Rule, also known as the Pareto principle or law, states that a small number of causes (20\%) is responsible for a large percentage (80\%) of the effect. Although widely recognized as a heuristic rule, this proportion has not been theoretically based. The article considers derivation of this 80/20 rule and some other standard quotients from the mean and its interval estimation for the total value defined by the product of two variables in the random partitioning model.", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematical Education in Science and Technology", journal-URL = "http://www.tandfonline.com/loi/tmes20", onlinedate = "19 Feb 2009", } @Article{Luque:2009:FDF, author = "Bartolo Luque and Lucas Lacasa", title = "The first digit frequencies of prime numbers and {Riemann} zeta zeros", journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI, volume = "465", number = "2107", pages = "2197--2216", day = "8", month = jul, year = "2009", CODEN = "PRLAAZ", DOI = "https://doi.org/10.1098/rspa.2009.0126", ISSN = "1364-5021 (print), 1471-2946 (electronic)", ISSN-L = "1364-5021", bibdate = "Mon Feb 25 10:44:43 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract", acknowledgement = ack-nhfb, fjournal = "Proceedings of the Royal Society A: Mathematical, Physical, \& Engineering Sciences", journal-URL = "http://rspa.royalsocietypublishing.org/", keywords = "Benford's Law", onlinedate = "22 April 2009", } @Article{Mahdian:2009:UNI, author = "Babak Mahdian and Stanislav Saic", title = "Using noise inconsistencies for blind image forensics", journal = j-IMAGE-VIS-COMPUT, volume = "27", number = "10", pages = "1497--1503", year = "2009", CODEN = "IVCODK", DOI = "https://doi.org/10.1016/j.imavis.2009.02.001", ISSN = "0262-8856 (print), 1872-8138 (electronic)", ISSN-L = "0262-8856", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib", note = "Special Section: Computer Vision Methods for Ambient Intelligence", URL = "http://www.sciencedirect.com/science/article/pii/S0262885609000146", abstract = "A commonly used tool to conceal the traces of tampering is the addition of locally random noise to the altered image regions. The noise degradation is the main cause of failure of many active or passive image forgery detection methods. Typically, the amount of noise is uniform across the entire authentic image. Adding locally random noise may cause inconsistencies in the image's noise. Therefore, the detection of various noise levels in an image may signify tampering. In this paper, we propose a novel method capable of dividing an investigated image into various partitions with homogeneous noise levels. In other words, we introduce a segmentation method detecting changes in noise level. We assume the additive white Gaussian noise. Several examples are shown to demonstrate the proposed method's output. An extensive quantitative measure of the efficiency of the noise estimation part as a function of different noise standard deviations, region sizes and various {JPEG} compression qualities is proposed as well.", acknowledgement = ack-nhfb, fjournal = "Image and Vision Computing", keywords = "Benford's Law; Digital forgery; Image forensics; Image segmentation; Image tampering; Noise inconsistency", } @Article{Mebane:2009:EFR, author = "Walter R. {Mebane, Jr.} and K. Kalinin", title = "Electoral Falsification in {Russia}: Complex Diagnostics Selections 2003--2004, 2007--2008", journal = "Russian Electoral Review", volume = "2", number = "??", pages = "57--70", month = "????", year = "2009", bibdate = "Sat Sep 10 14:30:23 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", language = "Russian", } @TechReport{Mebane:2009:NPE, author = "Walter R. {Mebane, Jr.}", title = "Note on the {Presidential} Election in {Iran}", type = "Report", number = "????", institution = "University of Michigan", address = "Ann Arbor, MI, USA", month = jun, year = "2009", bibdate = "Sat Sep 10 14:17:31 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/rvwmebane/note29jun2009.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Meintanis:2009:UAT, author = "Simos G. Meintanis", title = "A unified approach of testing for discrete and continuous {Pareto} laws", journal = j-STAT-PAPERS, volume = "50", number = "3", pages = "569--580", month = jun, year = "2009", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-007-0103-2", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:30 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-007-0103-2", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @TechReport{Moller:2009:MQA, author = "M. M{\"o}ller", title = "Measuring the Quality of Auditing Services with the Help of {Benford's Law} -- An Empirical Analysis and Discussion of this Methodical Approach", type = "Report", number = "??", institution = "Institute for Accounting and Control, University of Z{\"u}rich", address = "Z{\"u}rich, Switzerland", pages = "25", day = "24", month = apr, year = "2009", bibdate = "Tue Nov 22 20:40:12 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ssrn.com/abstract=1529307", abstract = "The so-called Benford's Law describes regularity in the distribution of digits of randomly selected numbers, which states that the relative frequency of the leading digits reduces in a systematic manner from the digit 1 to the digit 9. This distribution hypothesis is being discussed in recent times as an audit instrument in order to gain insights into possible conscious and inadvertent errors in data records. The present paper analyses the closing accounts of 1,373 annual financial statements of companies listed on the German DAX and compares these with the Benford's distribution hypothesis. It can be seen in the process that data pertaining to financial accounts, which have not been audited by the so-called ``Big 4'' audit firms, but by smaller external auditors, deviate to a significant extent from the regularity of Benford's Law, which appears to make the use of Benford's Law suitable as a benchmark to assess the quality of the audit.", acknowledgement = ack-nhfb, } @Article{Moret:2009:GSA, author = "M. A. Moret and V. de Senna and M. C. Santana and G. F. Zebende", title = "Geometric Structural Aspects of Proteins and {Newcomb--Benford Law}", journal = j-INT-J-MOD-PHYS-C, volume = "20", number = "12", pages = "1981--1988", month = "????", year = "2009", CODEN = "IJMPEO", DOI = "https://doi.org/10.1142/S0129183109014874", ISSN = "0129-1831 (print), 1793-6586 (electronic)", ISSN-L = "0129-1831", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M", acknowledgement = ack-nhfb, fjournal = "International Journal of Modern Physics C [Physics and Computers]", journal-URL = "http://www.worldscientific.com/loi/ijmpc", keywords = "Hydrophobicity, protein packing, complex systems, Time series analysis, Systems obeying scaling laws, Binary and multiple stars", } @Article{Ni:2009:BLD, author = "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren", title = "{Benford's Law} and $ \beta $-Decay Half-Lives", journal = j-COMM-THEOR-PHYS, volume = "51", number = "4", pages = "713--716", month = apr, year = "2009", CODEN = "CTPHDI", DOI = "https://doi.org/10.1088/0253-6102/51/4/25", ISSN = "0253-6102 (print), 1572-9494 (electronic)", ISSN-L = "0253-6102", bibdate = "Sun Nov 13 11:01:52 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N; http://stacks.iop.org/0253-6102/51/i=4/a=25", abstract = "The experimental values of 2059 $ \beta $-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford's law, which states that the frequency of occurrence of each figure, 1--9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford's logarithmic distribution of $ \beta $-decay half-lives can be explained in terms of Newcomb's justification of Benford's law and empirical exponential law of $ \beta $-decay half-lives. Moreover, we test the calculated values of 6721 $ \beta $-decay half-lives with the aid of Benford's law. This indicates that Benford's law is useful for theoretical physicists to test their methods for calculating $ \beta $-decay half-lives.", acknowledgement = ack-nhfb, fjournal = "Communications in theoretical physics", } @Article{Nigrini:2009:DDU, author = "Mark J. Nigrini and Steven J. Miller", title = "Data Diagnostics Using Second-Order Tests of {Benford's Law}", journal = j-AUDITING, volume = "28", number = "2", pages = "305--324", month = nov, year = "2009", CODEN = "????", DOI = "https://doi.org/10.2308/aud.2009.28.2.305", ISSN = "0278-0380 (print), 1558-7991 (electronic)", ISSN-L = "0278-0380", bibdate = "Tue Nov 15 09:11:56 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaapubs.org/loi/ajpt; http://link.aip.org/link/AJPTXX/v28/i2/p305/s1", abstract = "Auditors are required to use analytical procedures to identify the existence of unusual transactions, events, and trends. Benford's Law gives the expected patterns of the digits in numerical data, and has been advocated as a test for the authenticity and reliability of transaction level accounting data. This paper describes a new second-order test that calculates the digit frequencies of the differences between the ordered (ranked) values in a data set. These digit frequencies approximate the frequencies of Benford's Law for most data sets. The second-order test is applied to four sets of transactional data. The second-order test detected errors in data downloads, rounded data, data generated by statistical procedures, and the inaccurate ordering of data. The test can be applied to any data set and nonconformity usually signals an unusual issue related to data integrity that might not have been easily detectable using traditional analytical procedures", acknowledgement = ack-nhfb, fjournal = "Auditing: A Journal of Practice \& Theory", } @InCollection{Nisbet:2009:CFD, author = "Robert Nisbet and John Elder and Gary Miner", booktitle = "Handbook of Statistical Analysis and Data Mining Applications", title = "Chapter 17 --- Fraud Detection", publisher = "Academic Press", address = "Boston", pages = "347--361", year = "2009", DOI = "https://doi.org/10.1016/B978-0-12-374765-5.00017-6", ISBN = "0-12-374765-1", ISBN-13 = "978-0-12-374765-5", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/B9780123747655000176", abstract = "Fraud can be defined as a criminal activity, involving false representations to gain an unjust advantage. It occurs in a wide variety of forms and is ever changing as new technologies and new economic and social systems provide new opportunities for fraudulent activity. This chapter introduces fraud detection, provides a simple example of how to build a fraud model, and directs one to additional references to broaden and deepen the knowledge of the vast scope of fraud detection. Fraud is a form of human response that can be modeled in ways very similar to customer response in business. The temporal dimension of fraud provides a rich source of information related to fraud. The occurrence of a fraud event at a given time may be highly related to the pattern of events that happened in the past. These historical data are the most important source of attributes needed to sufficiently define the fraud signature in the data set. Fraud modeling requires the construction of reference objects based on relationships that are drawn in the past between various conditions and the incidence of fraud. The basic approach to fraud detection with an analytical model is to identify possible predictors of fraud associated with known fraudsters and their actions in the past. The most powerful fraud models are built on historical data.", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Rajabpour:2009:SRC, author = "M. A. Rajabpour and S. M. {Vaez Allaei}", title = "Scaling relations for contour lines of rough surfaces", journal = j-PHYS-REV-E, volume = "80", number = "1", pages = "011115", day = "13", month = jul, year = "2009", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.80.011115", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.80.011115", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", } @Article{Ramanana-Rahary:2009:APR, author = "Suzy Ramanana-Rahary and Michel Zitt and Ronald Rousseau", title = "Aggregation properties of relative impact and other classical indicators: Convexity issues and the {Yule--Simpson} paradox", journal = j-SCIENTOMETRICS, volume = "79", number = "2", pages = "311--327", month = may, year = "2009", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-009-0420-4", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:11 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib", URL = "http://link.springer.com/article/10.1007/s11192-009-0420-4", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Romero-Rochin:2009:DBL, author = "V. Romero-Rochin", title = "A derivation of {Benford's Law} \ldots{} and a vindication of {Newcomb}", journal = "ArXiv e-prints", month = sep, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R; http://arxiv.org/abs/0909.3822", abstract = "We show how Benford's Law (BL) for first, second, \ldots{}, digits, emerges from the distribution of digits of numbers of the type $ a^R $, with $a$ any real positive number and $R$ a set of real numbers uniformly distributed in an interval $ [P \log_a(10), (P + 1) \log_a(10)) $ for any integer $P$. The result is shown to be number base and scale invariant. A rule based on the mantissas of the logarithms allows for a determination of whether a set of numbers obeys BL or not. We show that BL applies to numbers obtained from the {\em multiplication\/} or {\em division\/} of numbers drawn from any distribution. We also argue that (most of) the real-life sets that obey BL are because they are obtained from such basic arithmetic operations. We exhibit that all these arguments were discussed in the original paper by Simon Newcomb in 1881, where he presented Benford's Law.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0909.3822", keywords = "Mathematics - Probability, Mathematics - History and Overview", pagecount = "12", primaryclass = "math.PR", } @Article{Roukema:2009:BLA, author = "Boudewijn F. Roukema", title = "{Benford's Law} anomalies in the 2009 {Iranian} presidential election", journal = "ArXiv e-prints", day = "16", month = jun, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R; http://arxiv.org/abs/0906.2789", abstract = "The vote count first digit frequencies of the 2009 Iranian presidential election are analysed assuming proportionality of candidates' votes to the total vote per voting area. This method is closely related to Benford's Law. A highly significant ($ p \approx 0.0007 $ ) excess of vote counts for candidate $K$ that start with the digit 7 is found (41 observed, 21.2--22 expected). Using this property as a selection criterion leads to the following coincidences. (i) Among the six most populous voting areas, this criterion selects those three that have greater proportions of votes for A than the other three. The probability that the two sub-groups are drawn from the same distribution is $ p \approx 0.1 $. (ii) $K$'s vote counts for these same three voting areas all have the same second digit. The probability of this is $ p \approx 0.01 $. (iii) Most (75\%) of the vote counts for $K$ in voting areas with 70 to 79 votes for $K$ are odd, and every even number occurs exactly once. The probability of the latter is $ p \approx 0.0005 $. Interpreting the big city effect (i) +( ii) as an overestimate of the true vote, assumed to be roughly 50\% to match other data, while retaining constant total vote numbers and increasing votes for the other three candidates in proportion to their average voting percentages, would imply that the difference between A's and M's vote totals would drop by about one million votes. These results do not exclude other anomalies.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "0906.2789", keywords = "Statistics - Applications", primaryclass = "stat.AP", remark = "It appears the title changed over six updates to this paper to the one in the final journal version \cite{Roukema:2014:FDA}.", xxtitle = "A first-digit anomaly in the 2009 {Iranian} {Presidential} election", } @Article{Sambridge:2009:ABL, author = "M. Sambridge and H. Tkalcic and A. Jackson", title = "On the applicability of {Benford's Law} in the Geosciences", journal = "AGU Fall Meeting Abstracts", pages = "A1756--??", month = dec, year = "2009", CODEN = "????", ISSN = "????", bibdate = "Tue Nov 15 06:32:38 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S", acknowledgement = ack-nhfb, keywords = "[1294] GEODESY AND GRAVITY / Instruments and techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM / Instruments and techniques, [3294] MATHEMATICAL GEOPHYSICS / Instruments and techniques, [7299] SEISMOLOGY / General or miscellaneous", } @Article{Shao:2009:FDD, author = "Lijing Shao and Bo-Qiang Ma", title = "First digit distribution of hadron full width", journal = j-MOD-PHYS-LETT-A, volume = "24", number = "40", pages = "3275--3282", month = "????", year = "2009", CODEN = "MPLAEQ", DOI = "https://doi.org/10.1142/S0217732309031223", ISSN = "0217-7323 (print), 1793-6632 (electronic)", ISSN-L = "0217-7323", bibdate = "Mon Nov 14 16:26:06 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $ 1, 2, \ldots {}, 9 $, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e., the law is scale-invariant, base-invariant, and power-invariant. This means that the lifetimes of hadrons follow also Benford's law.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1004.3077", fjournal = "Modern Physics Letters A (MPLA)", journal-URL = "http://www.worldscientific.com/loi/mpla", primaryclass = "hep-ph", } @Article{Shi:2009:FDL, author = "Yun Q. Shi", title = "{First Digit Law} and Its Application to Digital Forensics", journal = j-LECT-NOTES-COMP-SCI, volume = "5450", pages = "448--453", year = "2009", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-04438-0_37", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:32:48 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04438-0_37", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-04438-0", book-URL = "http://www.springerlink.com/content/978-3-642-04438-0", fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Speed:2009:YWP, author = "T. Speed", title = "You want proof?", journal = j-BULL-INST-MATH-STAT, volume = "38", number = "??", pages = "11--??", month = "????", year = "2009", CODEN = "SMBCVA", ISSN = "0146-3942", ISSN-L = "0146-3942", bibdate = "Wed Nov 16 07:00:01 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://bulletin.imstat.org/archive/", acknowledgement = ack-nhfb, fjournal = "Bulletin --- Institute of Mathematical Statistics", keywords = "Benford's Law", remark = "As of 16 November 2011, volume 38 is not yet online at the publisher Web site, although there are (broken) links for volumes 31 (2002) to date.", } @Article{Stosic:2009:CSM, author = "Borko D. Stosi{\'c} and Tatijana Stosi{\'c}", title = "Comment on {``Ising model on the scale-free network with a Cayley-tree-like structure''}", journal = j-PHYS-REV-E, volume = "79", number = apr, pages = "048101", day = "24", month = apr, year = "2009", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.79.048101", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.79.048101", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "2", } @Misc{Tao:2009:BLZ, author = "Terrence Tao", title = "{Benford}'s law, {Zipf}'s law, and the {Pareto} distribution", howpublished = "Web document.", year = "2009", bibdate = "Mon Nov 14 16:59:19 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/", acknowledgement = ack-nhfb, } @Article{Todter:2009:BLI, author = "Karl-Heinz T{\"o}dter", title = "{Benford's Law} as an Indicator of Fraud in Economics", journal = j-GER-ECON-REV, volume = "10", number = "3", pages = "339--351", month = aug, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1111/j.1468-0475.2009.00475.x", ISSN = "1465-6485 (print), 1468-0475 (electronic)", ISSN-L = "1465-6485", bibdate = "Mon Nov 14 17:09:33 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "German Economic Review", onlinedate = "16 Jun 2009", } @Article{Villasenor-Alva:2009:BGF, author = "Jos{\'e} A. Villase{\~n}or-Alva and Elizabeth Gonz{\'a}lez-Estrada", title = "A bootstrap goodness of fit test for the generalized {Pareto} distribution", journal = j-COMPUT-STAT-DATA-ANAL, volume = "53", number = "11", pages = "3835--3841", day = "1", month = sep, year = "2009", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:42:33 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947309001406", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @InProceedings{Wang:2009:UBL, author = "J. Wang and B. H. Cha and S. H. Cho and C. C. J. Kuo", editor = "{IEEE}", booktitle = "2009 IEEE International Conference on Multimedia and Expo", title = "Understanding {Benford's Law} and its vulnerability in image forensics", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1568--1571", month = jun, year = "2009", DOI = "https://doi.org/10.1109/ICME.2009.5202811", ISSN = "1945-7871", bibdate = "Sat Sep 10 11:29:36 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Application software; Authentication; Benford law; Benford's law; Digital images; forensic science; Forensics; Gaussian processes; generalized Benford's law; generalized Gaussian function; generalized Laplacian function; histogram manipulation; histogram manipulation attack; Histograms; image authentication; image coding; image forensics; Image processing; Laplace equations; message authentication; probability; Probability density function; probability density function; random processes; random variable; Random variables; Signal processing", } @Article{Xie:2009:FAS, author = "Tao Xie and Yao Sun", title = "A file assignment strategy independent of workload characteristic assumptions", journal = j-TOS, volume = "5", number = "3", pages = "10:1--10:??", month = nov, year = "2009", CODEN = "????", DOI = "https://doi.org/10.1145/1629075.1629079", ISSN = "1553-3077 (print), 1553-3093 (electronic)", ISSN-L = "1553-3077", bibdate = "Tue Mar 16 15:33:57 MDT 2010", bibsource = "http://www.acm.org/pubs/contents/journals/tos/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tos.bib", abstract = "The problem of statically assigning nonpartitioned files in a parallel I/O system has been extensively investigated. A basic workload characteristic assumption of most existing solutions to the problem is that there exists a strong inverse correlation between file access frequency and file size. In other words, the most popular files are typically small in size, while the large files are relatively unpopular. Recent studies on the characteristics of Web proxy traces suggested, however, the correlation, if any, is so weak that it can be ignored. Hence, the following two questions arise naturally. First, can existing algorithms still perform well when the workload assumption does not hold? Second, if not, can one develop a new file assignment strategy that is immune to the workload assumption? To answer these questions, we first evaluate the performance of three well-known file assignment algorithms with and without the workload assumption, respectively. Next, we develop a novel static nonpartitioned file assignment strategy for parallel I/O systems, called static round-robin (SOR), which is immune to the workload assumption. Comprehensive experimental results show that SOR consistently improves the performance in terms of mean response time over the existing schemes.", acknowledgement = ack-nhfb, articleno = "10", fjournal = "ACM Transactions on Storage", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J960", keywords = "File assignment; load balancing; parallel I/O; workload characteristics; Zipfian distribution", } @Article{Zhang:2009:ZDT, author = "Jianhua Zhang and Qinghua Chen and Yougui Wang", title = "{Zipf} distribution in top {Chinese} firms and an economic explanation", journal = j-PHYSICA-A, volume = "388", number = "10", pages = "2020--2024", day = "15", month = may, year = "2009", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2009.01.027", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437109000806", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @InProceedings{Zhao:2009:IFU, author = "Xi Zhao and A. T. S. Ho and Y. Q. Shi", booktitle = "2009 16th International Conference on Digital Signal Processing", title = "Image forensics using generalised {Benford's Law} for accurate detection of unknown {JPEG} compression in watermarked images", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1--8", month = jul, year = "2009", DOI = "https://doi.org/10.1109/ICDSP.2009.5201261", ISSN = "1546-1874", bibdate = "Sat Sep 10 11:42:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Authentication; average QF correct detection rate; data compression; DCT; Digital images; Forensics; generalised Benford law; Generalised Benford's Law; Image Authentication; Image coding; image coding; image forensics technique; Image storage; JPEG Compression; message authentication; object detection; Physics computing; Q factor; Q-factor; quality factors; Semi-fragile Watermarking; semifragile watermarking; Signal processing algorithms; Transform coding; unknown JPEG compression detection; watermarked images; Watermarking; watermarking", } @Article{Abourbih:2010:SSD, author = "Jonathan A. Abourbih and Luke Blaney and Alan Bundy and Fiona McNeill", title = "A Single-Significant-Digit Calculus for Semi-Automated Guesstimation", journal = j-LECT-NOTES-COMP-SCI, volume = "6173", pages = "354--368", year = "2010", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-14203-1_31", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:43:23 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-14203-1", book-URL = "http://www.springerlink.com/content/978-3-642-14203-1", fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Afify:2010:EEP, author = "W. M. Afify", title = "On estimation of the exponentiated {Pareto} distribution under different sample schemes", journal = j-STAT-METHODOL, volume = "7", number = "2", pages = "77--83", month = mar, year = "2010", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:41 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312709000653", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Misc{Alagoz:2010:MDB, author = "Ali Alag{\"o}z and Mustafa Ay", title = "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital Analiz. ({Turkish}) [{Benford Law}-Based Digital Analysis of Accounting Oversight]", pages = "17", day = "8", month = jan, year = "2010", bibdate = "Mon Feb 18 09:19:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf", acknowledgement = ack-nhfb, language = "Turkish", } @Article{Aldous:2010:WCO, author = "David Aldous and Tung Phan", title = "When Can One Test an Explanation? {Compare} and Contrast {Benford's Law} and the Fuzzy {CLT}", journal = j-AMER-STAT, volume = "64", number = "3", pages = "221--227", month = aug, year = "2010", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/tast.2010.09098", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2757166", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Altamirano:2010:PTS, author = "Carlo Altamirano and Alberto Robledo", title = "Possible thermodynamic structure underlying the laws of {Zipf} and {Benford}", journal = "ArXiv e-prints", day = "10", month = aug, year = "2010", bibdate = "Mon Nov 21 07:12:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1008.1614", abstract = "We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This structure is obtained from a deformed type of statistical mechanics that arises when configurational phase space is incompletely visited in a severe way. Specifically, the restriction is that the accessible fraction of this space has fractal properties. The focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials that when particularized to first digits leads to a previously existing generalization of Benford's law. The inverse functional of this expression leads to Zipf's law; but it naturally includes the bends or tails observed in real data for small and large rank. Remarkably, we find that the entire problem is analogous to the transition to chaos via intermittency exhibited by low-dimensional nonlinear maps. Our results also explain the generic form of the degree distribution of scale-free networks.", acknowledgement = ack-nhfb, remark = "To be published in European Physical Journal B.", } @Article{Anderson:2010:BLC, author = "Theresa Anderson and Larry Rolen and Ruth Stoehr", title = "{Benford's} Law For Coefficients of Modular Forms and Partition Functions", journal = "ArXiv e-prints", day = "3", month = sep, year = "2010", bibdate = "Mon Nov 21 07:10:51 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1009.0780", abstract = "Here we prove that Benford's law holds for coefficients of an infinite class of modular forms. Expanding the work of Bringmann and Ono on exact formulas for harmonic Maass forms, we derive the necessary asymptotics. This implies that the unrestricted partition function $ p(n) $, as well as other natural partition functions, satisfy Benford's law.", acknowledgement = ack-nhfb, pagecount = "10", } @Article{Bachmann:2010:APC, author = "Val{\'e}rie Bachmann and Martin H. Fischer and Hans-Peter Landolt and Peter Brugger", title = "Asymmetric prefrontal cortex functions predict asymmetries in number space", journal = j-BRAIN-COGN, volume = "74", number = "3", pages = "306--311", month = dec, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1016/j.bandc.2010.08.011", ISSN = "0278-2626 (print), 1090-2147 (electronic)", ISSN-L = "0278-2626", bibdate = "Tue Nov 22 11:28:19 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0278262610001272", acknowledgement = ack-nhfb, fjournal = "Brain and Cognition", keywords = "Benford's Law; small-number bias (SNB); Spatial Numerical Association of Response Codes (SNARC) effect", } @Article{Balanzario:2010:SCB, author = "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz", title = "Sufficient conditions for {Benford's Law}", journal = j-STAT-PROB-LETT, volume = "80", number = "23--24", pages = "1713--1719", day = "1--15", month = dec, year = "2010", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2010.07.014", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "62E10 (62E17)", MRnumber = "2734233 (2011i:62019)", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715210002087", abstract = "We present two sufficient conditions for an absolutely continuous random variable to obey Benford's Law for the distribution of the first significant digit. These two sufficient conditions suggest that Benford's Law will not often be observed in everyday sets of numerical data. On the other hand, we recall that there are two processes by way of which a random variable can come close to following Benford's Law. The first of these is the multiplication of independent random variables and the second is the exponentiation of a random variable to a large power. Our working tool is the Poisson sum formula of Fourier analysis. Like the central limit theorem, Benford's Law has an asymptotic nature.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law; First significant digit", } @Article{Balaz:2010:BLD, author = "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch", title = "{Benford}'s law and distribution functions of sequences in $ (0, 1) $", journal = j-MATH-NOTES-ACAD-SCI-USSR, volume = "88", number = "3--4", pages = "449--463", month = oct, year = "2010", CODEN = "MTHNB2", DOI = "https://doi.org/10.1134/S0001434610090178", ISSN = "0001-4346 (print), 1573-8876 (electronic)", ISSN-L = "0001-4346", bibdate = "Fri Nov 25 10:52:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1134/S0001434610090178", acknowledgement = ack-nhfb, fjournal = "Mathematical Notes of the {Academy of Sciences of the USSR = Matematicheskie Zametki}", } @Article{Balazh:2010:BLD, author = "V. Balazh and K. Nagasaka and O. Shtraukh", title = "{Benford}'s law and distribution functions of sequences in {$ (0, 1) $}", journal = j-MAT-ZAMETKI, volume = "88", number = "4", pages = "485--501", year = "2010", DOI = "https://doi.org/10.1134/S0001434610090178", ISSN = "0025-567X", ISSN-L = "0025-567X", MRclass = "11K06 (60E05)", MRnumber = "2882211", MRreviewer = "Michael Drmota", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie Zametki", journal-URL = "http://link.springer.com/journal/11006", } @TechReport{Bauer:2010:DDF, author = "J. Bauer and J. Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford's Law} on Regression Tables", type = "Report", institution = "Institute of Sociology, Ludwig-Maximilians-Universit{\"a}t", address = "M{\"u}nchen, Germany", pages = "????", year = "2010", bibdate = "Tue Nov 22 21:15:18 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Beber:2010:WNS, author = "Bernd Beber and Alexandria Scacco", title = "What the Numbers Say: a Digit-Based Test for Election Fraud", journal = j-POLIT-ANAL, volume = "20", number = "2", pages = "211--234", month = "Spring", year = "2010", DOI = "https://doi.org/10.1093/pan/mps003", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 17:29:42 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pan.oxfordjournals.org/content/20/2/211.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", journal-URL = "https://www.cambridge.org/core/journals/political-analysis/all-issues", keywords = "Benford's Law", } @TechReport{Berger:2010:FFFa, author = "A. Berger and T. P. Hill", title = "Fundamental Flaws in {Feller}'s Classical Derivation of {Benford's Law}", type = "Preprint", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", pages = "8", year = "2010", bibdate = "Mon Feb 18 17:31:57 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf", abstract = "Feller's classic text \booktitle{An Introduction to Probability Theory and its Applications} \cite{Feller:1968:IPT} contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition (`large spread') for a random variable $X$ to be approximately Benford distributed, that is, for $ \log_{10} X $ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstrate that large spread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of `spread' or measure of dispersion.", acknowledgement = ack-nhfb, } @Article{Berger:2010:FFFb, author = "Arno Berger and Theodore P. Hill", title = "Fundamental Flaws in {Feller}'s Classical Derivation of {Benford's Law}", journal = "ArXiv e-prints", month = may, year = "2010", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 18:23:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B; http://arxiv.org/abs/1005.2598", abstract = "Feller's classic text \booktitle{An Introduction to Probability Theory and its Applications} \cite{Feller:1968:IPT} contains a derivation of the well known significant-digit law called Benford's law. More specifically, Feller gives a sufficient condition (`large spread') for a random variable $X$ to be approximately Benford distributed, that is, for $ \log_{10}X $ to be approximately uniformly distributed modulo one. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstrate that large spread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of `spread' or measure of dispersion", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1005.2598", keywords = "Mathematics - Probability, Mathematics - Statistics, 62Axx", primaryclass = "math.PR", } @TechReport{Berger:2010:LSD, author = "A. Berger", title = "Large Spread Does Not Imply {Benford's Law}", type = "Preprint", institution = "Department of Mathematical and Statistical Sciences, University of Alberta", address = "Edmonton, AB, Canada", year = "2010", bibdate = "Sat Nov 12 16:46:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.ualberta.ca/~aberger/Publications.html", acknowledgement = ack-nhfb, } @Article{Block:2010:GEB, author = "Henry W. Block and Thomas H. Savits", title = "A General Example for {Benford} Data", journal = j-AMER-STAT, volume = "64", number = "4", pages = "335--339", month = nov, year = "2010", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/tast.2010.09169", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", MRnumber = "2758565", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Benford's Law deals, among other things, with the proportion of numbers whose first significant digit is a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first significant digit $1$) in a variety of datasets. In these datasets, which arise in various compendiums or as mixtures of various sets of numbers, the proportion of numbers with first significant digit one is $ 0.3010 $ which is much higher than the commonsense value of $ 1 / 9 $. The reasons for this occurrence have been elusive. Mathematical attempts to explain this phenomenon have been relatively fruitless. Methods involving probability have been somewhat more successful. In this article we give some simple reasons for this occurrence and also give an example of a general mixture of distributions which exactly satisfies this Law. Various other examples and counterexamples are also given.", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", } @Article{Bonache:2010:DFL, author = "A. B. Bonache and K. Moris and J. Maurice", title = "{D}{\'e}tection de fraudes et loi de {Benford}: Quelques risques associ{\'e}s. ({French}) [{Fraud} detection and {Benford}'s law: Some risks]", journal = "Revue Fran{\c{c}}aise de Comptabilit{\'e}", volume = "??", number = "431", pages = "24--27", month = apr, year = "2010", CODEN = "????", DOI = "????", ISSN = "0484-8764", ISSN-L = "0484-8764", bibdate = "Mon Feb 18 17:33:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "????", acknowledgement = ack-nhfb, journal-URL = "http://www.experts-comptables.fr/csoec/Publications/RFC", language = "French", } @InCollection{Brahler:2010:EMS, author = "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena Emke", booktitle = "{Ilmenauer Schriften zur Betriebswirtschaftslehre}. ({German}) [{Illmenauer} writings on economics]", title = "{Der Einsatz mathematisch-statistischer Methoden in der digitalen Betriebspr{\"u}fung}. ({German}) [{The} use of mathematical and statistical methods in the digital audit]", volume = "4/2010", publisher = "Verlag proWiWi e.V.", address = "Ilmenau, Germany", pages = "48", month = apr, year = "2010", ISBN = "3-940882-23-2", ISBN-13 = "978-3-940882-23-3", ISSN = "1866-2145 (print), 2192-4643 (electronic)", LCCN = "????", bibdate = "Mon Feb 18 17:35:58 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Bravo-Marquez:2010:HLM, author = "Felipe Bravo-Marquez and Gaston L'Huillier and Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez", title = "Hypergeometric Language Model and {Zipf}-Like Scoring Function for {Web} Document Similarity Retrieval", journal = j-LECT-NOTES-COMP-SCI, volume = "6393", pages = "303--308", year = "2010", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-16321-0_32", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:49:42 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-16321-0", book-URL = "http://www.springerlink.com/content/978-3-642-16321-0", fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Burns:2010:PL, author = "John Burns", title = "Probably likely", journal = j-NEW-SCIENTIST, volume = "208", number = "2786", pages = "32-", year = "2010", CODEN = "NWSCAL", DOI = "https://doi.org/10.1016/S0262-4079(10)62810-2", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0262407910628102", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law", } @Article{Cartlidge:2010:NNO, author = "Edwin Cartlidge", title = "In nature, number one dominates", journal = "Institute of Physics, Environmental Research Letters", volume = "??", number = "??", pages = "??--??", day = "25", month = oct, year = "2010", DOI = "????", bibdate = "Mon Feb 18 17:38:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://environmentalresearchweb.org/cws/article/news/44124", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Cifarelli:2010:GSP, author = "D. Michele Cifarelli and R. P. Gupta and K. Jayakumar", title = "On generalized semi-{Pareto} and semi-{Burr} distributions and random coefficient minification processes", journal = j-STAT-PAPERS, volume = "51", number = "1", pages = "193--208", month = jan, year = "2010", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-008-0132-5", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:31 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-008-0132-5", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Misc{Conway:2010:CFM, author = "D. Conway", title = "{Benford's Law} Tests for {Wikileaks} Data", howpublished = "Zero Intelligence Agents website.", day = "1", month = aug, year = "2010", bibdate = "Mon Feb 18 17:39:45 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.drewconway.com/zia/?p=2234", acknowledgement = ack-nhfb, } @InCollection{Corazza:2010:CFM, author = "Marco Corazza and Andrea Ellero and Alberto Zorzi", booktitle = "Mathematical and statistical methods for actuarial sciences and finance", title = "Checking financial markets via {Benford}'s law: the {S\&P 500} case", publisher = "Springer Italia", address = "Milan, Italy", pages = "93--102", year = "2010", DOI = "https://doi.org/10.1007/978-88-470-1481-7_10", MRclass = "62P05", MRnumber = "2676191", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/chapter/10.1007/978-88-470-1481-7_10", acknowledgement = ack-nhfb, } @Article{Corominas-Murtra:2010:UZL, author = "Bernat Corominas-Murtra and Ricard V. Sol{\'e}", title = "Universality of {Zipf}'s law", journal = j-PHYS-REV-E, volume = "82", number = "1", pages = "011102", day = "1", month = jul, year = "2010", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.82.011102", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", MRclass = "82B03 (62B10)", MRnumber = "2736361 (2011j:82002)", MRreviewer = "N. N. Ganikhodjaev", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.011102", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "9", } @Article{Courtland:2010:CML, author = "Rachel Courtland", title = "Curious mathematical law is rife in nature", journal = j-NEW-SCIENTIST, volume = "208", number = "2782", pages = "10--10", day = "16", month = oct, year = "2010", CODEN = "NWSCAL", DOI = "https://doi.org/10.1016/S0262-4079(10)62497-9", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0262407910624979", abstract = "Disparate data sets produced by natural phenomena all follow Benford's law, suggesting new ways to detect earthquakes or scientific anomalies", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law; earthquake detection", xxISSN = "0262-4079, 0028-6664", } @InCollection{Crato:2010:MB, author = "Nuno Crato", booktitle = "Figuring It Out: Entertaining Encounters with Everyday Math", title = "{Mr. Benford}", publisher = pub-SV, address = pub-SV:adr, bookpages = "ix + 227", pages = "173--178", year = "2010", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/978-3-642-04833-3_41", ISBN = "3-642-04832-3 (hardcover)", ISBN-13 = "978-3-642-04832-6 (hardcover)", bibdate = "Wed Aug 12 09:28:13 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-04833-3_41.pdf", abstract = "This is a book of mathematical stories, funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand.", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-04833-3", tableofcontents = "Everyday Matters. \\ The dinner table algorithm \\ Cutting the Christmas cake \\ Oranges and computers \\ When two and two don't make four \\ Getting more intelligent every day \\ The other lane always goes faster \\ Shoelaces and neckties \\ Number puzzles \\ Tossing a coin \\ The switch \\ Eubulides, the heap and the Euro \\ The Earth is Round. \\ How GPS works \\ Gear wheels \\ February 29 \\ The Nonius scale \\ Pedro Nunes' map \\ Lighthouse geometry \\ Asteroids and least squares \\ The useful man and the genius \\ Secret Affairs. \\ Alice and Bob \\ Inviolate cybersecrets \\ Quantum cryptography \\ The FBI wavelet \\ The enigma machine \\ Art and Geometry. \\ The Vitruvian man \\ The golden number \\ The geometry of A4 paper sizes \\ The strange worlds of Escher \\ Escher and the M{\"o}bius strip \\ Picasso, Einstein and the fourth dimension \\ Pollock's fractals \\ Voronoi diagrams \\ The Platonic solids \\ Pythagorean mosquitoes \\ The most beautiful of all \\ Mathematical Objects. \\ The power of math \\ Doubts in the realm of certainty \\ When chance enhances reliability \\ The difficulty of chance \\ Conjectures and proofs \\ Mr. Benford \\ Financial fractals \\ Turing's test \\ DNA computers \\ Magical multiplication \\ Pi day \\ The best job in the world \\ Out of This World. \\ Electoral paradoxes \\ The melon paradox \\ The cupcake paradox \\ Infinity \\ Unfair games \\ Monsieur Bertrand \\ Boy or girl? \\ A puzzle for Christmas \\ Crisis time for Easter eggs", } @Article{Debreceny:2010:DMJ, author = "Roger S. Debreceny and Glen L. Gray", title = "Data mining journal entries for fraud detection: An exploratory study", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "157--181", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "https://doi.org/10.1016/j.accinf.2010.08.001", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See discussion \cite{Grabski:2010:DDM,Kriel:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000540; http://www.sciencedirect.com/science/journal/14670895", abstract = "Fraud detection has become a critical component of financial audits and audit standards have heightened emphasis on journal entries as part of fraud detection. This paper canvasses perspectives on applying data mining techniques to journal entries. In the past, the impediment to researching journal entry data mining is getting access to journal entry data sets, which may explain why the published research in this area is a null set. For this project, we had access to journal entry data sets for 29 different organizations. Our initial exploratory test of the data sets had interesting preliminary findings. (1) For all 29 entities, the distribution of first digits of journal dollar amounts differed from that expected by Benford's Law. (2) Regarding last digits, unlike first digits, which are expected to have a logarithmic distribution, the last digits would be expected to have a uniform distribution. Our test found that the distribution was not uniform for many of the entities. In fact, eight entities had one number whose frequency was three times more than expected. (3) We compared the number of accounts related to the top five most frequently occurring three last digit combinations. Four entities had a very high occurrences of the most frequent three digit combinations that involved only a small set of accounts, one entity had a low occurrences of the most frequent three digit combination that involved a large set of accounts and 24 had a low occurrences of the most frequent three digit combinations that involved a small set of accounts. In general, the first four entities would probably pose the highest risk of fraud because it could indicate that the fraudster is covering up or falsifying a particular class of transactions. In the future, we will apply more data mining techniques to discover other patterns and relationships in the data sets. We also want to seed the dataset with fraud indicators (e.g., pairs of accounts that would not be expected in a journal entry) and compare the sensitivity of the different data mining techniques to find these seeded indicators.", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Accounting information systems; Auditing; Benford's Law; Data mining; Fraud; Journal entries; XBRL GL", remark = "2009 Research Symposium on Information Integrity \& Information Systems Assurance.", } @TechReport{Deckert:2010:IBL, author = "Joseph Deckert and Mikhail Myagkov and Peter C. Ordeshook", title = "The Irrelevance of {Benford's Law} for Detecting Fraud in Elections", type = "{CALTECH} working paper", number = "9", institution = "California Institute of Technology", address = "Pasadena, CA, USA", pages = "27", day = "9", month = mar, year = "2010", bibdate = "Mon Feb 18 17:40:53 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://vote.caltech.edu/drupal/node/327", acknowledgement = ack-nhfb, remark = "From the abstract: ``..., we argue here that Benford's Law is essentially useless as a forensic indicator of fraud.''", } @Article{Deligny:2010:RRL, author = "H. Deligny and P. Jolissaint", title = "Relations de r{\'e}currence lin{\'e}aires, primitivit{\'e} et loi de {Benford}. ({French}) [{Linear} recurrence relations, primitivity, and {Benford's Law}]", journal = "ArXiv e-prints", day = "23", month = jul, year = "2010", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 18:14:51 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D; http://arxiv.org/abs/1007.5349", abstract = "We prove that many sequences of positive numbers $ (a_n) $ defined by finite linear difference equations $ a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0 a_n $ with suitable nonnegative reals coefficients $ c_i $ satisfy Benford's Law on the first digit in many bases $ b > 2 $. Our techniques rely on Perron--Frobenius theory via the companion matrix of the characteristic polynomial of the defining equation.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1007.5349", keywords = "Mathematics - Dynamical Systems, Mathematics - Rings and Algebras, 11A99", language = "French", primaryclass = "math.DS", } @Article{Diekmann:2010:BLF, author = "Andreas Diekmann and Ben Jann", title = "{Benford's Law} and Fraud Detection: Facts and Legends", journal = j-GER-ECON-REV, volume = "11", number = "3", pages = "397--401", month = aug, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1111/j.1468-0475.2010.00510.x", ISSN = "1465-6485 (print), 1468-0475 (electronic)", ISSN-L = "1465-6485", bibdate = "Mon Nov 14 17:09:33 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "German Economic Review", keywords = "Benford's law; false negative; false positive; fraud detection; regression coefficients", onlinedate = "6 Apr 2010", } @Article{Dixit:2010:EEP, author = "U. J. Dixit and M. Jabbari Nooghabi", title = "Efficient estimation in the {Pareto} distribution", journal = j-STAT-METHODOL, volume = "7", number = "6", pages = "687--691", month = nov, year = "2010", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:44 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312710000419", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Article{Egghe:2010:BCN, author = "Leo Egghe", title = "Brief Communication: A new short proof of {Naranan}'s theorem, explaining {Lotka's Law} and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "61", number = "12", pages = "2581--2583", month = dec, year = "2010", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.21431", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:42:58 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "27 Sep 2010", } @Article{Egghe:2010:CSS, author = "L. Egghe", title = "Characteristic scores and scales in a {Lotkaian} framework", journal = j-SCIENTOMETRICS, volume = "83", number = "2", pages = "455--462", month = may, year = "2010", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-009-0009-y", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:20 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-009-0009-y", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Egghe:2010:NSP, author = "Leo Egghe", title = "A new short proof of {Naranan}'s theorem, explaining {Lotka's Law} and {Zipf's Law}", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "61", number = "12", pages = "2581--2583", year = "2010", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.21431", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @Article{Farkas:2010:SUN, author = "Janos Farkas and Gy{\"o}rgy Gyurky", title = "The significance of using the {Newcomb--Benford} law as a test of nuclear half-life calculations", journal = j-ACTA-PHYS-POL-B, volume = "41", number = "6", pages = "1213--1221", year = "2010", CODEN = "APOBBB", ISSN = "0587-4254 (print), 1509-5770 (electronic)", ISSN-L = "0587-4254", bibdate = "Mon Nov 14 16:21:42 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F; http://arxiv.org/abs/1006.3615", abstract = "Half-life number sequences collected from nuclear data charts are found to obey the Newcomb--Benford law. Based on this fact, it has been suggested recently, that this law should be used to test the quality of nuclear decay models. In this paper we briefly recall how, when and why the Newcomb--Benford law can be observed in a set of numbers with a given probability distribution. We investigate the special case of nuclear half-lives, and show that the law provides no additional clue in understanding decay half-lives. Thus, it can play no significant role in testing nuclear decay theories.", acknowledgement = ack-nhfb, ajournal = "Acta Phys. Pol. B", ajournal-2 = "Acta Phys. Polon. B", archiveprefix = "arXiv", eprint = "1006.3615", fjournal = "Acta Physica Polonica B", journal-URL = "http://www.actaphys.uj.edu.pl/pl/acta_physica_polonica_b", primaryclass = "math-ph", } @Article{Ferrer-i-Cancho:2010:RTD, author = "Ramon Ferrer-i-Cancho and Brita Elvev{\aa}g", title = "Random Texts Do Not Exhibit the Real {Zipf's Law}-Like Rank Distribution", journal = j-PLOS-ONE, volume = "5", number = "3", pages = "e9411:1--e9411:10", month = mar, year = "2010", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0009411", ISSN = "1932-6203", bibdate = "Wed Aug 12 08:54:42 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009411", abstract = "Zipf's law states that the relationship between the frequency of a word in a text and its rank (the most frequent word has rank 1, the 2nd most frequent word has rank 2, \ldots{}) is approximately linear when plotted on a double logarithmic scale. It has been argued that the law is not a relevant or useful property of language because simple random texts --- constructed by concatenating random characters including blanks behaving as word delimiters --- exhibit a Zipf's law-like word rank distribution.", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", } @Article{Fischer:2010:HCS, author = "Martin H. Fischer and Richard A. Mills and Samuel Shaki", title = "How to cook a {SNARC}: Number placement in text rapidly changes spatial-numerical associations", journal = j-BRAIN-COGN, volume = "72", number = "3", pages = "333--336", month = apr, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1016/j.bandc.2009.10.010", ISSN = "0278-2626 (print), 1090-2147 (electronic)", ISSN-L = "0278-2626", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0278262609002024", abstract = "Most theoreticians believe that reading habits explain why Western adults associate small numbers with left space and large numbers with right space (the {SNARC} effect). We challenge this belief by documenting, in both English and Hebrew, that {SNARC} changes during reading: small and large numbers in our texts appeared near the left or right ends of the lines, positioned either spatially congruent or incongruent with reading habits. In English, the congruent group showed reliable {SNARC} before and after reading and the incongruent group's {SNARC} was significantly reduced. In Hebrew the incongruent reading condition even induced a reverse SNARC. These results show that {SNARC} is a fleeting aspect of number representation that captures multiple spatial associations.", acknowledgement = ack-nhfb, fjournal = "Brain and Cognition", keywords = "Benford's Law; Number line; Numerical cognition; Reading; Spatial Numerical Association of Response Codes (SNARC); Spatial numerical associations; {SNARC} effect", } @Article{Formann:2010:NBL, author = "Anton K. Formann", title = "The {Newcomb--Benford Law} in Its Relation to Some Common Distributions", journal = j-PLOS-ONE, volume = "5", number = "5", pages = "e10541:1--e10541:13", month = may, year = "2010", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0010541", ISSN = "1932-6203", ISSN-L = "1932-6203", bibdate = "Mon Nov 14 18:19:09 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010PLoSO...510541F", abstract = "An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors.", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", } @Article{Genolini:2010:EIP, author = "Christophe Genolini and Tarak Driss", title = "Eveiller l'int{\'e}r{\^e}t pour la statistique par l'exemple. ({French}) [{Raising} interest in statistics by example]", journal = "Statistique et Enseignement", volume = "1", number = "2", pages = "49--57", month = "????", year = "2010", CODEN = "????", DOI = "????", ISSN = "2108-6745", ISSN-L = "2108-6745", bibdate = "Mon Feb 18 17:43:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16", acknowledgement = ack-nhfb, journal-URL = "http://www.statistique-et-enseignement.fr/", keywords = "Benford's Law", language = "French", } @Article{Giuliano:2010:UPI, author = "Rita Giuliano and {\'E}lise Janvresse", title = "A unifying probabilistic interpretation of {Benford}'s law", journal = "Uniform Distribution Theory", volume = "5", number = "2", pages = "169--182", year = "2010", CODEN = "????", ISSN = "1336-913X", ISSN-L = "1336-913X", MRclass = "60J10 (11K99 60A99)", MRnumber = "2781415", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf", acknowledgement = ack-nhfb, ajournal = "Unif. Distrib. Theory", fjournal = "Uniform Distribution Theory", } @InProceedings{Gonzalez-Jimenez:2010:BLN, author = "D. Gonzalez-Jimenez and E. Argones-Rua and F. Perez-Gonzalez and J. L. Alba-Castro", editor = "IEEE", booktitle = "IEEE International Conference on Image Processing", title = "{Benford's Law} for Natural and Synthetic Images", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1245--1248", year = "2010", bibdate = "Sat Sep 10 11:34:53 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "Not found in IEEE Xplore database??", } @Article{Grabski:2010:DDM, author = "Severin Grabski", title = "Discussion of {``Data mining journal entries for fraud detection: An exploratory study''}", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "182--185", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "https://doi.org/10.1016/j.accinf.2010.07.008", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000394", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law", remark = "2009 Research Symposium on Information Integrity \& Information Systems Assurance", } @Article{Herron:2010:EPO, author = "Erik S. Herron", title = "The effect of passive observation methods on {Azerbaijan}'s 2008 presidential election and 2009 referendum", journal = j-ELECT-STUDIES, volume = "29", number = "3", pages = "417--424", year = "2010", DOI = "https://doi.org/10.1016/j.electstud.2010.03.013", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Special Symposium: Voters and Coalition Governments", URL = "http://www.sciencedirect.com/science/article/pii/S0261379410000259", abstract = "Election observation is used by domestic and international groups to assess election quality and deter fraud. However, a limited amount of research has assessed its effectiveness. This article adds to the literature by analyzing how a passive monitoring tool affected the process and outcome of voting in two elections in Azerbaijan. The analysis shows that the placement of webcams in polling stations is consistently associated with lower reported turnout and inconsistently associated with lower regime support.", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Azerbaijan; Benford's Law; Election observation; Fraud", } @Article{Hickman:2010:DAC, author = "Matthew Hickman and Stephen Rice", title = "Digital Analysis of Crime Statistics: Does Crime Conform to {Benford's Law}?", journal = j-J-QUANT-CRIMINOL, volume = "26", number = "3", pages = "333--349", month = sep, year = "2010", CODEN = "JQCRE6", DOI = "https://doi.org/10.1007/s10940-010-9094-6", ISSN = "0748-4518 (print), 1573-7799 (electronic)", ISSN-L = "0748-4518", bibdate = "Fri Nov 25 10:30:30 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Quantitative Criminology", keywords = "Benford distribution; Benford's law; Crime data; Crime statistics; Data errors; Digital analysis; Fabricated data; First digit; Fraud detection; Uniform crime reports", } @MastersThesis{Jasak:2010:BZR, author = "Zoran Jasak", title = "Benfordov zakon i reinforcement u{\v{c}}enje. ({Bosnian}) [{Benford's Law} and reinforcement learning]", type = "{Magistarski Rad} ({M.Sc.} Thesis)", school = "Prirodno-Matematicki Fakultet, Odsjek za matematiku, Ju Univerzitet u Tuzla", address = "Tuzla, Bosnia and Herzegovina", pages = "124", month = dec, year = "2010", bibdate = "Mon Feb 18 17:48:33 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf", acknowledgement = ack-nhfb, keywords = "action; Adaptive Benford's method; Adaptivna Benfordova metoda; akcija; Benford's law; Benfordov zakon; confidence intervals; contamination level; intervali povjerenja; koli{\v{c}}nik; nivo kontaminacije; Q learning; Q u{\v{c}}enje; quotient; reinforcement learning; reinforcement u{\v{c}}enje; Sarsa; stanje; state", language = "Bosnian", } @Article{Jiang:2010:NMS, author = "Weina Jiang and Anthony T. S. Ho and Helen Treharne and Yun Q. Shi", title = "A Novel Multi-size Block {Benford's Law} Scheme for Printer Identification", journal = j-LECT-NOTES-COMP-SCI, volume = "6297", pages = "643--652", year = "2010", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-15702-8_59", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Mon Jan 21 17:47:23 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-15702-8", book-URL = "http://www.springerlink.com/content/978-3-642-15702-8", fjournal = "Lecture Notes in Computer Science", journal-URL = "http://link.springer.com/bookseries/558", } @Article{Kaynar:2010:FSM, author = "B. Kaynar and A. Berger and T. P. Hill and A. Ridder", title = "Finite-state {Markov} Chains obey {Benford's Law}", journal = "ArXiv e-prints", day = "2", month = mar, year = "2010", CODEN = "????", ISSN = "????", MRclass = "60J22, 11K06, 15B51", bibdate = "Tue Nov 15 06:30:53 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K; http://arxiv.org/abs/1003.0562", abstract = "A sequence of real numbers ($ x_n$) is Benford if the significands, i.e. the fraction parts in the floating-point representation of ($ x_n$) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with probability transition matrix $P$ and limiting matrix $ P*$ is Benford if every component of both sequences of matrices $ (P^n - P*)$ and $ (P^{n + 1} - P^n)$ is Benford or eventually zero. Using recent tools that established Benford behavior both for Newton's method and for finite-dimensional linear maps, via the classical theories of uniform distribution modulo $1$ and Perron-Frobenius, this paper derives a simple sufficient condition (nonresonant) guaranteeing that $P$, or the Markov chain associated with it, is Benford. This result in turn is used to show that almost all Markov chains are Benford, in the sense that if the transition probabilities are chosen independently and continuously, then the resulting Markov chain is Benford with probability one. Concrete examples illustrate the various cases that arise, and the theory is complemented with several simulations and potential applications.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1003.0562", keywords = "Mathematics - Probability", primaryclass = "math.PR", } @Article{Kibria:2010:PTE, author = "B. M. Golam Kibria and A. K. Md. E. Saleh", title = "Preliminary test estimation of the parameters of exponential and {Pareto} distributions for censored samples", journal = j-STAT-PAPERS, volume = "51", number = "4", pages = "757--773", month = dec, year = "2010", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-008-0163-y", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:33 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-008-0163-y", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Klar:2010:ZLL, author = "B. Klar and P. R. Parthasarathy and N. Henze", title = "{Zipf} and {Lerch} limit of birth and death processes", journal = j-PROB-ENG-INFO-SCI, volume = "24", number = "1", pages = "129--144", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1017/S0269964809990179", ISSN = "0269-9648 (print), 1469-8951 (electronic)", ISSN-L = "0269-9648", MRclass = "60J27 (91F20)", MRnumber = "2575846 (2010m:60254)", bibdate = "Sat Mar 23 12:53:04 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Probab. Engrg. Inform. Sci.", fjournal = "Probability in the Engineering and Informational Sciences", keywords = "Zipf's Law", } @Article{Kriel:2010:DDM, author = "Eckhardt Kriel", title = "Discussion of {``Data mining journal entries for fraud detection: An exploratory study''}", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "11", number = "3", pages = "186--188", month = sep, year = "2010", CODEN = "IJAIA7", DOI = "https://doi.org/10.1016/j.accinf.2010.07.009", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.", URL = "http://www.sciencedirect.com/science/article/pii/S1467089510000400", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Benford's Law", remark = "2009 Research Symposium on Information Integrity \& Information Systems Assurance.", } @Book{Lagarias:2010:UCP, editor = "Jeffrey C. Lagarias", title = "The ultimate challenge: the $ 3 x + 1 $ problem", publisher = pub-AMS, address = pub-AMS:adr, pages = "xiv + 344", year = "2010", ISBN = "0-8218-4940-9", ISBN-13 = "978-0-8218-4940-8", LCCN = "QA292 .U48 2010", MRclass = "11B83; 37A45; 11B37; 68Q99", bibdate = "Sat Sep 10 13:02:05 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", abstract = "The $ 3 x + 1 $ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then ``multiply by three and add one'', while if it is even then ``divide by two''. The $ 3 x + 1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $ x < 5.4 \cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Sequences (Mathematics); Polynomials; Harmonic analysis; Number theory -- Sequences and sets -- Special sequences and polynomials.; Dynamical systems and ergodic theory -- Ergodic theory -- Relations with number theory and harmonic analysis.; Number theory -- Sequences and sets -- Recurrences.; Computer science -- Theory of computing -- None of the above, but in this section.", tableofcontents = "The $ 3 x + 1 $ problem: an overview \\ The $ 3 x + 1 $ problem and its generalizations / Jeffrey C. Lagarias \\ Survey papers \\ A $ 3 x + 1 $ survey: number theory and dynamical systems / Marc Chamberland \\ Generalized $ 3 x + 1 $ mappings: Markov chains and ergodic theory / K. R. Matthews \\ Generalized $ 3 x + 1 $ functions and the theory of computation / Pascal Michel and Maurice Margenstern \\ Stochastic modelling and computation papers \\ Stochastic models for the $ 3 x + 1 $ and $ 5 x + 1$ problems and related problems / Alex V. Kontorovich and Jeffrey C. Lagarias \\ Empirical verification of the $ 3 x + 1 $ and related conjectures / Tom{\'a}s Oliveira E Silva \\ Reprinted early papers \\ Cyclic sequences and frieze patterns (The fourth Felix Behrend Memorial Lecture) / H. S. M. Coxeter \\ Unpredictable iterations / J. H. Conway \\ Iteration of the number-theoretic function: $f(2n) = n$, $f(2n + 1) = 3n + 2$ / C. J. Everett \\ Don't try to solve these problems! / Richard K. Guy \\ On the motivation and origin of the $(3n + 1)$-problem / Lothar Collatz \\ FRACTRAN: a simple universal programming language for arithmetic / J. H. Conway \\ The $ 3 x + 1 $ problem: an annotated bibliography (1963--1999) / Jeffrey C. Lagarias", } @Article{Lee:2010:SAR, author = "Joanne Lee and Wendy K. Tam Cho and George G. Judge", title = "{Stigler}'s approach to recovering the distribution of first significant digits in natural data sets", journal = j-STAT-PROB-LETT, volume = "80", number = "2", pages = "82--88", day = "15", month = jan, year = "2010", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2009.09.015", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167715209003563", abstract = "Benford's Law can be seen as one of the many first significant digit (FSD) distributions in a family of monotonically decreasing distributions. We examine the interrelationship between Benford and other monotonically decreasing distributions such as those arising from Stigler, Zipf, and the power laws. We examine the theoretical basis of the Stigler distribution and extend his reasoning by incorporating {FSD} first-moment information into information-theoretic methods. We present information-theoretic methods as a way to describe, connect, and unify these related distributions and thereby extend the reach of Benford's Law and {FSD} research more generally.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law", } @Article{Liu:2010:CIE, author = "Hongyan Liu and Xiaoyu Wang and Yinghui Yang", title = "Comments on {``An integrated efficient solution for computing frequent and top-$k$ elements in data streams''}", journal = j-TODS, volume = "35", number = "2", pages = "15:1--15:??", month = apr, year = "2010", CODEN = "ATDSD3", DOI = "https://doi.org/10.1145/1735886.1735894", ISSN = "0362-5915 (print), 1557-4644 (electronic)", ISSN-L = "0362-5915", bibdate = "Wed Apr 28 13:44:08 MDT 2010", bibsource = "http://www.acm.org/pubs/contents/journals/tods/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Metwally:2006:IES}.", abstract = "We investigate a well-known algorithm, {\em Space-Saving\/} [Metwally et al. 2006], which has been proven efficient and effective at mining frequent elements in data streams. We discovered an error in one of the theorems in Metwally et al. [2006]. Experiments are conducted to illustrate the error.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "ACM Transactions on Database Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J777", keywords = "approximate queries; data streams; frequent elements; top-$k$ elements; Zipfian distributions", } @Article{Lu:2010:BLP, author = "Ocean Fan Lu and David E. Giles", title = "{Benford's Law} and psychological barriers in certain {eBay} auctions", journal = j-APPL-ECON-LETT, volume = "17", number = "10", pages = "1005--1008", month = "????", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1080/13504850802631814", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Sat Jan 07 09:10:23 2012", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814", abstract = "Using generalizations of Benford's Law we test for the absence of psychological barriers at various price levels in eBay auctions for professional football tickets. Our empirical results indicate that this hypothesis cannot be rejected.", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", journal-URL = "http://www.tandfonline.com/loi/rael20", onlinedate = "16 Jun 2009", } @Article{Mahdian:2010:BBM, author = "Babak Mahdian and Stanislav Saic", title = "A bibliography on blind methods for identifying image forgery", journal = j-SIGNAL-PROCESS-IMAGE-COMMUN, volume = "25", number = "6", pages = "389--399", month = jul, year = "2010", CODEN = "SPICEF", DOI = "https://doi.org/10.1016/j.image.2010.05.003", ISSN = "0923-5965 (print), 1879-2677 (electronic)", ISSN-L = "0923-5965", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0923596510000536", abstract = "Verifying the integrity of digital images and detecting the traces of tampering without using any protecting pre-extracted or pre-embedded information have become an important and hot research field. The popularity of this field and the rapid growth in papers published during the last years have put considerable need on creating a complete bibliography addressing published papers in this area. In this paper, an extensive list of blind methods for detecting image forgery is presented. By the word blind we refer to those methods that use only the image function. An attempt has been made to make this paper complete by listing most of the existing references and by providing a detailed classification group.", acknowledgement = ack-nhfb, fjournal = "Signal Processing: Image Communication", keywords = "Benford's Law; Blind forgery detection; Digital forgery; Image forensics; Image tampering; Multimedia security", } @Article{Manoochehrnia:2010:BLA, author = "P. Manoochehrnia and F. Rachidi and M. Rubinstein and W. Schulz and G. Diendorfer", title = "{Benford's Law} and Its Application to Lightning Data", journal = j-IEEE-TRANS-ELECTROMAGN-COMPAT, volume = "52", number = "4", pages = "956--961", month = nov, year = "2010", CODEN = "IEMCAE", DOI = "https://doi.org/10.1109/TEMC.2010.2067218", ISSN = "0018-9375 (print), 1558-187X (electronic)", ISSN-L = "0018-9375", bibdate = "Mon Nov 21 22:24:43 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Electromagnetic Compatibility", journal-URL = "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=15", } @InProceedings{Mebane:2010:EFR, author = "Walter R. {Mebane, Jr.} and K. Kalinin", editor = "????", booktitle = "{Proceedings of the 2010 Annual Meeting of the Midwest Political Science Association, Chicago, IL, April 22--25, 2010}", title = "Electoral Fraud in {Russia}: Vote Counts Analysis Using Second-Digit Mean Tests", publisher = "????", address = "????", pages = "??--??", year = "2010", bibdate = "Sat Sep 10 14:32:06 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InProceedings{Mebane:2010:EFSa, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{Proceedings of the 2010 Annual Meeting of the Midwest Political Science Association, Chicago, IL, April 22--25, 2010}", title = "Election Fraud or Strategic Voting?", publisher = "????", address = "????", pages = "??--??", year = "2010", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Sat Sep 10 14:19:52 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InProceedings{Mebane:2010:EFSb, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{2010 Summer Meeting of the Political Methodology Society, University of Iowa, July 22--24, 2010}", title = "Election Fraud or Strategic Voting? {Can} Second-digit Tests Tell the Difference?", publisher = "????", address = "????", pages = "1--49", year = "2010", ISBN = "????", ISBN-13 = "????", bibdate = "Sat Feb 16 11:56:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/pm10.pdf", acknowledgement = ack-nhfb, } @Article{Mebane:2010:FPE, author = "Walter R. {Mebane, Jr.}", title = "Fraud in the {2009 Presidential Election} in {Iran}?", journal = j-CHANCE, volume = "23", number = "1", pages = "6--15", month = mar, year = "2010", CODEN = "CNDCE4", DOI = "https://doi.org/10.1007/s00144-010-0003-4", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Mon Feb 18 17:50:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/content/0337v415563q0753/abstract/", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", xxnote = "Publisher archive at \path=http://amstat.tandfonline.com/loi/ucha20= is missing volumes 18 (2005)--24 (2011). Those volumes are available at \path=http://link.springer.com/journal/144=", } @TechReport{Mebane:2010:MSD, author = "Walter R. {Mebane, Jr.}", title = "Memo on second-digit tests done on precinct counts for {Democratic Senate} primary in {South Carolina}, 2010", type = "Report", institution = "University of Michigan", address = "Ann Arbor, MI, USA", day = "12", month = jun, year = "2010", bibdate = "Sat Feb 16 12:06:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf", acknowledgement = ack-nhfb, } @Article{Morrison:2010:MG, author = "Kent E. Morrison", title = "The Multiplication Game", journal = j-MATH-MAG, volume = "83", number = "??", pages = "100--110", month = apr, year = "2010", CODEN = "MAMGA8", DOI = "????", ISSN = "0025-570X", ISSN-L = "0025-570X", bibdate = "Mon Feb 18 17:51:50 2013", bibsource = "http://www.maa.org/pubs/mag_apr10_toc.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf", acknowledgement = ack-nhfb, fjournal = "Mathematics Magazine", journal-URL = "http://www.maa.org/pubs/mathmag.html", keywords = "Benford's Law", } @Book{Newbold:2010:SBE, author = "Paul Newbold and William L. Carlson and Betty Thorne", title = "Statistics for Business and Economics", publisher = "Pearson", address = "Boston, MA, USA", edition = "Seventh", pages = "986 + 16", year = "2010", ISBN = "0-13-507248-4", ISBN-13 = "978-0-13-507248-6", LCCN = "QA276.18 .N49 2010", bibdate = "Fri Mar 22 09:03:48 MDT 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @Book{Nillsen:2010:RRD, author = "Rodney Victor Nillsen", title = "Randomness and recurrence in dynamical systems: a real analysis approach", volume = "31", publisher = pub-MATH-ASSOC-AMER, address = pub-MATH-ASSOC-AMER:adr, pages = "xviii + 357", year = "2010", ISBN = "0-88385-043-5", ISBN-13 = "978-0-88385-043-5", LCCN = "QA614.8 .N55 2010", bibdate = "Mon Feb 18 17:53:28 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "The Carus mathematical monographs", acknowledgement = ack-nhfb, subject = "Differentiable dynamical systems; Measure theory", tableofcontents = "Background ideas and knowledge \\ Irrational numbers and dynamical systems \\ Probability and randomness \\ Recurrence \\ Averaging in time and space", } @Article{Novikov:2010:APB, author = "V. P. Novikov", title = "Aspectual Principle, {Benford's Law} and {Russell's Paradox}", journal = "ArXiv e-prints", month = dec, year = "2010", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 18:11:57 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N; http://arxiv.org/abs/1012.5537", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1012.5537", keywords = "Mathematics - Classical Analysis and ODEs", pagecount = "5", primaryclass = "math.CA", } @Book{Oleksy:2010:DMB, author = "Marius Oleksy", title = "{Data Mining und Benford's Law als Controllinginstrumente}. ({German}) [{Data} Mining and {Benford's Law} as controlling instruments]", volume = "45", publisher = "Europ{\"a}ischer Hochschulverlag", address = "Bremen, Germany", pages = "181 (est.)", year = "2010", ISBN = "3-86741-405-X", ISBN-13 = "978-3-86741-405-0", LCCN = "????", bibdate = "Mon Feb 18 17:54:59 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "{Wismarer Schriften zu Management und Recht}", URL = "http://www.amazon.de/Data-Mining-Benfords-Law-Controllinginstrumente/dp/386741405X", acknowledgement = ack-nhfb, language = "German", } @Article{Orita:2010:UBL, author = "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and Kazuki Ohno", title = "Use of {Benford's Law} in drug discovery data", journal = j-DRUG-DISCOVERY-TODAY, volume = "15", number = "9--10", pages = "328--331", month = may, year = "2010", CODEN = "DDTOFS", DOI = "https://doi.org/10.1016/j.drudis.2010.03.003", ISSN = "1359-6446 (print), 1878-5832 (electronic)", ISSN-L = "1359-6446", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1359644610000796", abstract = "Benford's law states that the distribution of the first digit of many data sets is not uniform. The first digit of any random number will be 1 almost 30\% of the time, and larger digits occur as the first digit with lower and lower frequency, to the point where 9 occurs as a first digit only 5\% of the time. Here, we demonstrate that several data sets in the field of drug discovery follow Benford's distribution, whereas doctored data do not. Our findings indicate the applicability of Benford's law in assessing data quality in the field of drug discovery. We also propose a useful index of evaluating data quality based on Benford's law.", acknowledgement = ack-nhfb, fjournal = "Drug Discovery Today", keywords = "Benford's Law", } @Misc{Pan:2010:EJC, author = "Da Pan and Lijing Shao and Bo-Qiang Ma", title = "{Benford's Law} in Statistical Physics", howpublished = "Wolfram Online Demonstrations Projects.", year = "2010", bibdate = "Mon Feb 18 18:00:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://demonstrations.wolfram.com/BenfordsLawInStatisticalPhysics/", acknowledgement = ack-nhfb, } @Article{Peng:2010:SFW, author = "Fei Peng and Re-Si Guo and Chang-Tsun Li and Min Long", title = "A semi-fragile watermarking algorithm for authenticating {$2$D} {CAD} engineering graphics based on log-polar transformation", journal = j-COMPUT-AIDED-DES, volume = "42", number = "12", pages = "1207--1216", year = "2010", CODEN = "CAIDA5", DOI = "https://doi.org/10.1016/j.cad.2010.08.004", ISSN = "0010-4485 (print), 1879-2685 (electronic)", ISSN-L = "0010-4485", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0010448510001491", abstract = "Copyright violation and illegal manipulation of digital data have been acute challenges for many sectors since the very same set of enabling techniques for generating and processing digital data started to emerge. Although traditional protective methods, such as encryption and digital signatures, have been in use for decades, their inability to provide protection after decryption and locating tampering has prompted the development of digital watermarking. In this paper, a semi-fragile watermarking algorithm for authenticating 2D {CAD} engineering graphics based on log-polar coordinate mapping is proposed. Firstly, the vertices are divided into groups, and for each group, the vertices for carrying a watermark are mapped to the log-polar coordinate system. Then the watermark is embedded in the mantissa of the real-valued log-polar coordinates via bit substitution. Theoretical analysis and experimental results show that the proposed algorithm is not only robust against incidental global operations such as rotation, translation and scaling, but can also detect and locate malicious attacks such as entity modification and entity addition/deletion.", acknowledgement = ack-nhfb, fjournal = "Computer-Aided Design", journal-URL = "http://www.sciencedirect.com/science/journal/00104485", keywords = "Benford's Law; Content authentication; Data hiding; Engineering graphics; Integrity verification; Semi-fragile watermarking", } @Article{Peng:2010:ZLC, author = "Guohua Peng", title = "{Zipf}'s law for {Chinese} cities: {Rolling} sample regressions", journal = j-PHYSICA-A, volume = "389", number = "18", pages = "3804--3813", day = "15", month = sep, year = "2010", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2010.05.004", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S037843711000381X", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Perc:2010:ZLL, author = "Matja{\v{z}} Perc", title = "{Zipf}'s law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of {Slovenia's} research as an example", journal = j-J-INFORMETRICS, volume = "4", number = "3", pages = "358--364", day = "1", month = jul, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1016/j.joi.2010.03.001", ISSN = "1751-1577 (print), 1875-5879 (electronic)", ISSN-L = "1751-1577", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1751157710000234", acknowledgement = ack-nhfb, fjournal = "Journal of Informetrics", journal-URL = "http://www.sciencedirect.com/science/journal/17511577", keywords = "Zipf's Law", } @Book{Posch:2010:ZNB, author = "Peter N. Posch", title = "{Ziffernanalyse mit dem Newcomb--Benford Gesetz in Theorie und Praxis}. ({German}) [{Digit} analysis with the {Newcomb--Benford} law in theory and practice]", publisher = "Verlag Europ{\"a}ische Wirtschaft", address = "Munich, Germany", edition = "Second", pages = "105 (est.)", year = "2010", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Mon Feb 18 18:01:16 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @InProceedings{Qadir:2010:EJC, author = "G. Qadir and X. Zhao and A. T. S. Ho", booktitle = "{Society of Photo-Optical Instrumentation Engineers (SPIE)} Conference Series", title = "Estimating {JPEG2000} compression for image forensics using {Benford's Law}", volume = "7723", publisher = pub-SPIE, address = pub-SPIE:adr, month = apr, year = "2010", DOI = "https://doi.org/10.1117/12.855085", bibdate = "Mon Nov 14 18:25:16 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series", URL = "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q", acknowledgement = ack-nhfb, } @Article{Raqab:2010:PPD, author = "Mohammad Z. Raqab and A. Asgharzadeh and R. Valiollahi", title = "Prediction for {Pareto} distribution based on progressively {Type-II} censored samples", journal = j-COMPUT-STAT-DATA-ANAL, volume = "54", number = "7", pages = "1732--1743", day = "1", month = jul, year = "2010", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:00 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947310000563", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Rezayan:2010:SRG, author = "Hani Rezayan and Mahmoud Reza Delavar and Andrew Ulrich Frank and A. Mansouri", title = "Spatial rules that generate urban patterns: Emergence of the power law in the distribution of axial line length", journal = "International Journal of Applied Earth Observation and Geoinformation", volume = "12", number = "5", pages = "317--330", year = "2010", DOI = "https://doi.org/10.1016/j.jag.2010.04.003", ISSN = "0303-2434", ISSN-L = "0303-2434", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0303243410000413", abstract = "This paper studies emergence/generation of power law in rank-order distribution of axial line length, which is a global pattern observed in real cities, due to interaction of a set of seven simple spatial rules at a local scale. These rules and their interactions form a model expected to simulate the morphological structure of free spaces in unplanned organic pedestrian small cities. Effects of each of the seven rules are discussed through repeated simulations of eight possible combinations of the rules, using a bottom-up process. The results show that the rules generate environments with statistically stable rank-order distribution of axial line length that follows the power law. It means that the axial maps of the simulated environments have a scale-free hierarchical structure such that their distributions lean toward short axial lines. It also represents dominance of local spatial structure, as the model renders a faster rate of growth at a local scale while allowing a steady growth at a global scale.", acknowledgement = ack-nhfb, keywords = "Axial line; Axial map; Axial representation; Benford's Law; Emergence; Power law", } @Article{Rousseau:2010:AFO, author = "Christiane Rousseau", title = "Apprendre {\`a} frauder ou {\`a} d{\'e}tecter les fraudes. ({French}) [{Learning} to defraud or to detect fraud]", journal = "Accrom$\alpha$th", volume = "5", pages = "2--7", month = "{\'E}t{\'e}--automne", year = "2010", ISSN = "1911-0197", bibdate = "Mon Feb 18 18:07:49 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://accromath.uqam.ca/contents/pdf/Benford.pdf", acknowledgement = ack-nhfb, journal-URL = "http://www.accromath.ca/", language = "French", } @Book{Saichev:2010:TZL, author = "Alexander Saichev and Yannick Malevergne and Didier Sornette", title = "Theory of {Zipf}'s law and beyond", volume = "632", publisher = pub-SV, address = pub-SV:adr, pages = "xii + 171", year = "2010", DOI = "https://doi.org/10.1007/978-3-642-02946-2", ISBN = "3-642-02945-0", ISBN-13 = "978-3-642-02945-5", MRclass = "91-02 (91B70 91B82)", MRnumber = "2569206 (2011b:91008)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Economics and Mathematical Systems", ZMnumber = "Zbl 1189.91009", acknowledgement = ack-nhfb, } @Article{Saldana-Zepeda:2010:GFT, author = "Dayna P. Salda{\~n}a-Zepeda and Humberto Vaquera-Huerta and Barry C. Arnold", title = "A goodness of fit test for the {Pareto} distribution in the presence of Type {II} censoring, based on the cumulative hazard function", journal = j-COMPUT-STAT-DATA-ANAL, volume = "54", number = "4", pages = "833--842", day = "1", month = apr, year = "2010", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:42:57 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947309004071", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Sambridge:2010:BLN, author = "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A. Jackson", title = "{Benford}'s law in the natural sciences", journal = j-GEOPHYS-RES-LETT, volume = "37", number = "22", pages = "L22301--L22306", month = "????", year = "2010", CODEN = "GPRLAJ", DOI = "https://doi.org/10.1029/2010GL044830", ISSN = "0094-8276 (print), 1944-8007 (electronic)", ISSN-L = "0094-8276", bibdate = "Sun Nov 13 11:03:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S; http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml", abstract = "More than 100 years ago it was predicted that the distribution of first digits of real world observations would not be uniform, but instead follow a trend where measurements with lower first digit (1, 2, \ldots {}) occur more frequently than those with higher first digits (\ldots {}, 8, 9). This result has long been known but regarded largely as a mathematical curiosity and received little attention in the natural sciences. Here we show that the first digit rule is likely to be a widespread phenomenon and may provide new ways to detect anomalous signals in data. We test 15 sets of modern observations drawn from the fields of physics, astronomy, geophysics, chemistry, engineering and mathematics, and show that Benford's law holds for them all. These include geophysical observables such as the length of time between geomagnetic reversals, depths of earthquakes, models of Earth's gravity, geomagnetic and seismic structure. In addition we find it also holds for other natural science observables such as the rotation frequencies of pulsars; green-house gas emissions, the masses of exoplanets as well as numbers of infectious diseases reported to the World Health Organization. The wide range of areas where it is manifested opens up new possibilities for exploitation. An illustration is given of how seismic energy from an earthquake can be detected from just the first digit distribution of displacement counts on a seismometer, i.e., without actually looking at the details of a seismogram at all. This led to the first ever detection of an earthquake using first digit information alone.", acknowledgement = ack-nhfb, ajournal = "Geophys. Res. Lett.", fjournal = "Geophysical research letters", keywords = "earthquakes; large data sets; observational seismology; statistics", } @TechReport{Schraepler:2010:BLI, author = "J{\"o}rg-Peter Schraepler", title = "{Benford's Law} as an instrument for fraud detection in surveys using the data of the {Socio-Economic Panel (SOEP)}", type = "{SOEP} paper", number = "273", institution = "Socio-Economic Panel, Deutsches Institut f{\"u}r Wirtschaftsforschung", address = "Berlin, Germany", pages = "ii + 56", day = "2", month = mar, year = "2010", ISSN = "1864-6689", ISSN-L = "1864-6689", bibdate = "Mon Feb 18 18:10:18 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf", acknowledgement = ack-nhfb, } @Article{Shao:2010:EMD, author = "Lijing Shao and Bo-Qiang Ma", title = "Empirical Mantissa Distributions of Pulsars", journal = j-ASTROPART-PHYS, volume = "33", number = "4", pages = "255--262", month = may, year = "2010", CODEN = "APHYEE", DOI = "https://doi.org/10.1016/j.astropartphys.2010.02.003", ISSN = "0927-6505 (print), 1873-2852 (electronic)", ISSN-L = "0927-6505", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1005.1702; http://www.sciencedirect.com/science/article/pii/S0927650510000447", abstract = "The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's Law. Here, we investigate systematically the mantissa distributions of some pulsar quantities, and find that for most quantities their first digits conform to this law. However, the barycentric period shows significant deviation from the usual distribution, but satisfies a generalized Benford's Law roughly. Therefore pulsars can serve as an ideal assemblage to study the first digit distributions of real world data, and the observations can be used to constrain theoretical models of pulsar behavior.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1005.1702", fjournal = "Astroparticle Physics", journal-URL = "http://www.sciencedirect.com/science/journal/09276505", keywords = "Benford's Law; First digit law; Mantissa distribution; Pulsar", primaryclass = "astro-ph.IM", } @Article{Shao:2010:FDD, author = "Lijing Shao and Bo-Qiang Ma", title = "First Digit Distribution of Hadron Full Width", journal = "ArXiv e-prints", day = "19", month = apr, year = "2010", bibdate = "Mon Nov 21 07:21:00 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1004.3077", abstract = "A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $ 1, 2, \ldots {}, 9 $, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e., the law is scale-invariant, base-invariant, and power-invariant. This means that the lifetimes of hadrons follow also Benford's law.", acknowledgement = ack-nhfb, pagecount = "8", } @Article{Shao:2010:FDLa, author = "Lijing Shao and Bo-Qiang Ma", title = "First-Digit Law in Nonextensive Statistics", journal = "ArXiv e-prints", year = "2010", bibdate = "Mon Nov 21 07:09:52 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1010.2699", abstract = "Nonextensive statistics, characterized by a nonextensive parameter $q$, is a promising and practically useful generalization of the Boltzmann statistics to describe power-law behaviors from physical and social observations. We here explore the unevenness of the first digit distribution of nonextensive statistics analytically and numerically. We find that the first-digit distribution follows Benford's law and fluctuates slightly in a periodical manner with respect to the logarithm of the temperature. The fluctuation decreases when $q$ increases, and the result converges to Benford's law exactly as $q$ approaches 2. The relevant regularities between nonextensive statistics and Benford's law are also presented and discussed.", acknowledgement = ack-nhfb, } @Article{Shao:2010:FDLb, author = "Lijing Shao and Bo-Qiang Ma", title = "First-digit law in nonextensive statistics", journal = j-PHYS-REV-E, volume = "82", number = "4", pages = "041110", month = oct, year = "2010", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.82.041110", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Mon Feb 18 18:11:37 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.82.041110; http://pre.aps.org/abstract/PRE/v82/i4/e041110", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", } @Article{Shao:2010:SDL, author = "Lijing Shao and Bo-Qiang Ma", title = "The significant digit law in statistical physics", journal = j-PHYSICA-A, volume = "389", number = "16", pages = "3109--3116", month = may, year = "2010", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2010.04.021", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "82B03", MRnumber = "2652860 (2011d:82007)", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1005.0660; http://inspirehep.net/record/855898; http://inspirehep.net/record/873155; http://www.sciencedirect.com/science/article/pii/S0378437110003596", abstract = "The occurrence of the nonzero leftmost digit, i.e., $ 1, 2, \ldots {}, 9 $, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic distribution, named Benford's Law. We investigate three kinds of widely used physical statistics, i.e., the Boltzmann--Gibbs (BG) distribution, the Fermi--Dirac (FD) distribution, and the Bose--Einstein (BE) distribution, and find that the BG and FD distributions both fluctuate slightly in a periodic manner around Benford's distribution with respect to the temperature of the system, while the BE distribution conforms to it exactly whatever the temperature is. Thus Benford's Law seems to present a general pattern for physical statistics and might be even more fundamental and profound in nature. Furthermore, various elegant properties of Benford's Law, especially the mantissa distribution of data sets, are discussed.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; First digit law; Mantissa distribution; Statistical physics", } @Article{Shebaro:2010:LTC, author = "Bilal Shebaro and Fernando Perez-Gonzalez and Jedidiah R. Crandall", title = "Leaving timing-channel fingerprints in hidden service log files", journal = "Digital Investigation", volume = "7, Supplement", number = "0", pages = "S104--S113", year = "2010", DOI = "https://doi.org/10.1016/j.diin.2010.05.013", ISSN = "1742-2876 (print), 1873-202X (electronic)", ISSN-L = "1742-2876", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The Proceedings of the Tenth Annual {DFRWS} Conference", URL = "http://www.sciencedirect.com/science/article/pii/S174228761000040X", abstract = "Hidden services are anonymously hosted services that can be accessed over an anonymity network, such as Tor. While most hidden services are legitimate, some host illegal content. There has been a fair amount of research on locating hidden services, but an open problem is to develop a general method to prove that a physical machine, once confiscated, was in fact the machine that had been hosting the illegal content. In this paper we assume that the hidden service logs requests with some timestamp, and give experimental results for leaving an identifiable fingerprint in this log file as a timing channel that can be recovered from the timestamps. In 60 min, we are able to leave a 36-bit fingerprint that can be reliably recovered. The main challenges are the packet delays caused by the anonymity network that requests are sent over and the existing traffic in the log from the actual clients accessing the service. We give data to characterize these noise sources and then describe an implementation of timing-channel fingerprinting for an Apache web server based hidden service on the Tor network, where the fingerprint is an additive channel that is superencoded with a Reed Solomon code for reliable recovery. Finally, we discuss the inherent tradeoffs and possible approaches to making the fingerprint more stealthy.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Fingerprints; Hidden services; Timestamps; Timing channel; Tor network", } @InProceedings{Shengmin:2010:DSC, author = "Z. Shengmin and W. Wenchao", editor = "{IEEE}", booktitle = "{2010 International Conference on Management and Service Science (MASS), 24--26 Aug. 2010, Wuhan, China}", title = "Does [sic] {Chinese} Stock Indices Agree with {Benford's Law}?", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1--3", year = "2010", DOI = "https://doi.org/10.1109/ICMSS.2010.5575999", ISBN = "1-4244-5325-9, 1-4244-5326-7", ISBN-13 = "978-1-4244-5325-2, 978-1-4244-5326-9", LCCN = "????", bibdate = "Mon Feb 18 18:12:46 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Singleton:2010:FAF, author = "Tommie Singleton and Aaron J. Singleton", title = "Fraud auditing and forensic accounting", publisher = pub-WILEY, address = pub-WILEY:adr, edition = "Fourth", pages = "xiv + 317", year = "2010", ISBN = "0-470-56413-X", ISBN-13 = "978-0-470-56413-4", LCCN = "HV8079.W47 B65 2010", bibdate = "Tue Nov 22 10:31:33 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley corporate F and A", URL = "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg; http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html; http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html; http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html", abstract = "Completely revised and updated, Fraud Auditing and Forensic Accounting, Fourth Edition reveals how to develop an investigative eye toward both internal and external fraud and provides crucial information on how to deal with it when discovered. With new chapters on the physiological aspects of the fraudster and on fraud response, as well as new material on non-financial aspects of fraud investigation, body language, discourse analysis, and interviewing techniques, this authoritative, timely book equips auditors, investigators, corporate attorneys, and accountants to identify the signs of financial fraud and successfully investigate it", acknowledgement = ack-nhfb, remark = "Derived from third edition (2006). This book does not discuss Benford's Law, but may be helpful background for application of that law to the detection of fraud.", subject = "White collar crime investigation; United States; Forensic accounting; Fraud investigation", tableofcontents = "Background of Fraud Auditing and Forensic Accounting \\ Fraud Principles \\ Fraud Schemes \\ Red Flags \\ Fraud Risk Assessment \\ Fraud Prevention \\ Fraud Detection \\ Fraud Response \\ Computer Crime \\ Fraud and the Accounting Information System \\ Gathering Evidence \\ Cyber Forensics \\ Obtaining and Evaluating Nonfinancial Evidence in a Fraud Examination \\ General Criteria and Standards for Establishing an Expert Witness's Qualifications \\ The Legal Role and Qualifications of an Expert Witness \\ Effective Tactics and Procedures for the Expert Witness in Court \\ Fraud and the Public Accounting Profession", } @Article{Stalcup:2010:BLH, author = "Ken Stalcup", title = "{Benford's Law}: How a Simple Misconception can Trip up a Fraudster and How a Savvy {CFE} Can Spot It", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2010", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 07:57:24 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=203", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", } @Article{Strzalka:2010:SPB, author = "Dominik Strza{\l}ka", title = "On some properties of {Benford}'s law", journal = "Journal of the {Korean Mathematical Society}", volume = "47", number = "5", pages = "1055--1075", year = "2010", CODEN = "JKMSDG", DOI = "https://doi.org/10.4134/JKMS.2010.47.5.1055", ISSN = "0304-9914", ISSN-L = "0304-9914", MRclass = "11A63", MRnumber = "2723008", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "J. {Korean Math. Soc.}", fjournal = "Journal of the {Korean Mathematical Society}", } @Article{Sudhier:2010:BLS, author = "K. G. Sudhier", title = "{Bradford's law} of Scattering Revisited: A study based on the References in Doctoral theses in the area of Physics", journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE, volume = "4", number = "2", pages = "35--47", year = "2010", CODEN = "????", DOI = "https://doi.org/10.1080/09737766.2010.10700891", ISSN = "0973-7766 (print), 2168-930X (electronic)", ISSN-L = "0973-7766", bibdate = "Thu Sep 10 17:47:06 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib", acknowledgement = ack-nhfb, fjournal = "Collnet Journal of Scientometrics and Information Management", journal-URL = "http://www.tandfonline.com/loi/tsim20", } @Article{Suh:2010:CAB, author = "Ikseon Suh and T. Christopher Headrick", title = "A comparative analysis of the bootstrap versus traditional statistical procedures applied to digital analysis based on {Benford's Law}", journal = "Journal of Forensic and Investigative Accounting", volume = "2", number = "2", pages = "144--175", month = jul # "\slash " # dec, year = "2010", CODEN = "????", DOI = "????", ISSN = "2165-3755", bibdate = "Mon Feb 18 18:16:07 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://epublications.marquette.edu/account_fac/31; http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/FullText/2010v2n2a7.pdf; http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/v2n2.htm", acknowledgement = ack-nhfb, journal-URL = "http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/articles.htm", } @Article{Szewczak:2010:LTR, author = "Zbigniew S. Szewczak", title = "A limit theorem for random sums modulo $1$", journal = j-STAT-PROB-LETT, volume = "80", number = "9--10", pages = "747--751", month = may, year = "2010", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2010.01.005", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715210000106", abstract = "Residues of partial sums in a class of dependent random variables, including functionals of uniformly recurrent Markov chains, are in the domain of attraction of the uniform distribution. These types of limit theorems arise for example in the multiplication of floating-point numbers.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law", } @Article{Uzer:2010:MTC, author = "Ali Uzer", title = "Multiplicative type complex calculus as an alternative to the classical calculus", journal = j-COMPUT-MATH-APPL, volume = "60", number = "10", pages = "2725--2737", month = nov, year = "2010", CODEN = "CMAPDK", DOI = "https://doi.org/10.1016/j.camwa.2010.08.089", ISSN = "0898-1221 (print), 1873-7668 (electronic)", ISSN-L = "0898-1221", bibdate = "Thu Feb 14 05:56:39 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0898122110006747", acknowledgement = ack-nhfb, fjournal = "Computers and Mathematics with Applications", journal-URL = "http://www.sciencedirect.com/science/journal/08981221", remark = "From the paper: ``\ldots{} an important work of Benford that was published 70 years ago implies many physical quantities in the nature are of exponentially varying type.''.", } @Misc{Wagon:2010:BLD, author = "S. Wagon", title = "{Benford's Law} and Data Spread", year = "2010", bibdate = "Sat Nov 12 16:59:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Web site.", URL = "http://demonstrations.wolfram.com/BenfordsLawAndDataSpread", acknowledgement = ack-nhfb, } @Article{Zhao:2010:IFU, author = "Xi Zhao and Anthony Tung Shuen Ho and Yun Q. Shi", title = "Image Forensics Using Generalised {Benford's Law} for Improving Image Authentication Detection Rates in Semi-Fragile Watermarking", journal = "International Journal of Digital Crime and Forensics", volume = "2", number = "2", pages = "1--20", month = "????", year = "2010", CODEN = "????", DOI = "https://doi.org/10.4018/jdcf.2010040101", ISSN = "1941-6210 (print), 1941-6229 (electronic)", ISSN-L = "1941-6210", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/ijdcf/ijdcf2.html#ZhaoHS10", acknowledgement = ack-nhfb, ajournal = "Int. J. Digit. Crime Forensics", dblp-key = "journals/ijdcf/ZhaoHS10", dblp-mdate = "2020-08-12", fjournal = "International Journal of Digital Crime and Forensics", journal-URL = "https://www.igi-global.com/gateway/journal/1112", } @Article{Abrantes-Metz:2011:TLR, author = "R. M. Abrantes-Metz and S. B. Villas-Boas and G. Judge", title = "Tracking the {Libor} rate", journal = j-APPL-ECON-LETT, volume = "18", number = "10", pages = "893--899", month = "????", year = "2011", DOI = "https://doi.org/10.1080/13504851.2010.515197", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Mon Feb 18 18:17:20 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", journal-URL = "http://www.tandfonline.com/loi/rael20", keywords = "Benford's Second-Digit Law", remark = "From the abstract: ``Libor rates depart significantly from the expected Benford reference distribution. This raises potential concerns relative to the unbiased nature of the signals coming from the 16 banks from which the Libor is computed and the usefulness of the Libor as a major economic indicator.''", } @Article{Adamic:2011:CSU, author = "Lada Adamic", title = "Complex systems: Unzipping {Zipf}'s law", journal = j-NATURE, volume = "474", number = "7350", pages = "164--165", day = "8", month = jun, year = "2011", CODEN = "NATUAS", DOI = "https://doi.org/10.1038/474164a", ISSN = "0028-0836 (print), 1476-4687 (electronic)", ISSN-L = "0028-0836", bibdate = "Tue Nov 15 09:29:15 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html", acknowledgement = ack-nhfb, fjournal = "Nature", journal-URL = "http://www.nature.com/nature/archive/", onlinedate = "09 June 2011", } @Article{Altamirano:2011:PTS, author = "C. Altamirano and A. Robledo", title = "Possible thermodynamic structure underlying the laws of {Zipf} and {Benford}", journal = j-EUR-PHYS-J-B, volume = "81", number = "3", pages = "345--351", month = jun, year = "2011", CODEN = "EPJBFY", DOI = "https://doi.org/10.1140/epjb/e2011-10968-5", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Mon Nov 14 17:53:47 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011EPJB...81..345A", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1008.1614", fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", primaryclass = "cond-mat.stat-mech", } @Article{Anderson:2011:BLC, author = "Theresa C. Anderson and Larry Rolen and Ruth Stoehr", title = "{Benford}'s law for coefficients of modular forms and partition functions", journal = j-PROC-AM-MATH-SOC, volume = "139", number = "5", pages = "1533--1541", year = "2011", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/S0002-9939-2010-10577-4", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "11F12 (11F20 11P83)", MRnumber = "2763743", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @Article{Andrew:2011:OBM, author = "Alex M. Andrew", title = "Obituary: {Beno{\^\i}t Mandelbrot: 20 November 1924--14 October 2010}", journal = "Kybernetes", volume = "40", number = "1--2", pages = "??--??", month = "????", year = "2011", CODEN = "KBNTA3", ISSN = "0368-492X (print), 1758-7883 (electronic)", ISSN-L = "0368-492X", bibdate = "Fri Nov 25 07:32:54 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://en.wikipedia.org/wiki/ernst_von_glasersfeld; http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf; http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825; http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary; http://www.math.yale.edu/mandelbrot/; http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html", acknowledgement = ack-nhfb, } @Misc{Anonymous:2011:BLH, author = "Anonymous", title = "{Benford's Law} --- How mathematics can detect fraud!", howpublished = "Web video lecture (10m47s).", day = "9", month = apr, year = "2011", bibdate = "Fri Oct 09 06:40:54 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.youtube.com/watch?v=vIsDjbhbADY", acknowledgement = ack-nhfb, xxauthor = "Brady Haran", } @Article{Archambault:2011:EMA, author = "J. Archambault and M. Archambault", title = "Earnings management among firms during the pre-{SEC} era: a {Benford}'s law analysis", journal = j-ACCOUNT-HIST-J, volume = "38", number = "2", pages = "145--170", month = "????", year = "2011", ISSN = "0148-4184", ISSN-L = "0148-4184", bibdate = "Mon Feb 18 11:32:23 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Accounting Historians Journal", journal-URL = "http://www.jstor.org/action/showPublication?journalCode=accohistjour; http://www.aahhq.org/", remark = "JSTOR has a 3-year moving wall, so this article is not yet in that archive; the publisher's Web site is poor, and I cannot find the article there.", } @Article{Baek:2011:ZLU, author = "Seung Ki Baek and Sebastian Bernhardsson and Petter Minnhagen", title = "{Zipf}'s law unzipped", journal = j-NEW-J-PHYS, volume = "13", number = "4", pages = "043004", month = "????", year = "2011", CODEN = "NJOPFM", DOI = "https://doi.org/10.1088/1367-2630/13/4/043004", ISSN = "1367-2630", ISSN-L = "1367-2630", bibdate = "Tue Nov 15 09:32:45 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://iopscience.iop.org/1367-2630/13/4/043004", abstract = "Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be citizens of a country and the groups family names, or the elements can be all the words making up a novel and the groups the unique words, or the elements could be inhabitants and the groups the cities in a country and so on. A random group formation (RGF) is presented from which a Bayesian estimate is obtained based on minimal information: it provides the best prediction for the number of groups with $k$ elements, given the total number of elements, groups and the number of elements in the largest group. For each specification of these three values, the RGF predicts a unique group distribution $ N(k) \propto \exp ( - b k) / k^\gamma $, where the power-law index $ \gamma $ is a unique function of the same three values. The universality of the result is made possible by the fact that no system-specific assumptions are made about the mechanism responsible for the group division. The direct relation between $ \gamma $ and the total number of elements, groups and the number of elements in the largest group is calculated. The predictive power of the RGF model is demonstrated by direct comparison with data from a variety of systems. It is shown that $ \gamma $ usually takes values in the interval $ 1 \leq \gamma \leq 2 $ and that the value for a given phenomenon depends in a systematic way on the total size of the dataset. The results are put in the context of earlier discussions on Zipf's and Gibrat's laws, $ N(k) \propto k^{-2} $ and the connection between growth models and RGF is elucidated.", acknowledgement = ack-nhfb, fjournal = "New Journal of Physics", journal-URL = "http://iopscience.iop.org/1367-2630", pagecount = "21", } @Misc{Barnes:2011:LCS, author = "K. Barnes", title = "Letter to {China Shen Zhou Mining and Resources (AMEX: SHZ)} current shareholders and potential investors from {Absaroka Capital}", howpublished = "Absaroka Capital Management, LLP, Wyoming, USA.", year = "2011", bibdate = "Fri Mar 22 08:42:58 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", } @InCollection{Barrale:2011:SID, author = "Tom Barrale and R. Hendel and Michael Sluys", booktitle = "{Proceedings of the 14th international conference on Fibonacci numbers and their applications, Morelia, Mexico, July 5--9, 2010}", title = "Sequences of the initial digits of {Fibonacci} numbers", publisher = "Sociedad Matem\'atica Mexicana", address = "M{\'e}xico, DF, M{\'e}xico", pages = "25--42", year = "2011", ISBN = "607-02-2543-0 (paperback)", ISBN-13 = "978-607-02-2543-7 (paperback)", MRnumber = "11B37 11B39", bibdate = "Sat Sep 10 10:27:11 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "1287.11017", acknowledgement = ack-nhfb, keywords = "Benford's Law; Fibonacci numbers", } @Article{Bauer:2011:DDF, author = "Johannes Bauer and Jochen Gross", title = "Difficulties Detecting Fraud? {The} Use of {Benford?s Law} on Regression Tables", journal = "Journal of Economics and Statistics (Jahrb{\"u}cher f{\"u}r National{\"o}konomie und Statistik)", volume = "231", number = "5--6", pages = "733--748", month = nov, year = "2011", DOI = "????", bibdate = "Mon Feb 18 18:18:45 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html", acknowledgement = ack-nhfb, journal-URL = "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/", } @Article{Bawden:2011:BMS, author = "David Bawden", title = "{Beno{\^\i}t Mandelbrot} and the self-similarity of information", journal = j-J-DOC, volume = "67", number = "2", pages = "??--??", month = "????", year = "2011", CODEN = "JDOCAS", ISSN = "0022-0418 (print), 1758-7379 (electronic)", ISSN-L = "0022-0418", bibdate = "Fri Nov 25 07:40:34 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717", acknowledgement = ack-nhfb, fjournal = "Journal of Documentation", journal-URL = "http://www.emeraldinsight.com/loi/jd", } @Article{Becker:2011:BLC, author = "T. Becker and A. Greaves-Tunnell and Steven J. Miller and R. Ronan and F. W. Strauch", title = "{Benford's Law} and Continuous Dependent Random Variables", journal = "ArXiv e-prints", month = nov, year = "2011", CODEN = "????", ISSN = "????", bibdate = "Mon Nov 14 17:50:20 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B; http://arxiv.org/abs/1111.0568", abstract = "Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $ 2^n $, equals 1 not 10\% or 11\% of the time, as one would expect if all digits were equally likely, but about 30\% of the time. This phenomenon, known as Benford's Law, has many applications, ranging from detecting tax fraud for the IRS to analyzing round-off errors in computer science.\par The central question is determining which data sets follow Benford's law. Inspired by natural processes such as particle decay, our work examines models for the decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow. The main difficulty is that the resulting random variables are dependent, which we handle by a careful analysis of the dependencies and tools from Fourier analysis to obtain quantified convergence rates.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1111.0568", keywords = "Mathematics - Probability, 11K06, 60A10 (primary), 60E10 (secondary)", primaryclass = "math.PR", } @Article{Berger:2011:BLS, author = "Arno Berger and Theodore P. Hill", title = "{Benford}'s law strikes back: no simple explanation in sight for mathematical gem", journal = j-MATH-INTEL, volume = "33", number = "1", pages = "85--91", month = mar, year = "2011", CODEN = "MAINDC", DOI = "https://doi.org/10.1007/s00283-010-9182-3", ISSN = "0343-6993 (print), 1866-7414 (electronic)", ISSN-L = "0343-6993", MRclass = "62A99 (60E05)", MRnumber = "2774458", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/amstat2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See letter \cite{Hill:2011:LEB}.", URL = "http://link.springer.com/article/10.1007/s00283-010-9182-3", acknowledgement = ack-nhfb, fjournal = "The Mathematical Intelligencer", journal-URL = "http://link.springer.com/journal/283", } @Article{Berger:2011:BTB, author = "Arno Berger and Theodore P. Hill", title = "A basic theory of {Benford's Law}", journal = j-PROBAB-SURV, volume = "8", number = "??", pages = "1--126", month = "????", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1214/11-PS175", ISSN = "1549-5787", ISSN-L = "1549-5787", MRclass = "37A45 (11K06 60-02 60F15 60G57 62E10)", MRnumber = "2846899 (2012h:37015)", MRreviewer = "Steven Joel Miller", bibdate = "Tue Nov 15 11:07:49 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/probabsurv.bib", URL = "http://projecteuclid.org/euclid.ps/1311860830", abstract = "Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as {\em Benford's Law\/} (BL) or, in a special case, as the {\em First Digit Law}. The invariance properties that characterize BL are developed in detail. Special attention is given to the emergence of BL in a wide variety of deterministic and random processes. Though mainly expository in nature, the article also provides strengthened versions of, and simplified proofs for, many key results in the literature. Numerous intriguing problems for future research arise naturally.", acknowledgement = ack-nhfb, fjournal = "Probability Surveys", journal-URL = "http://projecteuclid.org/all/euclid.ps", keywords = "base-invariance; Benford's Law; difference equation; mixture of distributions; random probability measure; scale-invariance; shadowing; significant digits; sum-invariance; uniform distribution mod 1", } @Article{Berger:2011:FSM, author = "Arno Berger and Theodore P. Hill and Bahar Kaynar and Ad Ridder", title = "Finite-state {Markov} Chains Obey {Benford's Law}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "32", number = "3", pages = "665--684", month = "????", year = "2011", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/100789890", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15B51 (11J71 60J22 65C40)", MRnumber = "2825319 (2012h:15058)", MRreviewer = "E. Seneta", bibdate = "Wed Aug 24 11:18:18 MDT 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", URL = "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1; https://dblp.org/db/journals/siammax/siammax32.html#BergerHKR11", acknowledgement = ack-nhfb, dblp-key = "journals/siammax/BergerHKR11", dblp-mdate = "2020-05-26", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "July 21, 2011", } @Article{Berger:2011:SDP, author = "Arno Berger", title = "Some dynamical properties of {Benford} sequences", journal = j-J-DIFFERENCE-EQU-APPL, volume = "17", number = "2", pages = "137--159", year = "2011", CODEN = "JDEAEA", DOI = "https://doi.org/10.1080/10236198.2010.549012", ISSN = "1023-6198 (print), 1563-5120 (electronic)", ISSN-L = "1023-6198", MRclass = "37A45 (11K06 37Bxx)", MRnumber = "2783341", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012", acknowledgement = ack-nhfb, ajournal = "J. Difference Equ. Appl.", fjournal = "Journal of Difference Equations and Applications", journal-URL = "http://www.informaworld.com/1023-6198", } @Article{Bernhardsson:2011:PPM, author = "Sebastian Bernhardsson and Seung Ki Baek and Petter Minnhagen", title = "A paradoxical property of the monkey book", journal = j-J-STAT-MECH-THEORY-EXP, volume = "2011", number = "??", pages = "P07013", month = jul, year = "2011", CODEN = "JSMTC6", DOI = "https://doi.org/10.1088/1742-5468/2011/07/P07013", ISSN = "1742-5468", ISSN-L = "1742-5468", bibdate = "Mon Nov 21 21:57:13 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1103.2681; http://iopscience.iop.org/1742-5468/2011/07/P07013/", abstract = "A `monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a `spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a `monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Mechanics: Theory and Experiment", journal-URL = "http://iopscience.iop.org/1742-5468/", keywords = "Heaps' Law", } @Article{Bhattacharya:2011:ABA, author = "Sukanto Bhattacharya and Dongming Xu and Kuldeep Kumar", title = "An {ANN}-based auditor decision support system using {Benford}'s law", journal = j-DEC-SUPP-SYS, volume = "50", number = "3", pages = "576--584", month = feb, year = "2011", CODEN = "DSSYDK", DOI = "https://doi.org/10.1016/j.dss.2010.08.011", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "On quantitative methods for detection of financial fraud", URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001351", abstract = "While there is a growing professional interest on the application of Benford's law and digit analysis in financial fraud detection, there has been relatively little academic research to demonstrate its efficacy as a decision support tool in the context of an analytical review procedure pertaining to a financial audit. We conduct a numerical study using a genetically optimized artificial neural network. Building on an earlier work by others of a similar nature, we assess the benefits of Benford's law as a useful classifier in segregating naturally occurring (i.e. non-concocted) numbers from those that are made up. Alongside the frequency of the first and second significant digits and their mean and standard deviation, a posited set of non-digit input variables categorized as information theoretic, distance-based and goodness-of-fit measures, help to minimize the critical classification errors that can lead to an audit failure. We come up with the optimal network structure for every instance corresponding to a $ 3 \times 3 $ Manipulation Involvement matrix that is drawn to depict the different combinations of the level of sophistication in data manipulation by the perpetrators of a financial fraud and also the extent of collusive involvement.", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "ANNs; ARPs; Auditor decision support system; Benford's law; Benford's Law; Benford's law; Benford's Law; Genetic optimization; {ANNs}; {ARPs}", } @Article{Bose:2011:QMD, author = "Indranil Bose and Selwyn Piramuthu and Michael J. Shaw", title = "Quantitative methods for Detection of Financial Fraud", journal = j-DEC-SUPP-SYS, volume = "50", number = "3", pages = "557--558", month = feb, year = "2011", CODEN = "DSSYDK", DOI = "https://doi.org/10.1016/j.dss.2010.08.005", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "On quantitative methods for detection of financial fraud", URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001296", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law", } @InCollection{Brahler:2011:BGS, author = "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph Jakobi", editor = "????", booktitle = "Ilmenauer Schriften zur Betriebswirtschaftslehre", title = "{Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}. ({German}) [{The} {Benford} law and its applicability in the digital examination of logbooks]", volume = "3/2011", publisher = "Verlag proWiWi e.V.", address = "Ilmenau, Germany", pages = "??--??", month = mar, year = "2011", ISBN = "3-940882-28-3", ISBN-13 = "978-3-940882-28-8", ISSN = "1866-2145 (print), 2192-4643 (electronic)", LCCN = "????", bibdate = "Mon Feb 18 18:21:29 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Breunig:2011:SEI, author = "Christian Breunig and Achim Goerres", title = "Searching for electoral irregularities in an established democracy: Applying {Benford's Law} tests to {Bundestag} elections in {Unified Germany}", journal = j-ELECT-STUDIES, volume = "30", number = "3", pages = "534--545", month = sep, year = "2011", CODEN = "????", DOI = "https://doi.org/10.1016/j.electstud.2011.03.005", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "Special Symposium on the Politics of Economic Crisis", URL = "http://www.sciencedirect.com/science/article/pii/S0261379411000370", abstract = "This article investigates electoral irregularities in the 1990 to 2005 Bundestag elections of unified Germany. Drawing on the Second Digit Benford Law (2BL) by Mebane (2006), the analysis consists of comparing the observed frequencies of numerals of candidate votes and party votes at the precinct level against the expected frequencies according to Benford's Law. Four central findings stand out. First, there is no evidence for systematic fraud or mismanagement with regard to candidate votes from districts where fraud would be most instrumental. Second, at the state level (Bundesland), there are 51 violations in 190 tests of the party list votes. Third, East German states are not more prone to violations than Western ones. This finding refutes the notion that the East's more recent transition to democracy poses problems in electoral management. Fourth, a strong variation in patterns of violation across Bundesl{\"a}nder exists: states with dominant party control are more likely to display irregularities. The article concludes by hypothesizing and exploring the notion that partisan composition of nominees involved in the counting may produce a higher likelihood of violation and be a cause of L{\"a}nder variation. This may especially be the case when a party dominates in a Bundesland or opponents to the former socialist regime party are involved in the counting.", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Benford's Law; Bundestag; Fraud; Germany", } @TechReport{Bul:2011:BGG, author = "K. Bul", title = "{Das Benford'sche Gesetz}. ({German}) [{Benford's Law}]", type = "Working paper", institution = "Max-von-Laue-gymnasium", address = "Koblenz, Germany", year = "2011", bibdate = "Fri Mar 22 08:44:32 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", language = "German", } @Article{Campanario:2011:BLC, author = "Juan Campanario and Mar{\'\i}a Coslado", title = "{Benford}'s law and citations, articles and impact factors of scientific journals", journal = j-SCIENTOMETRICS, volume = "88", number = "2", pages = "421--432", month = aug, year = "2011", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-011-0387-9", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Fri Nov 25 10:43:36 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11192-011-0387-9", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Cantu:2011:FDA, author = "F. Cantu and S. M. Saiegh", title = "Fraudulent Democracy? {An} Analysis of {Argentina}'s Infamous Decade Using Supervised Machine Learning", journal = j-POLIT-ANAL, volume = "19", number = "4", pages = "409--433", month = "Autumn", year = "2011", DOI = "https://doi.org/10.1093/pan/mpr033", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 18:24:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://pan.oxfordjournals.org/content/19/4/409.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", journal-URL = "https://www.cambridge.org/core/journals/political-analysis/all-issues", keywords = "Benford's Law", } @Article{Chang:2011:CGR, author = "Harry M. Chang", title = "Constructing $n$-gram rules for natural language models through exploring the limitation of the {Zipf--Mandelbrot} law", journal = j-COMPUTING, volume = "91", number = "3", pages = "241--264", month = mar, year = "2011", CODEN = "CMPTA2", DOI = "https://doi.org/10.1007/s00607-010-0116-x", ISSN = "0010-485X (print), 1436-5057 (electronic)", ISSN-L = "0010-485X", MRclass = "68T50", MRnumber = "2776088", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241", acknowledgement = ack-nhfb, fjournal = "Computing. Archives for Scientific Computing", journal-URL = "http://link.springer.com/journal/607", } @Article{Chida:2011:LSI, author = "Satoshi Chida and Naoto Miyoshi", title = "Limiting size index distributions for ball-bin models with {Zipf}-type frequencies", journal = j-ANN-INST-STAT-MATH-TOKYO, volume = "63", number = "4", pages = "745--768", year = "2011", CODEN = "AISXAD", DOI = "https://doi.org/10.1007/s10463-010-0276-7", ISSN = "0020-3157 (print), 1572-9052 (electronic)", ISSN-L = "0020-3157", MRclass = "60C05 (60F15 60J27)", MRnumber = "2805906 (2012f:60035)", MRreviewer = "Elvira Di Nardo", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annals of the Institute of Statistical Mathematics (Tokyo)", journal-URL = "http://link.springer.com/journal/10463", } @Article{Corominas-Murtra:2011:EZL, author = "Bernat Corominas-Murtra and Jordi Fortuny and Ricard V. Sol{\'e}", title = "Emergence of {Zipf}'s law in the evolution of communication", journal = j-PHYS-REV-E, volume = "83", number = "1", pages = "036115", day = "28", month = mar, year = "2011", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.83.036115", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036115", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "9", } @Article{Deckert:2011:BLD, author = "Joseph Deckert and Mikhail Myagkov and Peter C. Ordeshook", title = "{Benford's Law} and the Detection of Election Fraud", journal = j-POLIT-ANAL, volume = "19", number = "3", pages = "245--268", month = "Summer", year = "2011", DOI = "https://doi.org/10.1093/pan/mpr014", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Mon Feb 18 18:26:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Mebane:2011:CBL} for a rebuttal.", URL = "http://pan.oxfordjournals.org/content/19/3/245.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", journal-URL = "https://www.cambridge.org/core/journals/political-analysis/all-issues", remark = "The authors argue that application of Benford's Law tests to election results to detect fraud is inconclusive and ``essentially equivalent to a toss of a coin''.", } @Article{Dixit:2011:EEP, author = "U. J. Dixit and M. Jabbari Nooghabi", title = "Efficient estimation in the {Pareto} distribution with the presence of outliers", journal = j-STAT-METHODOL, volume = "8", number = "4", pages = "340--355", month = jul, year = "2011", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:47 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312711000141", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Article{Doyle:2011:ITA, author = "Laurance R. Doyle and Brenda McCowan and Simon Johnston and Sean F. Hanser", title = "Information theory, animal communication, and the search for extraterrestrial intelligence", journal = j-ACTA-ASTRONAUT, volume = "68", number = "3--4", pages = "406--417", month = feb # "\slash " # mar, year = "2011", CODEN = "AASTCF", DOI = "https://doi.org/10.1016/j.actaastro.2009.11.018", ISSN = "0094-5765 (print), 1879-2030 (electronic)", ISSN-L = "0094-5765", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", note = "{SETI} Special Edition", URL = "http://www.sciencedirect.com/science/article/pii/S0094576509005682", abstract = "We present ongoing research in the application of information theory to animal communication systems with the goal of developing additional detectors and estimators for possible extraterrestrial intelligent signals. Regardless of the species, for intelligence (i.e., complex knowledge) to be transmitted certain rules of information theory must still be obeyed. We demonstrate some preliminary results of applying information theory to socially complex marine mammal species (bottlenose dolphins and humpback whales) as well as arboreal squirrel monkeys, because they almost exclusively rely on vocal signals for their communications, producing signals which can be readily characterized by signal analysis. Metrics such as Zipf's Law and higher-order information-entropic structure are emerging as indicators of the communicative complexity characteristic of an intelligent message content within these animals signals, perhaps not surprising given these species social complexity. In addition to human languages, for comparison we also apply these metrics to pulsar signals perhaps (arguably) the most organized of stellar systems as an example of astrophysical systems that would have to be distinguished from an extraterrestrial intelligence message by such information theoretic filters. We also look at a message transmitted from Earth (Arecibo Observatory) that contains a lot of meaning but little information in the mathematical sense we define it here. We conclude that the study of non-human communication systems on our own planet can make a valuable contribution to the detection of extraterrestrial intelligence by providing quantitative general measures of communicative complexity. Studying the complex communication systems of other intelligent species on our own planet may also be one of the best ways to deprovincialize our thinking about extraterrestrial communication systems in general.", acknowledgement = ack-nhfb, fjournal = "Acta Astronautica", keywords = "Animal communication; Benford's Law; Information theory; Zipf's Law; {SETI}", } @Article{Edwards:2011:LFP, author = "Roderick Edwards and Laura Collins", title = "Lexical Frequency Profiles and {Zipf's Law}", journal = "Language Learning", volume = "61", number = "1", pages = "1--30", year = "2011", DOI = "https://doi.org/10.1111/j.1467-9922.2010.00616.x", ISSN = "0023-8333 (print), 1467-9922 (electronic)", ISSN-L = "0023-8333", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "L2 vocabulary learning; L2 vocabulary size; modeling vocabulary learning; Zipf's law", } @Article{Egghe:2011:BLS, author = "Leo Egghe", title = "{Benford}'s law is a simple consequence of {Zipf}'s law", journal = "ISSI Newsletter", volume = "7", number = "3", pages = "55--56", month = sep, year = "2011", DOI = "????", bibdate = "Mon Feb 18 18:27:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.issi-society.info/archives/newsletter27.pdf", abstract = "We show that benford's law (describing the logarithmic distribution of the numbers 1, 2, \ldots{}, 9 as first digits of data in decimal form) can be deduced from the classical law of zipf. this explains Bensford's law as a scientometric or informetric law.", acknowledgement = ack-nhfb, } @TechReport{Eliahou:2011:MDP, author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique Schneider", title = "On the mantissa distribution of powers of natural and prime numbers", type = "Preprint", institution = "Universit{\'e} du Littoral C{\^o}te d'Opale", address = "Nord-Pas-de-Calais, France", pages = "14", day = "15", month = nov, year = "2011", bibdate = "Mon Feb 18 18:27:51 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale; http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf", acknowledgement = ack-nhfb, } @Article{Eliazar:2011:LLZ, author = "Iddo Eliazar", title = "Limit laws for {Zipf}'s law", journal = j-J-PHYS-A, volume = "44", number = "2", pages = "022001", year = "2011", CODEN = "JPHAC5", DOI = "https://doi.org/10.1088/1751-8113/44/2/022001", ISSN = "1751-8113 (print), 1751-8121 (electronic)", ISSN-L = "0305-4470", MRclass = "62G30 (91D20)", MRnumber = "2749082 (2011i:62083)", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", ZMnumber = "Zbl 1204.62196", acknowledgement = ack-nhfb, fjournal = "Journal of Physics. A. Mathematical and Theoretical", journal-URL = "http://iopscience.iop.org/0305-4470", pagecount = "6", } @Misc{Farbaniec:2011:AFD, author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c", title = "Application of the first digit law in credibility evaluation of the financial accounting data based on particular cases", howpublished = "Lecture slides for 10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Krak{\'o}w, September 14--16, 2011.", pages = "27", year = "2011", bibdate = "Thu Dec 01 21:27:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://benford.pl/documents/benford_pikw.pdf", acknowledgement = ack-nhfb, } @InProceedings{Farbaniec:2011:UBL, author = "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c", editor = "????", booktitle = "10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Krak{\'o}w, September 14--16, 2011", title = "Using {Benford}'s law to detect irregularities in the collection of data", publisher = "????", address = "????", pages = "??--??", year = "2011", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Thu Dec 01 21:32:03 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Garcia:2011:FPA, author = "Juan Manuel Garcia Garcia", title = "A fixed-point algorithm to estimate the {Yule-Simon} distribution parameter", journal = j-APPL-MATH-COMP, volume = "217", number = "21", pages = "8560--8566", day = "1", month = jul, year = "2011", CODEN = "AMHCBQ", DOI = "https://doi.org/10.1016/j.amc.2011.03.092", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Tue Oct 25 12:05:30 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/science/journal/00963003", URL = "http://www.sciencedirect.com/science/article/pii/S0096300311004607", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003", } @InCollection{Gauvrit:2011:SRI, author = "N. Gauvrit and J-P. Delahaye", title = "Scatter and Regularity Implies {Benford's Law}\ldots{} and More", crossref = "Zenil:2011:RTC", pages = "53--69", year = "2011", bibdate = "Mon Feb 18 18:29:00 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Giuliano:2011:WCS, author = "Rita Giuliano", title = "Weak convergence of sequences from fractional parts of random variables and applications", journal = j-THEORY-PROBAB-MATH-STAT, volume = "83", number = "??", pages = "49--58", month = "????", year = "2011", CODEN = "TPMSCO", DOI = "????", ISSN = "0094-9000 (print), 1547-7363 (electronic)", ISSN-L = "0094-9000", MRclass = "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)", MRnumber = "http://www.ams.org/mathscinet-getitem?mr=2768848", bibdate = "Mon Feb 18 17:47:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf", acknowledgement = ack-nhfb, fjournal = "Theory of Probability and Mathematical Statistics", journal-URL = "http://www.ams.org/publications/journals/journalsframework/tpms", keywords = "Benford's Law", } @Book{Henriques:2011:WLB, author = "Diana B. Henriques", title = "The wizard of lies: {Bernie Madoff} and the death of trust", publisher = "Times Books/Henry Holt", address = "New York, NY, USA", pages = "xxiv + 419", year = "2011", ISBN = "0-8050-9134-3", ISBN-13 = "978-0-8050-9134-2", LCCN = "HV6692.M33 H46 2011", bibdate = "Fri Mar 22 08:51:50 MDT 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Madoff, Bernard L; Swindlers and swindling; United States; Biography; Ponzi schemes; Commercial crimes", tableofcontents = "An earthquake on Wall Street \\ Becoming bernie \\ The hunger for yield \\ The big four \\ The cash spigot \\ What they wanted to believe \\ Warning signs \\ A near-death experience \\ Madoff's world \\ The year of living dangerously \\ Waking up in the rubble \\ Reckoning the damage \\ Net winners and net losers \\ The sins of the father \\ The wheels of justice \\ Hope, lost and found", } @Article{Hill:2011:LEB, author = "Theodore P. Hill", title = "Letter to the Editor: {Benford's Law} Blunders", journal = j-AMER-STAT, volume = "65", number = "2", pages = "141--141", month = may, year = "2011", CODEN = "ASTAAJ", DOI = "https://doi.org/10.1198/tast.2011.10179", ISSN = "0003-1305 (print), 1537-2731 (electronic)", ISSN-L = "0003-1305", bibdate = "Mon Feb 18 18:34:43 2013", bibsource = "http://www.amstat.org/publications/tas/; https://www.math.utah.edu/pub/tex/bib/amstat2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011", acknowledgement = ack-nhfb, fjournal = "The American Statistician", journal-URL = "http://www.tandfonline.com/loi/utas20", remark = "Brief comment on a error in Feller's derivation of Benford's Law, with pointer to a corrected proof in \cite{Berger:2011:BLS}.", } @Article{Hisano:2011:PVD, author = "Ryohei Hisano and Didier Sornette and Takayuki Mizuno", title = "Predicted and verified deviations from {Zipf}'s law in ecology of competing products", journal = j-PHYS-REV-E, volume = "84", number = "2", pages = "026117", day = "24", month = aug, year = "2011", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.84.026117", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.84.026117", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Zipf's Law", pagecount = "8", } @Article{Hui:2011:BLN, author = "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min", title = "{Benford's Law} in Nuclear Structure Physics", journal = j-CHIN-PHYS-LETT, volume = "28", number = "3", pages = "32101--32104", month = mar, year = "2011", CODEN = "CPLEEU", DOI = "https://doi.org/10.1088/0256-307X/28/3/032101", ISSN = "0256-307X (print), 1741-3540 (electronic)", ISSN-L = "0256-307X", bibdate = "Fri Nov 25 10:37:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Chinese Physics Letters", } @Article{Janvresse:2011:AAU, author = "{\'E}lise Janvresse and Thierry {De La Rue}", title = "Averaging along Uniform Random Integers", journal = "ArXiv e-prints", year = "2011", bibdate = "Mon Nov 21 07:06:41 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1103.1719", abstract = "Motivated by giving a meaning to ``The probability that a random integer has initial digit $d$'', we define a URI-set as a random set $E$ of natural integers such that each $ n > 0$ belongs to $E$ with probability $ 1 / n$, independently of other integers. This enables us to introduce two notions of densities on natural numbers: The URI-density, obtained by averaging along the elements of $E$, and the local URI-density, which we get by considering the $k$-th element of $E$ and letting $k$ go to infinity. We prove that the elements of $E$ satisfy Benford's law, both in the sense of URI-density and in the sense of local URI-density. Moreover, if $ b_1 $ and $ b_2 $ are two multiplicatively independent integers, then the mantissae of a natural number in base $ b_1 $ and in base $ b_2 $ are independent. Connections of URI-density and local URI-density with other well-known notions of densities are established: Both are stronger than the natural density, and URI-density is equivalent to log-density. We also give a stochastic interpretation, in terms of URI-set, of the $ H_\infty $-density.", acknowledgement = ack-nhfb, } @Article{Jiang:2011:BLN, author = "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao", title = "{Benford}'s law in nuclear structure physics", journal = j-CHIN-PHYS-LETT, volume = "28", number = "3", pages = "032101", month = "????", year = "2011", CODEN = "CPLEEU", DOI = "https://doi.org/10.1088/0256-307X/28/3/032101", ISSN = "0256-307X (print), 1741-3540 (electronic)", ISSN-L = "0256-307X", bibdate = "Mon Nov 14 16:16:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See also \cite{Ferreira:2015:LPA}.", acknowledgement = ack-nhfb, ajournal = "Chin. Phys. Lett.", fjournal = "Chinese Physics Letters", pagecount = "4", } @InProceedings{Kalinin:2011:UEF, author = "K. Kalinin and Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{Proceedings of the 2011 Annual Meeting of the Midwest Political Science Association, Chicago, IL, March 31--April 2, 2011}", title = "Understanding Electoral Frauds through Evolution of {Russian} Federalism: From ``Bargaining Loyalty'' to ``Signaling Loyalty''", publisher = "????", address = "????", pages = "??--??", year = "2011", bibdate = "Sat Sep 10 12:37:47 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Kim:2011:ZAS, author = "SeongKi Kim and HaYoon Song and SangYong Han", title = "{ZipfAllocation}: an algorithm for static allocation of movies in a cluster of video servers", journal = j-SPE, volume = "41", number = "6", pages = "695--716", month = may, year = "2011", CODEN = "SPEXBL", DOI = "https://doi.org/10.1002/spe.1027", ISSN = "0038-0644 (print), 1097-024X (electronic)", ISSN-L = "0038-0644", bibdate = "Tue Jun 21 17:09:57 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Soft{\-}ware\emdash Prac{\-}tice and Experience", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X", onlinedate = "25 Nov 2010", } @Misc{Li:2011:ZLB, author = "Wentian Li", title = "{Zipf's Law} bibliography", howpublished = "Web site.", month = aug, year = "2011", bibdate = "Fri Nov 25 08:58:21 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "The site holds 870 references (in untagged reference-list form) up to 11 August 2011.", URL = "http://www.nslij-genetics.org/wli/zipf/", acknowledgement = ack-nhfb, lastaccess = "25 November 2011", } @Article{Liu:2011:BLC, author = "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren", title = "{Benford}'s law and cross-sections of {$ A(n, \alpha) B $} reactions", journal = j-EUR-PHYS-J-A, volume = "47", pages = "78", month = jun, year = "2011", CODEN = "EPJAFV", DOI = "https://doi.org/10.1140/epja/i2011-11078-3", ISSN = "1434-6001 (print), 1434-601X (electronic)", ISSN-L = "1434-6001", bibdate = "Mon Nov 14 18:00:32 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011EPJA...47...78L", acknowledgement = ack-nhfb, fjournal = "European Physical Journal A: Hadrons and Nuclei", journal-URL = "http://www.springerlink.com/content/1434-6001", } @InProceedings{Lyons:2011:NSF, author = "M. Lyons and E. Carl-Ludwig Siegel", booktitle = "APS March Meeting Abstracts", title = "{NON-Shor} Factorization via {BEQS BEC}: {Watkins} Number-Theory ``Pure''-Mathematics $ \cup $ with Statistical-Physics: {Benford} Log-Law Inversion to {ONLY} {BEQS} digit $ d = 0 $ {BEC}!!!", publisher = "American Physical Society", address = "????", pages = "K1142", month = mar, year = "2011", bibdate = "Mon Nov 14 18:08:39 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L", acknowledgement = ack-nhfb, } @Article{Malevergne:2011:TPA, author = "Yannick Malevergne and Vladilen Pisarenko and Didier Sornette", title = "Testing the {Pareto} against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities", journal = j-PHYS-REV-E, volume = "83", number = "3", pages = "036111", day = "22", month = mar, year = "2011", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.83.036111", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Feb 26 06:40:57 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.83.036111", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", keywords = "Pareto distribution; Zipf's Law", pagecount = "11", } @Article{Martinez-Rodriguez:2011:MUE, author = "A. M. Mart{\'\i}nez-Rodr{\'\i}guez and A. J. S{\'a}ez-Castillo and A. Conde-S{\'a}nchez", title = "Modelling using an extended {Yule} distribution", journal = j-COMPUT-STAT-DATA-ANAL, volume = "55", number = "1", pages = "863--873", day = "1", month = jan, year = "2011", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:03 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947310002872", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Masse:2011:SWD, author = "Bruno Mass{\'e} and Dominique Schneider", title = "A survey on weighted densities and their connection with the first digit phenomenon", journal = j-ROCKY-MOUNTAIN-J-MATH, volume = "41", number = "5", pages = "1395--1415", month = "????", year = "2011", CODEN = "RMJMAE", DOI = "https://doi.org/10.1216/RMJ-2011-41-5-1395", ISSN = "0035-7596 (print), 1945-3795 (electronic)", ISSN-L = "0035-7596", MRclass = "60B10 (11B05 11K99)", MRnumber = "2838069 (2012k:60009)", MRreviewer = "Radhakrishnan Nair", bibdate = "Mon Feb 18 18:47:30 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf", acknowledgement = ack-nhfb, fjournal = "Rocky Mountain Journal of Mathematics", journal-URL = "http://projecteuclid.org/euclid.rmjm", keywords = "Benford's law; first digit phenomenon; hierarchy; mantissa; weighted density", } @Book{McGrayne:2011:TWH, author = "Sharon Bertsch McGrayne", title = "The theory that would not die: how {Bayes}' rule cracked the {Enigma} code, hunted down {Russian} submarines, and emerged triumphant from two centuries of controversy", publisher = pub-YALE, address = pub-YALE:adr, pages = "xiii + 320", year = "2011", ISBN = "0-300-16969-8", ISBN-13 = "978-0-300-16969-0", LCCN = "QA279.5 .M415 2011", bibdate = "Wed May 11 14:42:54 MDT 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", abstract = "Bayes' rule appears to be a straightforward, one-line theorem: by updating our initial beliefs with objective new information, we get a new and improved belief. To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok. In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years --- at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information, even breaking Germany's Enigma code during World War II, and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security. Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.", acknowledgement = ack-nhfb, remark = "This book has important comments on the battles among Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl Pearson, supplementing the extensive discussion of those conflicts in \cite{Ziliak:2008:CSS}.", subject = "Bayesian statistical decision theory; history; science / history; mathematics / history and philosophy", } @Article{Mebane:2011:CBL, author = "Walter R. {Mebane, Jr.}", title = "Comment on {Benford's Law} and the Detection of Election Fraud", journal = j-POLIT-ANAL, volume = "19", number = "3", pages = "269--272", day = "18", month = "Summer", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1093/pan/mpr024", ISSN = "1047-1987 (print), 1476-4989 (electronic)", ISSN-L = "1047-1987", bibdate = "Fri Nov 25 11:00:46 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Deckert:2011:BLD}.", URL = "http://pan.oxfordjournals.org/content/19/3/269.abstract", acknowledgement = ack-nhfb, fjournal = "Political Analysis", journal-URL = "https://www.cambridge.org/core/journals/political-analysis/all-issues", } @Article{Michel:2011:QAC, author = "Jean-Baptiste Michel and Yuan Kui Shen and Aviva Presser Aiden and Adrian Veres and Matthew K. Gray and {The Google Books Team} and Joseph P. Pickett and Dale Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant and Steven Pinker and Martin A. Nowak and Erez Lieberman Aiden", title = "Quantitative Analysis of Culture Using Millions of Digitized Books", journal = j-SCIENCE, volume = "331", number = "6014", pages = "176--182", day = "14", month = jan, year = "2011", CODEN = "SCIEAS", DOI = "https://doi.org/10.1126/science.1199644", ISSN = "0036-8075 (print), 1095-9203 (electronic)", ISSN-L = "0036-8075", bibdate = "Fri Dec 09 11:06:28 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencemag.org/content/331/6014/176.abstract", acknowledgement = ack-nhfb, fjournal = "Science", journal-URL = "http://www.sciencemag.org/archive/", keywords = "Zipf's law", remark = "This papers reports results from a large study of cultural phenomena, fame, and word usage from 4\% of all books ever printed. Among the findings is this quote from the first page: ``we estimated the number of words in the English lexicon as 544,000 in 1900, 597,000 in 1950, and 1,022,000 in 2000. The lexicon is enjoying a period of enormous growth: The addition of $ \approx 8500 $ words/year has increased the size of the language by over 70\% during the past 50 years.'' From page 177: ``Consistent with Zipf's famous law, a large fraction of the words in our lexicon (63\%) were in this lowest-frequency bin. As a result, we estimated that 52\% of the English lexicon --- the majority of the words used in English books --- consists of lexical `dark matter' undocumented in standard references (12).''", } @Article{Mir:2011:LLD, author = "Tariq Ahmad Mir", title = "Law of the leading digits and the ideological struggle for numbers", journal = "ArXiv e-prints", pages = "11", year = "2011", bibdate = "Mon Nov 21 07:02:48 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1104.3948", abstract = "Benford's law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger ones. We investigate here numerical data on the country-wise adherent distribution of seven major world religions i.e., Christianity, Islam, Buddhism, Hinduism, Sikhism, Judaism and Baha'ism to see if the proportion of the leading digits occurring in the distribution conforms to Benford's law. We find that the adherent data of all the religions, except Christianity, excellently does conform to Benford's law. Furthermore, unlike the adherent data on Christianity, the significant digit distribution of the three major Christian denominations i.e. Catholicism, Protestantism and Orthodoxy obeys the law. Thus in spite of their complexity general laws can be established for the evolution of the religious groups.", acknowledgement = ack-nhfb, } @Article{Muller:2011:HAS, author = "Hans Christian M{\"u}ller", title = "How an arcane statistical law could have prevented the {Greek} disaster", journal = "Economics Intelligence", volume = "??", number = "??", pages = "??", day = "28", month = jul, year = "2011", CODEN = "????", ISSN = "????", bibdate = "Sun Nov 20 10:04:08 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/", abstract = "If we had known what we know today, Greece would not have been able to enter the Euro area. The macroeconomic data the country reported to Eurostat in Luxembourg were heavily tweaked. Unfortunately, however, this only became clear years after it was too late.", acknowledgement = ack-nhfb, } @InCollection{Nigrini:2011:BLA, author = "Mark J. Nigrini", title = "{Benford's Law}: Assessing Conformity", crossref = "Nigrini:2011:FAM", pages = "109--129", year = "2011", DOI = "https://doi.org/10.1002/9781118386798.ch6", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; Kolmogorov-Smirnoff tests; mantissa arc test; mean absolute deviation; Z-statistic", tableofcontents = "One Digit at a Time: The Z-statistic \\ The Chi-square and Kolmogorov--Smirnoff Tests \\ The Mean Absolute Deviation (MAD) Test \\ Tests Based on the Logarithmic Basis of Benford's Law \\ Creating a Perfect Synthetic Benford Set \\ The Mantissa Arc Test \\ Summary", } @InCollection{Nigrini:2011:BLB, author = "Mark J. Nigrini", title = "{Benford's Law}: The Basics", crossref = "Nigrini:2011:FAM", pages = "85--108", year = "2011", DOI = "https://doi.org/10.1002/9781118386798.ch5", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, tableofcontents = "An Overview of Benford's Law \\ From Theory to Application in 60 Years \\ Which Data Sets should Conform to Benford's Law? \\ The Effect of Data Set Size \\ The Basic Digit Tests \\ Running the First-Two Digits Test in Access \\ Summary", } @InCollection{Nigrini:2011:BLN, author = "Mark J. Nigrini", title = "{Benford's Law}: The Number Duplication and Last-Two Digits Tests", crossref = "Nigrini:2011:FAM", pages = "153--172", year = "2011", DOI = "https://doi.org/10.1002/9781118386798.ch8", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; COUNTIF formula; digits tests; last-two digits tests; number duplication", tableofcontents = "The Number Duplication Test \\ Running the Number Duplication Test in Access \\ Running the Number Duplication Test in Excel \\ The Last-Two Digits Test \\ Summary", } @InCollection{Nigrini:2011:BLS, author = "Mark J. Nigrini", title = "{Benford's Law}: The Second-Order and Summation Tests", crossref = "Nigrini:2011:FAM", pages = "130--152", year = "2011", DOI = "https://doi.org/10.1002/9781118386798.ch7", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law; digits tests; second-order; second-order test; summation test", tableofcontents = "A Description of the Second-Order Test \\ The Summation Test \\ Summary", } @Article{Osareh:2011:LLA, author = "Farideh Osareh and Esmaeel Mostafavi", title = "{Lotka's Law} and authorship distribution in Computer Science using {Web of Science (WoS)} during 1986--2009", journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE, volume = "5", number = "2", pages = "171--183", year = "2011", CODEN = "????", DOI = "https://doi.org/10.1080/09737766.2011.10700911", ISSN = "0973-7766 (print), 2168-930X (electronic)", ISSN-L = "0973-7766", bibdate = "Thu Sep 10 17:47:07 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib", acknowledgement = ack-nhfb, fjournal = "Collnet Journal of Scientometrics and Information Management", journal-URL = "http://www.tandfonline.com/loi/tsim20", } @Article{Pericchi:2011:QAD, author = "Luis Pericchi and David Torres", title = "Quick anomaly detection by the {Newcomb--Benford} law, with applications to electoral processes data from the {USA}, {Puerto} {Rico} and {Venezuela}", journal = j-STAT-SCI, volume = "26", number = "4", pages = "502--516", year = "2011", CODEN = "STSCEP", DOI = "https://doi.org/10.1214/09-STS296", ISSN = "0883-4237 (print), 2168-8745 (electronic)", ISSN-L = "0883-4237", MRnumber = "2951385", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://projecteuclid.org/euclid.ss/1330437932", acknowledgement = ack-nhfb, fjournal = "Statistical Science. A Review Journal of the Institute of Mathematical Statistics", journal-URL = "http://projecteuclid.org/all/euclid.ss", } @InProceedings{Qadir:2011:IFG, author = "G. Qadir and X. Zhao and A. T. Ho and M. Casey", booktitle = "2011 IEEE International Symposium of Circuits and Systems (ISCAS)", title = "Image forensic of glare feature for improving image retrieval using {Benford's Law}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "2661--2664", month = may, year = "2011", DOI = "https://doi.org/10.1109/ISCAS.2011.5938152", ISSN = "0271-4302", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benfords law; Brightness; computer forensics; discrete wavelet high high sub bands; Discrete wavelet transforms; Equations; Forensics; glare feature; glare-based problems; Histograms; image analysis; image forensic tool; image retrieval; light intensity measurement; Mathematical model; probability; Probability; probability intensity histogram; salient features identification; visual examination", } @Article{Rauch:2011:FFE, author = "Bernhard Rauch and Max G{\"o}ttsche and Gernot Br{\"a}hler and Stefan Engel", title = "Fact and Fiction in {EU}-Governmental Economic Data", journal = j-GER-ECON-REV, volume = "12", number = "3", pages = "243--255", month = aug, year = "2011", DOI = "https://doi.org/10.1111/j.1468-0475.2011.00542.x", ISSN = "1465-6485 (print), 1468-0475 (electronic)", ISSN-L = "1465-6485", bibdate = "Sun Nov 20 09:58:25 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract", abstract = "To detect manipulations or fraud in accounting data, auditors have successfully used Benford's law as part of their fraud detection processes. Benford's law proposes a distribution for first digits of numbers in naturally occurring data. Government accounting and statistics are similar in nature to financial accounting. In the European Union (EU), there is pressure to comply with the Stability and Growth Pact criteria. Therefore, like firms, governments might try to make their economic situation seem better. In this paper, we use a Benford test to investigate the quality of macroeconomic data relevant to the deficit criteria reported to Eurostat by the EU member states. We find that the data reported by Greece shows the greatest deviation from Benford's law among all euro states.", acknowledgement = ack-nhfb, fjournal = "German Economic Review", keywords = "auditing; Benford's law; fraud detection; government statistics", onlinedate = "28 April 2011", } @Article{Ravisankar:2011:DFS, author = "P. Ravisankar and V. Ravi and G. Raghava Rao and I. Bose", title = "Detection of financial statement fraud and feature selection using data mining techniques", journal = j-DEC-SUPP-SYS, volume = "50", number = "2", pages = "491--500", month = jan, year = "2011", CODEN = "DSSYDK", DOI = "https://doi.org/10.1016/j.dss.2010.11.006", ISSN = "0167-9236 (print), 1873-5797 (electronic)", ISSN-L = "0167-9236", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0167923610001879", abstract = "Recently, high profile cases of financial statement fraud have been dominating the news. This paper uses data mining techniques such as Multilayer Feed Forward Neural Network (MLFF), Support Vector Machines (SVM), Genetic Programming (GP), Group Method of Data Handling (GMDH), Logistic Regression (LR), and Probabilistic Neural Network (PNN) to identify companies that resort to financial statement fraud. Each of these techniques is tested on a dataset involving 202 Chinese companies and compared with and without feature selection. {PNN} outperformed all the techniques without feature selection, and {GP} and {PNN} outperformed others with feature selection and with marginally equal accuracies.", acknowledgement = ack-nhfb, fjournal = "Decision Support Systems", keywords = "Benford's Law; Data mining; Feature selection; Financial fraud detection; Neural networks; t-statistic; {GP}; {SVM}", } @Article{Robledo:2011:LZB, author = "Alberto Robledo", title = "Laws of {Zipf} and {Benford}, intermittency, and critical fluctuations", journal = "Chinese Science Bulletin", volume = "56", number = "34", publisher = "SP Science China Press", pages = "3643--3648", year = "2011", DOI = "https://doi.org/10.1007/s11434-011-4827-y", ISSN = "1001-6538 (print), 1861-9541 (electronic)", ISSN-L = "1001-6538", bibdate = "Wed Aug 12 09:46:47 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11434-011-4827-y", acknowledgement = ack-nhfb, keywords = "Benford's law; critical clusters; generalized statistical mechanics; tangent bifurcation; Zipf's law", } @Article{Romano:2011:NLR, author = "Paul K. Romano and Harry McLaughlin", title = "On Non-Linear Recursive Sequences and {Benford's Law}", journal = j-FIB-QUART, volume = "49", number = "2", pages = "134--138", month = may, year = "2011", CODEN = "FIBQAU", ISSN = "0015-0517", ISSN-L = "0015-0517", MRclass = "11K31 (11B37)", MRnumber = "2801800", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "http://www.fq.math.ca/49-2.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Abstracts/49-2/romano.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Ross:2011:BLG, author = "Kenneth A. Ross", title = "{Benford's Law}, a Growth Industry", journal = j-AMER-MATH-MONTHLY, volume = "118", number = "7", pages = "571--583", month = aug # "\slash " # sep, year = "2011", CODEN = "AMMYAE", DOI = "https://doi.org/10.4169/amer.math.monthly.118.07.571", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "62A99 (60F99)", MRnumber = "2826449 (2012g:62014)", bibdate = "Mon Jan 30 08:58:20 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/10.4169/amermathmont.118.issue-7; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/10.4169; http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.07.571.pdf; http://www.maa.org/history/presidents/ross.html", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", remark = "The author was President of the Mathematical Association of America (1995--1996).", } @Article{Sambridge:2011:BLF, author = "Malcolm Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and Pierre Arroucau", title = "{Benford}'s law of first digits: from mathematical curiosity to change detector", journal = j-ASIA-PAC-MATH-NEWSL, volume = "1", number = "4", pages = "1--6", month = oct, year = "2011", ISSN = "2010-3484", MRclass = "62A99", MRnumber = "2894867", MRreviewer = "Vladimir S. Anashin", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Asia Pac. Math. Newsl.", fjournal = "Asia Pacific Mathematics Newsletter", } @Article{SenDe:2011:BLD, author = "Aditi {Sen De} and Ujjwal Sen", title = "{Benford}'s law detects quantum phase transitions similarly as earthquakes", journal = j-EUROPHYS-LETT, volume = "95", number = "5", pages = "50008", month = sep, year = "2011", CODEN = "EULEEJ", DOI = "https://doi.org/10.1209/0295-5075/95/50008", ISSN = "0295-5075 (print), 1286-4854 (electronic)", ISSN-L = "0295-5075", bibdate = "Mon Nov 14 17:52:09 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1103.5398", abstract = "A century ago, it was predicted that the first significant digit appearing in a data would be nonuniformly distributed, with the number one appearing with the highest frequency. This law goes by the name of Benford's law. It holds for data ranging from infectious disease cases to national greenhouse gas emissions. Quantum phase transitions are cooperative phenomena where qualitative changes occur in many-body systems at zero temperature. We show that the century-old Benford's law can detect quantum phase transitions, much like it detects earthquakes. Therefore, being certainly of very different physical origins, seismic activity and quantum cooperative phenomena may be detected by similar methods. The result has immediate implications in precise measurements in experiments in general, and for realizable quantum computers in particular. It shows that estimation of the first significant digit of measured physical observables is enough to detect the presence of quantum phase transitions in macroscopic systems.", acknowledgement = ack-nhfb, archiveprefix = "arXiv", eprint = "1103.5398", fjournal = "Europhysics Letters", journal-URL = "http://iopscience.iop.org/0295-5075", primaryclass = "quant-ph", } @Misc{Shi:2011:ESP, author = "Yun-Quing Shi and DongDong Fu", title = "Apparatus and method for a generalized {Benford's Law} analysis of {DCT} and {JPEG} coefficients", howpublished = "US Patent 7940989.", day = "10", month = may, year = "2011", bibdate = "Mon Feb 18 18:49:54 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "US Patent Application 11/772,636 filed 2 July 2007. US Patent issued 10 May 2011.", URL = "http://www.google.com/patents/US7940989", acknowledgement = ack-nhfb, } @Article{Shikano:2011:WDD, author = "S. Shikano and V. Mack", title = "When does 2nd Digit {Benford's Law}-Test signal an election fraud? {Facts} or misleading test results", journal = "Jahrb{\"u}cher f{\"u}r National{\"o}konomie und Statistik", volume = "231", number = "5--6", pages = "719--732", month = "????", year = "2011", DOI = "????", bibdate = "Mon Feb 18 18:51:04 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://benfordonline.net/fullreference/1015", acknowledgement = ack-nhfb, } @Article{Tang:2011:ESP, author = "Lian Tang and Da Hui Wang", title = "An explanation of the shift parameter {$ \rho $} in the {Zipf--Mandelbrot} law", journal = "Beijing Shifan Daxue Xuebao", volume = "47", number = "1", pages = "97--100", year = "2011", CODEN = "BSDKDH", ISSN = "0476-0301", ISSN-L = "0476-0301", MRclass = "94A17", MRnumber = "2807603", bibdate = "Sat Nov 12 09:13:23 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Beijing Shifan Daxue Xuebao. Ziran Kexue Ban. Journal of Beijing Normal University (Natural Science)", } @Article{Urzua:2011:TZL, author = "Carlos M. Urz{\'u}a", title = "Testing for {Zipf}'s law: a common pitfall", journal = j-ECONOM-LETT, volume = "112", number = "3", pages = "254--255", day = "1", month = sep, year = "2011", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/j.econlet.2011.05.049", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "62F03 (91B82)", MRnumber = "2848721", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165176511002266", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", keywords = "Zipf's Law", } @Article{Vallee:2011:BMF, author = "Robert Vall{\'e}e", title = "{Beno{\^\i}t Mandelbrot} --- further notes", journal = "Kybernetes", volume = "40", number = "9--10", pages = "??--??", month = "????", year = "2011", CODEN = "KBNTA3", ISSN = "0368-492X (print), 1758-7883 (electronic)", ISSN-L = "0368-492X", bibdate = "Fri Nov 25 07:38:10 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=9/10&articleid=17003220", acknowledgement = ack-nhfb, } @Misc{Wang:2011:BLD, author = "Jialan Wang", title = "{Benford's Law} and the Decreasing Reliability of Accounting Data for {US} Firms. {Studies} in Everyday Life: Investigations and experiments on food, ethics, economics, and the environment", howpublished = "Blog posting", day = "9", month = oct, year = "2011", bibdate = "Mon Feb 18 18:54:40 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://econerdfood.blogspot.com/2011/10/benfords-law-and-decreasing-reliability.html", acknowledgement = ack-nhfb, } @Misc{Wang:2011:BLR, author = "Jialan Wang", title = "{Benford}'s law: a revised analysis", howpublished = "Blog posting", day = "24", month = oct, year = "2011", bibdate = "Tue Feb 19 10:33:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://econerdfood.blogspot.com/2011/10/benfords-law-revised-analysis.html", acknowledgement = ack-nhfb, } @Misc{Weisstein:2011:BL, author = "Eric W. Weisstein", title = "{Benford's Law}", howpublished = "MathWorld---A Wolfram Web Resource", year = "2011", bibdate = "Tue Nov 15 08:40:40 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://mathworld.wolfram.com/BenfordsLaw.html", acknowledgement = ack-nhfb, } @InProceedings{Winter:2011:DFU, author = "Christian Winter and Markus Schneider and York Yannikos", editor = "Gilbert Peterson and Sujeet Shenoi", booktitle = "{Advances in Digital Forensics VII: 7th IFIP WG 11.9 International Conference on Digital Forensics, Orlando, FL, USA, January 31-- February 2, 2011, Revised Selected Papers}", title = "Detecting Fraud Using Modified {Benford} Analysis", publisher = pub-SV, address = pub-SV:adr, bookpages = "xviii + 285", year = "2011", DOI = "https://doi.org/10.1007/978-3-642-24212-0_10", ISBN = "3-642-24211-1 (paperback), 3-642-24212-X (e-book)", ISBN-13 = "978-3-642-24211-3 (paperback), 978-3-642-24212-0 (e-book)", LCCN = "HV8079.C65 I357 2011", bibdate = "Wed Aug 12 09:41:22 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", price = "US\$", URL = "http://link.springer.com/chapter/10.1007/978-3-642-24212-0_10/", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-24212-0", } @Article{Xu:2011:PCG, author = "B. Xu and J. Wang and G. Liu and Y. Dai", title = "Photorealistic computer graphics forensics based on leading digit law", journal = "Journal of Electronics (China)", volume = "28", number = "1", pages = "95--100", month = "????", year = "2011", DOI = "https://doi.org/10.1007/s11767-011-0474-3", bibdate = "Mon Feb 18 18:55:38 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11767-011-0474-3", acknowledgement = ack-nhfb, } @Article{Zgela:2011:ATC, author = "Mario {\v{Z}}gela and Jasminka Dob{\v{s}}a", title = "Analysis of Top 500 {Central and East European} Companies Net Income Using {Benford's Law}", journal = j-J-INFO-ORG-SCI, volume = "35", number = "2", pages = "215--228", month = dec, year = "2011", ISSN = "1846-3312 (print), 1846-9418 (electronic)", ISSN-L = "1846-3312", bibdate = "Mon Feb 18 18:57:10 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Prosinac 2011 conference.", URL = "http://hrcak.srce.hr/file/111658; http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=111658", acknowledgement = ack-nhfb, fjournal = "Journal of Informational and Organizational Sciences", journal-URL = "http://jios.foi.hr/index.php/jios/index", } @Article{Zhang:2011:ETO, author = "Qunzhi Zhang and Didier Sornette", title = "Empirical test of the origin of {Zipf}'s law in growing social networks", journal = j-PHYSICA-A, volume = "390", number = "23--24", pages = "4124--4130", day = "1", month = nov, year = "2011", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2011.06.063", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437111005103", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Zorzi:2011:BL, author = "Alberto Zorzi", title = "95.22 {Benford}'s law and $ \pi $", journal = j-MATH-GAZ, volume = "95", number = "533", pages = "264--266", month = jul, year = "2011", CODEN = "MAGAAS", DOI = "https://doi.org/10.1017/S0025557200002990", ISSN = "0025-5572 (print), 2056-6328 (electronic)", ISSN-L = "0025-5572", bibdate = "Tue May 5 12:04:16 MDT 2015", bibsource = "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=95&issueId=533; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib", acknowledgement = ack-nhfb, ajournal = "Math. Gaz.", fjournal = "The Mathematical Gazette", journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620", remark = "The journal Web site lacks a search feature, and the archives only cover up to 2007. JSTOR has only issues up to 2007.", } @Article{Abrantes-Metz:2012:LM, author = "Rosa M. Abrantes-Metz and Michael Kraten and Albert D. Metz and Gim S. Seow", title = "Libor manipulation?", journal = "Journal of Banking \& Finance", volume = "36", number = "1", pages = "136--150", year = "2012", DOI = "https://doi.org/10.1016/j.jbankfin.2011.06.014", ISSN = "0378-4266 (print), 1872-6372 (electronic)", ISSN-L = "0378-4266", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378426611002032", abstract = "On May 29, 2008 the Wall Street Journal published an article alleging that several global banks were reporting Libor quotes significantly lower than those implied by prevailing credit default swap (CDS) spreads. While acknowledging that the analysis doesn t prove that banks are lying or manipulating Libor, it nevertheless conjectures that these banks may have been low-balling their borrowing rates to avoid looking desperate for cash. In this paper we compare Libor with other short-term borrowing rates, analyze individual bank quotes, and compare these individual quotes to {CDS} spreads and market capitalization data during three periods: 1/1/07 8/8/07 (Period 1), 8/9/07 4/16/08 (Period 2), and 4/17/08 5/30/08 (Period 3). We find some anomalous individual quotes, but the evidence is inconsistent with a material manipulation of the {US} dollar 1-month Libor rate.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Bid-rigging; Collusion; Conspiracies; Credit default swap spreads; Libor; Manipulations; Price-fixing", } @Article{Anonymous:2012:SB, author = "Anonymous", title = "The scam busters", journal = j-ECONOMIST, volume = "??", number = "??", pages = "??--??", day = "15", month = dec, year = "2012", CODEN = "EONOEH", ISSN = "0013-0613 (print), 1476-8860 (electronic)", ISSN-L = "0013-0613", bibdate = "Mon Feb 18 19:01:02 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters", acknowledgement = ack-nhfb, fjournal = "The Economist", keywords = "Benford's Law", } @TechReport{Balanzario:2012:BLM, author = "E. P. Balanzario", title = "{Benford}'s law for mixtures", type = "Preprint", institution = "????", address = "????", month = "????", year = "2012", bibdate = "Mon Feb 18 19:02:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Bharath:2012:BLT, author = "H. M. Bharath", title = "{Benford's Law}: A theoretical explanation for base $2$", journal = "arXiv.org", day = "24", month = nov, year = "2012", bibdate = "Tue Jan 26 09:55:55 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2012arXiv1211.7008B", acknowledgement = ack-nhfb, eprint = "1211.7008", keywords = "Statistics - Other Statistics", primaryclass = "stat.OT", } @Article{Bharati:2012:CCO, author = "Rakesh Bharati and Susan J. Crain and Vincent Kaminski", title = "Clustering in crude oil prices and the target pricing zone hypothesis", journal = "Energy Economics", volume = "34", number = "4", pages = "1115--1123", year = "2012", DOI = "https://doi.org/10.1016/j.eneco.2011.09.009", ISSN = "0140-9883 (print), 1873-6181 (electronic)", ISSN-L = "0140-9883", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0140988311002258", abstract = "This paper studies the target pricing zone (TPZ) hypothesis for crude oil by examining price clustering in the dollar digit. It is hypothesized that price clustering occurs within an established {TPZ} if {OPEC} is able to defend the upper and lower bounds through output changes. The results show that prices strongly cluster around the dollar digit value of 9 within the {TPZ} sub-periods, but not outside the sub-periods. Furthermore, the degree of clustering declines when production capacity utilization is high and when production significantly exceeds quotas, consistent with OPEC's inability to defend the zone. Nine-centered clustering also results in lower contemporaneous and next-day volatility. These results support the target pricing zone hypothesis of crude oil.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Clustering; Crude oil; Target pricing zone; {OPEC}", } @Article{Chen:2012:MRB, author = "Yanguang Chen", title = "The mathematical relationship between {Zipf}'s law and the hierarchical scaling law", journal = j-PHYSICA-A, volume = "391", number = "11", pages = "3285--3299", day = "1", month = jun, year = "2012", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2011.12.031", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437111009678", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Chen:2012:ZLF, author = "Yanguang Chen", title = "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "45", number = "1", pages = "63--73", day = "15", month = jan, year = "2012", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2011.10.001", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0960077911001901", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", keywords = "Zipf's Law", } @Article{Chen:2012:ZLH, author = "Yanguang Chen", title = "{Zipf}'s law, hierarchical structure, and cards-shuffling model for urban development", journal = j-DISCRETE-DYN-NAT-SOC, pages = "480196", year = "2012", CODEN = "DDNSFA", DOI = "https://doi.org/10.1155/2012/480196", ISSN = "1026-0226 (print), 1607-887X (electronic)", ISSN-L = "1026-0226", MRclass = "91D10", MRnumber = "2914043", MRreviewer = "Sandra L. Arlinghaus", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Discrete Dyn. Nat. Soc.", fjournal = "Discrete Dynamics in Nature and Society. An International Multidisciplinary Research and Review Journal", pagecount = "21", } @Article{Clippe:2012:BLT, author = "Paulette Clippe and Marcel Ausloos", title = "{Benford's Law} and {Theil} transform of financial data", journal = j-PHYSICA-A, volume = "391", number = "24", pages = "6556--6567", day = "15", month = dec, year = "2012", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2012.07.063", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437112007546", abstract = "Among econophysics investigations, studies of religious groups have been of interest. On the one hand, the present paper concerns the Antoinist community financial reports a community which appeared at the end of the 19-th century in Belgium. Several growth decay regimes have been previously found over different time spans. However, there is common suspicion about sect finances. In that spirit, the Antoinist community yearly financial reports, income and expenses, are hereby examined through the so-called Benford's Law. The latter is often used as a test about possible accounting wrongdoings. On the other hand, Benford's Law is known to be invariant under scale and base transformation. Therefore, as a further test, of both such data and the use of Benford's Law, the yearly financial reports are nonlinearly remapped through a sort of Theil transformation, i.e. based on a log-transformation. The resulting data is again analyzed along the Benford's Law scheme. Bizarre, puzzling, features are seen. However, it is emphasized that such a non-linear transformation can shift the argument toward a more objective conclusion. In an appendix, some brief discussion is made on why the original Theil mapping should not be used. In a second appendix, an imperfect Benford's Law-like form better suited for anomalous distributions is presented.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Benford's Laws; Expenses; Income; Religious community; Theil map; Time series", } @Article{Cristelli:2012:TMT, author = "Matthieu Cristelli and Michael Batty and Luciano Pietronero", title = "There is More than a Power Law in {Zipf}", journal = j-SCI-REP, volume = "2", number = "??", pages = "1--7", month = nov, year = "2012", CODEN = "SRCEC3", DOI = "https://doi.org/10.1038/srep00812", ISSN = "2045-2322", ISSN-L = "2045-2322", bibdate = "Tue Feb 26 07:32:11 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html", accepted = "28 August 2012", acknowledgement = ack-nhfb, articleno = "812", fjournal = "Scientific Reports", journal-URL = "http://www.nature.com/srep/", onlinedate = "08 November 2012", received = "15 August 2012", } @Article{Diekmann:2012:MUB, author = "Andreas Diekmann", title = "Making Use of ``{Benford's Law}'' for the Randomized Response Technique", journal = j-SOC-METH-RES, volume = "41", number = "2", pages = "325--334", month = may, year = "2012", DOI = "https://doi.org/10.1177/0049124112452525", ISSN = "0049-1241 (print), 1552-8294 (electronic)", ISSN-L = "0049-1241", MRnumber = "3190709", bibdate = "Mon Feb 18 19:03:24 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://smr.sagepub.com/content/41/2/325; http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf", acknowledgement = ack-nhfb, fjournal = "Sociological Methods and Research", } @Book{Dorrell:2012:FFB, author = "Darrell D. Dorrell and Gregory A. Gadawski", title = "Financial forensics body of knowledge", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xvi + 541", year = "2012", DOI = "https://doi.org/10.1002/9781119200734", ISBN = "0-470-88085-6 (hardcover), 1-118-21897-3 (e-book), 1-118-21896-5 (e-book), 1-118-21898-1 (e-book), 1-119-20073-3 (e-book)", ISBN-13 = "978-0-470-88085-2 (hardcover), 978-1-118-21897-6 (e-book), 978-1-118-21896-9 (e-book), 978-1-118-21898-3 (e-book), 978-1-119-20073-4 (e-book)", LCCN = "HV6769 .D675 2012", bibdate = "Thu Oct 13 06:54:34 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = "Wiley finance", URL = "http://catalogimages.wiley.com/images/db/jimages/9780470880852.jpg; http://site.ebrary.com/id/10534000", abstract = "The definitive, must-have guide for the forensic accounting professionalA comprehensive and practical overview of civil and criminal forensic accounting methodology, Forensic Accounting Body of Knowledge defines the profession of forensic accounting, capturing and codifying methods that define the body of knowledge. Filled with practical forensic accounting tips, tools and techniques, the book contains contributions from US and global professionals spanning all aspects of the financial community, including the law enforcement, investment, investigative, and regulatory arenas. Provides immediately useful tools Includes more than 200 tips and techniques Globally relevant content, with cutting-edge counterterrorism forensic accounting methodology Supported by a continually updated Internet-based software application Offers contributions from twenty financial experts in law enforcement, investigative, and regulatory fields Accompanied by a frequently updated Internet-based software application, Forensic Accounting Body of Knowledge will refine financial information users' approaches, techniques, and methods with useful tools and tips that reflect the continually growing body of forensic accounting knowledge.", acknowledgement = ack-nhfb, subject = "Commercial crimes; Forensic accounting; Fraud investigation", tableofcontents = "Foundational phase \\ Interpersonal phase \\ Data collection and analysis phase: part I \\ Data collection and analysis phase: part II \\ Data collection and analysis phase: part III \\ Trial and reports phase \\ Counterterrorism: conventional tools for unconventional warfare \\ Civil versus criminal law comparison \\ Appendix. Forensic inventory: forensic tools, techniques, methods, and methodologies", } @Article{Egghe:2012:AGL, author = "Leo Egghe and Raf Guns", title = "Applications of the generalized law of {Benford} to informetric data", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "63", number = "8", pages = "1662--1665", month = aug, year = "2012", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.22690", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Mon Feb 18 19:05:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract", abstract = "In a previous work (Egghe, 2011), the first author showed that Benford's law (describing the logarithmic distribution of the numbers 1, 2, \ldots{}, 9 as first digits of data in decimal form) is related to the classical law of Zipf with exponent 1. The work of Campanario and Coslado (2011), however, shows that Benford's law does not always fit practical data in a statistical sense. In this article, we use a generalization of Benford's law related to the general law of Zipf with exponent $ \beta > 0 $. Using data from Campanario and Coslado, we apply nonlinear least squares to determine the optimal $ \beta $ and show that this generalized law of Benford fits the data better than the classical law of Benford.", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", } @Article{Egghe:2012:BCA, author = "Leo Egghe and Raf Guns", title = "Brief Communication: Applications of the generalized law of {Benford} to informetric data", journal = j-J-AM-SOC-INF-SCI-TECHNOL, volume = "63", number = "8", pages = "1662--1665", month = aug, year = "2012", CODEN = "JASIEF", DOI = "https://doi.org/10.1002/asi.22690", ISSN = "1532-2882 (print), 1532-2890 (electronic)", ISSN-L = "1532-2882", bibdate = "Fri Sep 11 10:43:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jasist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Society for Information Science and Technology: JASIST", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890", onlinedate = "26 Jun 2012", } @Article{Egghe:2012:TPS, author = "Leo Egghe and Ronald Rousseau", title = "Theory and practice of the shifted {Lotka} function", journal = j-SCIENTOMETRICS, volume = "91", number = "1", pages = "295--301", month = apr, year = "2012", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-011-0539-y", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Thu Sep 3 07:35:27 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-011-0539-y", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Eliahou:2012:MDP, author = "Shalom Eliahou and Bruno Mass{\'e} and Dominique Schneider", title = "On the mantissa distribution of powers of natural and prime numbers", journal = "Acta Mathematica Hungarica", volume = "139", number = "1--2", pages = "1--5", month = apr, year = "2013", DOI = "https://doi.org/10.1007/s10474-012-0244-1", ISSN = "0001-5954, 0236-5294, 1588-2632", ISSN-L = "0001-5954", bibdate = "Mon Feb 18 19:06:54 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s10474-012-0244-1", acknowledgement = ack-nhfb, } @Article{Eliazar:2012:PLC, author = "Iddo I. Eliazar and Morrel H. Cohen", title = "Power-law connections: From {Zipf} to {Heaps} and beyond", journal = j-INFO-PROC-MAN, volume = "23", number = "3", pages = "56--74", day = "1", month = may, year = "2012", CODEN = "IPMADK", DOI = "https://doi.org/10.1016/j.aop.2013.01.013", ISSN = "0306-4573 (print), 1873-5371 (electronic)", ISSN-L = "0306-4573", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0003491613000171", acknowledgement = ack-nhfb, fjournal = "Information Processing and Management", journal-URL = "http://www.sciencedirect.com/science/journal/03064573", keywords = "Zipf's Law", } @Article{Friar:2012:GSB, author = "James L. Friar and Terrance Goldman and Juan P{\'e}rez-Mercader", title = "Genome Sizes and the {Benford} Distribution", journal = j-PLOS-ONE, volume = "7", number = "5", pages = "e36624:1--e36624:9", month = may, year = "2012", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0036624", ISSN = "1932-6203", ISSN-L = "1932-6203", bibdate = "Mon Feb 18 19:08:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0036624", abstract = "Data on the number of Open Reading Frames (ORFs) coded by genomes from the 3 domains of Life show the presence of some notable general features. These include essential differences between the Prokaryotes and Eukaryotes, with the number of ORFs growing linearly with total genome size for the former, but only logarithmically for the latter.", accepted = "11 April 2012", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", onlinedate = "18 May 2012", received = "7 April 2011", } @Article{Gambini:2012:PDD, author = "Alessandro Gambini and Giovanni Mingari Scarpello and Daniele Ritelli", title = "Probability of digits by dividing random numbers: A $ \psi $ and $ \zeta $ functions approach", journal = j-EXPO-MATH, volume = "30", number = "3", pages = "223--238", month = "????", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1016/j.exmath.2012.03.001", ISSN = "0723-0869 (print), 1878-0792 (electronic)", ISSN-L = "0723-0869", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0723086912000230", abstract = "This paper begins with the statistics of the decimal digits of $ n / d $ with $ (n, d) \in N^2 $ randomly chosen. Starting with a statement by Ces{\`a}ro on probabilistic number theory, see Ces{\`a}ro (1885) [3,4], we evaluate, through the Euler function, an integral appearing there. Furthermore the probabilistic statement itself is proved, using a different approach: in any case the probability of a given digit $r$ to be the first decimal digit after dividing a couple of random integers is $ p_r = 1 / 20 + 1 / 2 \{ \psi (r / 10 + 11 / 10) - \psi (r / 10 10 + 1) \} $. The theorem is then generalized to real numbers (Theorem 1, holding a proof of both $ n / d$ results) and to the $ \alpha $ th power of the ratio of integers (Theorem 2), via an elementary approach involving the function and the Hurwitz function. The article provides historic remarks, numerical examples, and original theoretical contributions: also it complements the recent renewed interest in {Benford's Law} among number theorists.", acknowledgement = ack-nhfb, ajournal = "Expo. Math.", fjournal = "Expositiones Mathematicae", hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) - psi(r/10 + 1)))", hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r, p(r)); println {""}", journal-URL = "http://www.sciencedirect.com/science/journal/07230869", keywords = "Benford's Law; Elementary probability; Euler $\psi$ function; Euler function; Hurwitz $\zeta$ function; Hurwitz function", remark = "This paper proves formulas for the probability of first-digit occurrences in the ratios of random integers, and compares the predictions with the somewhat different ones from Benford's Law. Their work simplifies a result of Ces{\`a}ro (1885), and predicts that the probability of the first quotient digit being $r$ is given by $ p(r) = 1 / 20 + (1 / 2)*(\psi ((r + 11) / 10) - \psi (r / 10 + 1)) $. That predicts these pairs of $ (r, p(r)) $: $ (0, 0.12673) $, $ (1, 0.11736) $, $ (2, 0.10992) $, $ (3, 0.10390) $, $ (4, 0.09894) $, $ (5, 0.09478) $, $ (6, 0.09125) $, $ (7, 0.08822) $, $ (8, 0.08560) $, $ (9, 0.08330) $. Those values may be compared with the Benford's Law prediction for the second digit (possibly zero) of $ (0, 0.120) $, $ (1, 0.114) $, $ (2, 0.109) $, $ (3, 0.104) $, $ (4, 0.100) $, $ (5, 0.097) $, $ (6, 0.093) $, $ (7, 0.090) $, $ (8, 0.088) $, and $ (9, 0.085) $.", } @Article{Geyer:2012:ABL, author = "A. Geyer and J. Mart{\'\i}", title = "Applying {Benford}'s law to volcanology", journal = "Geology", volume = "40", number = "4", pages = "327--330", month = apr, year = "2012", DOI = "https://doi.org/10.1130/G32787.1", bibdate = "Mon Feb 18 19:11:36 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://geology.gsapubs.org/content/40/4/327", acknowledgement = ack-nhfb, } @InCollection{Gorroochurn:2012:BPB, author = "Prakash Gorroochurn", title = "{Benford} and the Peculiar Behavior of the First Significant Digit (1938)", crossref = "Gorroochurn:2012:CPP", chapter = "27", pages = "233--239", year = "2012", DOI = "https://doi.org/10.1002/9781118314340.ch27", bibdate = "Sat Feb 23 17:26:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "(Benford) distribution; a distribution of distributions; and Benford's law; Benford and the peculiar behavior of the first significant digit (1938); First 100 Fibonacci Numbers; first-digit law or Benford's law; scale invariance; the leading digit and its behavior", } @InProceedings{Guettler:2012:BGQ, author = "S. Guettler and F. Thiemann and R. A. E. Mueller", editor = "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K. Hildebrand and B. Theuvsen", booktitle = "{Informationstechnologie f{\"u}r eine nachhaltige Landbewirtschaftung. Fokus Forstwirtschaft. Referate der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz 2012, Freising}. ({German}) [Information technology for sustainable land management. Focus on forestry. Papers of the 32nd GIL Annual Conference 29, February--1 March 2012, Freising]", title = "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r statistische Reihen angewendet auf Handelsdaten f{\"u}r Agrarprodukte}. ({German}) [{Benford's Law}: a quality test applied for statistical series on trade data for agricultural products]", volume = "194", publisher = "Gesellschaft f{\"u}r Informatik.", address = "Bonn, Germany", bookpages = "334 (est.)", pages = "111--114", year = "2012", ISBN = "3-88579-288-5", ISBN-13 = "978-3-88579-288-8", ISSN = "1617-5468", LCCN = "????", bibdate = "Tue Feb 19 05:44:08 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes in Informatics", URL = "http://www.gil-net.de/Publikationen/24_111.pdf", acknowledgement = ack-nhfb, language = "German", } @Article{Hein:2012:SFF, author = "J. Hein and R. Zobrist and C. Konrad and G. Schuepfer", title = "Scientific fraud in 20 falsified anesthesia papers", journal = "{Der Anaesthesist}", volume = "61", number = "6", pages = "543--549", month = jun, year = "2012", CODEN = "ANATAE", DOI = "https://doi.org/10.1007/s00101-012-2029-x", ISSN = "0003-2417 (print), 1432-055X (electronic)", ISSN-L = "0003-2417", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s00101-012-2029-x", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/101", keywords = "Benford's Law", } @Article{Henselmann:2012:ABL, author = "Klaus Henselmann and Elisabeth Scherr and Dominik Ditter", title = "Applying {Benford's Law} to individual financial reports: An empirical investigation on the basis of {SEC XBRL} filings", journal = "Working Papers in Accounting Valuation Auditing", volume = "2012-1", pages = "1--23", year = "2012", bibdate = "Thu Oct 13 07:14:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://hdl.handle.net/10419/88418; http://www.econstor.eu/bitstream/10419/88418/1/773918388.pdf", acknowledgement = ack-nhfb, } @MastersThesis{Iudica:2012:BLM, author = "Federico Iudica", title = "{Benford's Law}: Mathematical Properties and Forensic Accounting Applications", type = "{Master}'s Thesis", school = "Facolt{\`a} di Impresa e Management, Cattedra di Matematica, Luiss Guido Carli University", address = "Rome, Italy", pages = "iv + 56", year = "2012", bibdate = "Tue Feb 19 05:54:59 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf", acknowledgement = ack-nhfb, advisor = "Marco Dall'Aglio", } @Article{Janvresse:2012:AAU, author = "{\'E}lise Janvresse and Thierry {De La Rue}", title = "Averaging along Uniform Random Integers", journal = "Uniform Distribution Theory", volume = "7", number = "2", pages = "35--60", month = "????", year = "2012", DOI = "????", ISSN = "1336-913X", ISSN-L = "1336-913X", bibdate = "Tue Feb 19 05:56:13 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf", acknowledgement = ack-nhfb, journal-URL = "http://www.boku.ac.at/MATH/udt/", keywords = "Benford's Law", } @PhdThesis{Janvresse:2012:QCP, author = "{\'E}lise Janvresse", title = "Quelques contributions aux probabilit{\'e}s et {\`a} la th{\'e}orie ergodique. ({French}) [Some contributions to probability theory and ergodic theory]", type = "Document de synth{\`e}se pr{\'e}sent{\'e} pour l'{Habilitation {\`a} Diriger des Recherches}", school = "l'Universit{\'e} de Rouen", address = "Rouen, France", pages = "67", day = "17", month = feb, year = "2012", bibdate = "Tue Feb 19 05:57:33 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf", acknowledgement = ack-nhfb, keywords = "Benford's Law", language = "French", } @InProceedings{Khosravani:2012:TIB, author = "A. Khosravani and C. Rasinariu", title = "Transformation invariance of {Benford} variables and their numerical modeling", crossref = "Niola:2012:RRA", pages = "57--61", year = "2012", bibdate = "Tue Feb 19 06:01:26 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf", acknowledgement = ack-nhfb, } @Article{Kim:2012:BLN, author = "Sangrak Kim", title = "{Benford's Law} in non-equilibrium processes: Droplet collisions case", journal = j-PHYSICA-A, volume = "391", number = "20", pages = "4970--4975", day = "15", month = oct, year = "2012", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2012.05.043", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437112004141", abstract = "Benford's Law is investigated for the simulation results generated from non-equilibrium molecular dynamics. A statistic to measure how closely a set of the numbers follows Benford's Law is defined. The simulation data are from the collisions of two nano droplets with different impact velocities. When a non-equilibrium system returns to its equilibrium state, some physical quantities relevant to the non-equilibrium settings follow Benford's Law more closely. The initial settings for the non-equilibrium state can be interpreted as a data fabrication of its corresponding equilibrium state. A connection with the Shannon entropy for the first digit distribution is also discussed.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Molecular dynamics; Non-equilibrium process", } @Article{Kossovsky:2012:SNR, author = "Alex Ely Kossovsky", title = "Statistician's New Role as a Detective --- Testing Data for Fraud", journal = "Ciencias Econ{\'o}mica", volume = "30", number = "2", pages = "179--200", month = "????", year = "2012", ISSN = "0252-9521 (print), 2215-3489 (electronic)", ISSN-L = "0252-9521", bibdate = "Thu Oct 13 07:24:48 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://revistas.ucr.ac.cr/index.php/economicas/article/view/8015/7634", acknowledgement = ack-nhfb, journal-URL = "http://revistas.ucr.ac.cr/index.php/economicas/index", keywords = "Benford's Law", } @Article{Li:2012:DTR, author = "Xiang Hua Li and Yu Qian Zhao and Miao Liao and Frank Y. Shih and Yun Q. Shi", title = "Detection of tampered region for {JPEG} images by using mode-based first digit features", journal = j-EURASIP-J-ADV-SIGNAL-PROCESS, volume = "2012", number = "1", pages = "190:1--190:??", month = aug, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1186/1687-6180-2012-190", ISSN = "1687-6172 (print), 1687-6180 (electronic)", ISSN-L = "1687-6172", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1186/1687-6180-2012-190", acknowledgement = ack-nhfb, fjournal = "EURASIP Journal on Advances in Signal Processing", journal-URL = "http://www.asp.eurasipjournals.com/; http://asp.eurasipjournals.springeropen.com/", keywords = "Benford's Law", } @Article{LimKaiJie:2012:CES, author = "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan", title = "A Critical Evaluation of the Significance of Round Numbers in {European} Equity Markets in Light of the Predictions from {Benford's Law}", journal = "International Research Journal of Finance and Economics", volume = "95", number = "??", pages = "196--210", day = "28", month = aug, year = "2012", DOI = "????", ISSN = "1450-2887", bibdate = "Tue Feb 19 06:04:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://mpra.ub.uni-muenchen.de/40960/; http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf", acknowledgement = ack-nhfb, } @Misc{Marcus:2012:UFA, author = "Adam Marcus", title = "Update on {Fujii}: Anesthesia journal finds overwhelming statistical evidence of data fabrication", howpublished = "Web site article.", day = "8", month = mar, year = "2012", bibdate = "Wed Jun 20 14:33:00 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://retractionwatch.com/2012/03/08/update-on-fujii-anesthesia-journal-finds-overwhelming-statistical-evidence-of-data-fabrication/", acknowledgement = ack-nhfb, } @Article{Masse:2012:RNS, author = "Bruno Mass{\'e} and Dominique Schneider", title = "Random number sequences and the first digit phenomenon", journal = j-ELECTRON-J-PROBAB, volume = "17", pages = "86:1--86:17", year = "2012", CODEN = "????", DOI = "https://doi.org/10.1214/EJP.v17-1900", ISSN = "1083-6489", ISSN-L = "1083-6489", MRclass = "60B10 (11A63 11B05)", MRnumber = "2988401", MRreviewer = "Rita Giuliano Antonini", bibdate = "Mon Sep 1 19:06:47 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ejp.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://ejp.ejpecp.org/article/view/1900", abstract = "The sequences of mantissa of positive integers and of prime numbers are known not to be distributed as Benford's law in the sense of the natural density. We show that we can correct this defect by selecting the integers or the primes by means of an adequate random process and we investigate the rate of convergence. Our main tools are uniform bounds for deterministic and random trigonometric polynomials. We then adapt the random process to prove the same result for logarithms and iterated logarithms of integers. Finally we show that, in many cases, the mantissa law of the $n$ th randomly selected term converges weakly to the Benford's law.", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", keywords = "Benford's law; density; mantissa; weak convergence", } @InProceedings{Mebane:2012:SDT, author = "Walter R. {Mebane, Jr.}", editor = "????", booktitle = "{Proceedings of the 2012 Annual Meeting of the Midwest Political Science Association, Chicago, IL, April 11--14, 2012}", title = "Second-Digit Tests for Voters' Election Strategies and Election Fraud", publisher = "????", address = "????", pages = "??--??", year = "2012", DOI = "", ISBN = "", ISBN-13 = "", LCCN = "", bibdate = "Sat Sep 10 14:22:55 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Mir:2012:LDD, author = "T. A. Mir", title = "The leading digit distribution of the worldwide illicit financial flows", journal = "ArXiv e-prints", year = "2012", bibdate = "Tue Feb 19 06:07:33 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1201.3432", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Mir:2012:LLD, author = "Tariq Ahmad Mir", title = "The law of the leading digits and the world religions", journal = j-PHYSICA-A, volume = "391", number = "3", pages = "792--798", day = "1", month = feb, year = "2012", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2011.09.001", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; http://www.sciencedirect.com/", URL = "http://www.sciencedirect.com/science/article/pii/S0378437111007175", abstract = "Benford's Law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger ones. We investigate here numerical data on the country-wise adherent distribution of seven major world religions i.e. Christianity, Islam, Buddhism, Hinduism, Sikhism, Judaism and Baha'ism to see if the proportion of the leading digits occurring in the distribution conforms to Benford's Law. We find that the adherent data of all the religions, except Christianity, excellently does conform to Benford's Law. Furthermore, unlike the adherent data on Christianity, the significant digit distribution of the three major Christian denominations i.e., Catholicism, Protestantism and Orthodoxy obeys the law. Thus in spite of their complexity, general laws can be established for the evolution of religious groups.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Adherents; Benford's Law; Religion", } @Article{Nebel:2012:DHG, author = "J.-C. Nebel and S. Pezzulli", title = "Distribution of Human Genes Observes {Zipf's Law}", journal = "Kingston University Research \& Innovation Reports (KURIR)", volume = "8", number = "??", pages = "1--9", month = "????", year = "2012", DOI = "????", ISSN = "1749-5652", ISSN-L = "1749-5652", bibdate = "Tue Feb 19 06:09:05 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf", acknowledgement = ack-nhfb, journal-URL = "http://kurir.kingston.ac.uk/", remark = "Kingston University, London, UK. Year 2012 volume is not yet online on 19 February 2013.", } @Book{Nigrini:2012:BLA, author = "Mark J. (Mark John) Nigrini", title = "{Benford's Law}: Applications for Forensic Accounting, Auditing, and Fraud Detection", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xviii + 330", year = "2012", ISBN = "1-118-15285-9 (hardcover), 1-118-28226-4, 1-118-28284-1, 1-118-28686-3", ISBN-13 = "978-1-118-15285-0 (hardcover), 978-1-118-28226-7, 978-1-118-28284-7, 978-1-118-28686-9", LCCN = "HV6691 .N54 2012", bibdate = "Sun Feb 17 10:03:10 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.scribd.com/doc/86733139/Benford-s-Law-Applications-for-Forensic-Accounting-Auditing-and-Fraud-Detection", acknowledgement = ack-nhfb, tableofcontents = "Foreword / xi \\ Preface / xiii \\ About the Author / xix \\ Chapter 1: Introduction and Mathematical Foundations / 1 \\ Benford's Expected Digit Frequencies / 5 \\ Defining the First and First-Two Digits / 6 \\ Digit Patterns of U.S. Census Data / 8 \\ Logging on to Benford's Law / 10 \\ General Significant Digit Law / 13 \\ Log and Behold, the Census Data / 13 \\ Love at First Sight / 15 \\ Mantissa Test and Census Data / 19 \\ Number of Records and Benford's Law Tests / 20 \\ When Should Data Conform to Benford's Law? / 21 \\ Conclusions / 23 \\ Chapter 2: Theorems, Truisms, and a Little Trivia / 25 \\ Digits of Corporate Payments Data / 26 \\ Digits of Lake Data / 28 \\ Scale Invariance Theorem / 31 \\ Mean Absolute Deviation / 34 \\ Scale Invariance and Census Data / 34 \\ Scale Invariance and Corporate Payments / 35 \\ Scale Invariance and Lake Data / 36 \\ A Level Playing Field Becomes Benford / 38 \\ Multiplication by $1 / x$ / 42 \\ All Distributions Lead to Benford / 43 \\ Getting a Gripf on Benford and Zipf / 46 \\ Conclusions / 50 \\ Chapter 3: More Formulas and Facts, and a Little Fibonacci / 51 \\ Fibonacci Numbers / 51 \\ Lucas Numbers / 53 \\ Back to Square One / 55 \\ $3 n + 1$ Problem / 58 \\ Ultimate Uniform Distribution / 60 \\ Benford Embraces Other Bases / 62 \\ Nigrini's Second Last Theorem / 65 \\ Conclusions / 69 \\ Chapter 4: Primary Benford's Law Tests / 71 \\ Corporate Payments Data / 72 \\ Data Profile / 72 \\ First Come, First Served / 74 \\ Playing Second Fiddle / 75 \\ First-Two Digits Test / 78 \\ Running the Digit Tests in Excel / 80 \\ Running the Digit Tests in Access / 83 \\ Conclusions / 87 \\ Chapter 5: Advanced Benford's Law Tests / 89 \\ Summation Test / 90 \\ Running the Summation Test in Excel / 94 \\ Running the Summation Test in Access / 95 \\ Second-Order Test / 97 \\ An Analysis of Payments Data / 102 \\ An Analysis of Journal Entry Data / 104 \\ An Analysis of Census Data / 107 \\ Running the Second-Order Test in Excel / 108 \\ Excel, Thanks a Million(s) / 110 \\ Scale Invariance and the Second-Order Test / 113 \\ Conclusions / 114 \\ Chapter 6: Associated Benford's Law Tests / 117 \\ Number Duplication Test / 117 \\ An Analysis of Payments Data / 119 \\ An Analysis of Census Data / 121 \\ Running the Number Duplication Test in Excel / 122 \\ Running the Number Duplication Test in Access / 126 \\ Last-Two Digits Test / 129 \\ An Analysis of Payments Data / 130 \\ An Analysis of Census Data / 131 \\ An Analysis of Election Results / 132 \\ Running the Last-Two Digits Test in Excel / 135 \\ Running the Last-Two Digits Test in Access / 136 \\ Distortion Factor Model / 138 \\ Distortion and the Census Data / 145 \\ Conclusions / 146 \\ Chapter 7: Assessing Conformity to Benford's Law / 149 \\ $Z$-Statistic / 150 \\ Chi-Square Test / 153 \\ Kolmogorov--Smirnoff Test / 157 \\ Mean Absolute Deviation Test / 158 \\ The Logarithmic Basis of Benford's Law / 160 \\ Creating a Perfect Synthetic Benford Set / 163 \\ Mantissa Arc Test / 165 \\ Conclusions / 169 \\ Chapter 8: Examples of Fraudulent Data / 171 \\ The Inside Story / 172 \\ The Vendor Who Never Was / 174 \\ Not Paying Attention / 175 \\ Funny Money / 177 \\ The Heart of the Matter / 181 \\ Going the Extra Mile / 182 \\ Laugh All the Way to the Bank / 184 \\ Culture Shock / 187 \\ Having a Bad Hair Day / 189 \\ An Unclean Bill of Health / 191 \\ Turning the Table on Tax Evasion / 193 \\ Conclusions / 196 \\ Chapter 9: Fraudulent Financial Statements, Part I / 199 \\ Number Crunching / 200 \\ Wrong Numbers / 205 \\ A Look at Enron's and AIG's Numbers / 207 \\ Figuring Out the Controllers / 210 \\ Conclusions / 213 \\ Chapter 10: Fraudulent Financial Statements, Part II / 215 \\ Digital Yoga by Absaroka / 216 \\ Can't See the Forest for the Trees / 218 \\ Digit a Little Deeper into Papua New Guinea / 221 \\ The Good, the Bad, and the Ugly / 227 \\ Dig a Little Deeper / 233 \\ There Are More Questions than Answers / 237 \\ Conclusions / 244 \\ Chapter 11: Madoff and Other Ponzi Schemes / 247 \\ The Madoff Claims / 248 \\ Don't Bank on Kaupthing / 249 \\ The Whole Ball of Waxenberg / 252 \\ General Motors Demoted to Private / 253 \\ Chrysler Unable to Dodge Bankruptcy / 255 \\ Discussion of the Claims Results / 258 \\ A Review of the Madoff Returns / 259 \\ Apple, Dell, Berkshire, and Benford / 262 \\ Discussion of the Returns Results / 265 \\ Chapter 12: Earth Science and Income Tax Applications / 267 \\ Still Waters Run Deep / 268 \\ The Lay of the Lake / 274 \\ For a Few Dollars Less / 281 \\ A Clean Bill of Clinton / 286 \\ Conclusions / 290 \\ Chapter 13: Future Directions and Conclusions / 293 \\ My Law / 295 \\ Insights into Number Invention / 300 \\ Lehman's Charitable Gifts / 306 \\ The Bottom Line / 310 \\ Glossary of Selected Terms / 315 \\ References / 323 \\ Index / 327", } @InCollection{Odueke:2012:TFA, author = "Adeola Odueke and George R. S. Weir", editor = "George R. S. Weir and A. Al-Nemrat", booktitle = "Issues in Cybercrime, Security and Digtal Forensics", title = "Triage in Forensic Accounting using {Zipf's Law}", publisher = "University of Strathclyde Publishing", address = "Glasgow, UK", bookpages = "????", pages = "33--43", year = "2012", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Tue Feb 19 06:11:19 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.cis.strath.ac.uk/cis/research/publications/papers/strath_cis_publication_2590.pdf", acknowledgement = ack-nhfb, } @Misc{Regan:2012:BLB, author = "K. W. Regan", title = "{Benford's Law} and Baseball", howpublished = "Web document", day = "29", month = jul, year = "2012", bibdate = "Sat Feb 16 12:48:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://rjlipton.wordpress.com/2012/07/29/benfords-law-and-baseball/", acknowledgement = ack-nhfb, } @Article{Ross:2012:FDS, author = "Kenneth A. Ross", title = "First Digits of Squares and Cubes", journal = j-MATH-MAG, volume = "85", number = "1", pages = "37--43", month = feb, year = "2012", CODEN = "MAMGA8", ISSN = "0025-570X", ISSN-L = "0025-570X", bibdate = "Tue Feb 19 06:14:55 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.maa.org/history/presidents/ross.html", acknowledgement = ack-nhfb, fjournal = "Mathematics Magazine", journal-URL = "http://www.maa.org/pubs/mathmag.html", keywords = "Benford's Law", remark = "The author was President of the Mathematical Association of America (1995--1996).", } @Article{Schupfer:2012:FWG, author = "G. Sch{\"u}pfer and J. Hein and M. Casutt and L. Steiner and C. Konrad", title = "{Vom Finanz- zum Wissenschaftsbetrug: Methode, den Irrungen in der medizinischen Literatur beizukommen}. ({German}) [{From} financial to scientific fraud: Method to overcome errors in the medical literature]", journal = "Der Anaesthesist", volume = "61", number = "6", pages = "537--542", month = jun, year = "2012", DOI = "https://doi.org/10.1007/s00101-012-2028-y", ISSN = "0003-2417 (print), 1432-055X (electronic)", ISSN-L = "0003-2417", bibdate = "Wed Jun 20 14:26:36 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "https://link.springer.com/journal/101", keywords = "Benford's law; distribution; Medicine; scientific fraud; statistics", language = "German", } @Article{Shelburne:2012:ED, author = "Brian Shelburne", title = "The {ENIAC}'s 1949 Determination of $ \pi $", journal = j-IEEE-ANN-HIST-COMPUT, volume = "99", number = "PrePrints", year = "2012", CODEN = "IAHCEX", DOI = "https://doi.org/10.1109/MAHC.2011.61", ISSN = "1058-6180 (print), 1934-1547 (electronic)", ISSN-L = "1058-6180", bibdate = "Fri Feb 3 15:38:23 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib", abstract = "In January 1950, George W. Reitwiesner published ``An ENIAC Determination of $ \pi $ and $e$ to more than 2000 Decimal Places'' in Mathematical Tables and Other Aides to Computation \cite{Reitwiesner:1950:EDM} which described the first use of a computer, the ENIAC, to calculate the decimal expansion of $ \pi $. Since the history of $ \pi $ stretches back over thousands of years, the use of the ENIAC to determine $ \pi $ is an important historical and technological milestone. It is especially interesting since the ENIAC was not designed to perform this type of calculation as it could only store 200 decimal digits while the determination of e and $ \pi $ required manipulating numbers 2000+ digits long. Starting with Reitwiesner's description of the calculation, the known architecture of the ENIAC, how it was programmed, and the mathematics used, we examine why the calculation was undertaken, how the calculation had to be done, and what was subsequently learned.", acknowledgement = ack-nhfb, fjournal = "IEEE annals of the history of computing", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85", pdfdate = "8 August 2011", remark = "This paper contains an interesting survey of work on the calculation of $ \pi $ up to the early 1950s, with a detailed reconstruction of its determination on the ENIAC. From page 1 of the paper: ``Early in June, 1949, Professor John von Neumann expressed an interest in the possibility that the ENIAC might sometime be employed to determine the value of $ \pi $ and $e$ to many decimal places with a view toward obtaining a statistical measure of the randomness of the distribution of the digits.'' From page 2: ``\ldots{} Augustus De Morgan (1806--1871) who noticed the smaller number of appearances of the digit 7 in Shank's 607 digit determination of $ \pi $. It was later determined that Shank's determination had an error beginning at the 528th digit.'' From page 11: ``A preliminary investigation has indicated that the digits of $e$ deviate significantly from randomness (in the sense of staying closer to their expected values than a random sequence of this length normally would) while for $ \pi $ no significant deviations have so far been detected.'' See \cite{Metropolis:1950:STV} for that analysis.", } @Article{Song:2012:QEM, author = "Jongwoo Song and Seongjoo Song", title = "A quantile estimation for massive data with generalized {Pareto} distribution", journal = j-COMPUT-STAT-DATA-ANAL, volume = "56", number = "1", pages = "143--150", day = "1", month = jan, year = "2012", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:18 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947311002477", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @InCollection{Sorell:2012:ZLV, author = "C. Joseph Sorell", editor = "Carol A. Chapelle", booktitle = "The Encyclopedia of Applied Linguistics", title = "{Zipf's Law} and Vocabulary", publisher = pub-WILEY, address = pub-WILEY:adr, year = "2012", DOI = "https://doi.org/10.1002/9781405198431.wbeal1302", ISBN = "1-4051-9843-5", ISBN-13 = "978-1-4051-9843-1", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1002/9781405198431", keywords = "child language; computational linguistics; corpus; pragmatics; second language acquisition; vocabulary", } @Article{Sottili:2012:BLT, author = "Gianluca Sottili and Danilo M. Palladino and Biagio Giaccio and Paolo Messina", title = "{Benford's Law} in Time Series Analysis of Seismic Clusters", journal = j-MATH-GEOSCI, volume = "44", number = "5", pages = "619--634", month = jul, year = "2012", CODEN = "????", DOI = "https://doi.org/10.1007/s11004-012-9398-1", ISSN = "1874-8953 (print), 1874-8961 (electronic)", ISSN-L = "1874-8953", bibdate = "Tue Feb 19 06:15:52 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11004-012-9398-1", acknowledgement = ack-nhfb, fjournal = "Mathematical Geosciences", journal-URL = "http://link.springer.com/journal/11004", } @MastersThesis{Stanton:2012:DFU, author = "Gabriella Stanton", title = "Detecting Fraud: Utilizing New Technology to Advance the Audit Profession", type = "Honors thesis", school = "University of New Hampshire", address = "Durham, NH 03824, USA", pages = "26", month = "Spring", year = "2012", bibdate = "Thu Oct 13 09:10:26 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://scholars.unh.edu/cgi/viewcontent.cgi?article=1017&context=honors", acknowledgement = ack-nhfb, advisor = "Jake Rose", keywords = "Benford's Law; Zipf's Law", } @Article{Strauch:2012:UP, author = "O. Strauch", title = "Unsolved Problems", journal = "Uniform Distribution Theory", volume = "??", number = "??", publisher = "Mathematical Institute of the Slovak Academy of Sciences and BOKU --- University of Natural Resources and Life Sciences", address = "Bratislava, Slovakia and Vienna, Austria", pages = "1--98", month = "????", year = "2012", DOI = "????", ISSN = "1336-913X", ISSN-L = "1336-913X", bibdate = "Tue Feb 19 06:17:17 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Unsolved Problems Section on the home page of \booktitle{Uniform Distribution Theory}.", URL = "http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf", acknowledgement = ack-nhfb, journal-URL = "http://www.boku.ac.at/MATH/udt/", } @InProceedings{Taimori:2012:PTS, author = "A. Taimori and F. Razzazi and A. Behrad and A. Ahmadi and M. Babaie-Zadeh", booktitle = "2012 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT)", title = "A proper transform for satisfying {Benford's Law} and its application to double {JPEG} image forensics", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "000240--000244", month = dec, year = "2012", DOI = "https://doi.org/10.1109/ISSPIT.2012.6621294", ISSN = "2162-7843", ISSN-L = "2162-7843", bibdate = "Sat Sep 10 11:40:17 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ieeexplore.ieee.org/document/6621294/", acknowledgement = ack-nhfb, keywords = "2D discrete cosine transform; Benford law; Benford's Law; data compression; discrete cosine transform; discrete cosine transforms; Discrete wavelet transforms; double JPEG; double JPEG image forensics; filtering theory; image coding; image forensics; image manipulation; Kullback-Leibler divergence; Lighting; Matched filters; natural image data; normalized cross correlation; Pearson chi-square test statistic; significant digits statistics; single compressed images; statistical analysis; statistical fitness criteria; transform domain; variance filter; variance filtering", } @Article{Tavangar:2012:SUC, author = "Mahdi Tavangar and Majid Asadi", title = "Some unified characterization results on the generalized {Pareto} distributions based on generalized order statistics", journal = j-METRIKA, volume = "75", number = "7", pages = "997--1007", month = oct, year = "2012", CODEN = "MTRKA8", DOI = "https://doi.org/10.1007/s00184-011-0364-6", ISSN = "0026-1335 (print), 1435-926X (electronic)", ISSN-L = "0026-1335", bibdate = "Mon Feb 2 16:28:42 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/metrika.bib", URL = "http://link.springer.com/article/10.1007/s00184-011-0364-6", acknowledgement = ack-nhfb, fjournal = "Metrika", journal-URL = "http://link.springer.com/journal/184", } @Article{Valadier:2012:BPR, author = "Michel Valadier", title = "The {Benford} phenomenon for random variables. {Discussion} of {Feller}'s way", journal = "ArXiv e-prints", pages = "23", day = "9", month = mar, year = "2012", bibdate = "Tue Feb 19 06:20:32 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1203.2518", acknowledgement = ack-nhfb, } @Article{Wang:2012:LPW, author = "Dongbo Wang and Danhao Zhu and Xinning Su", title = "{Lotka} phenomenon in the words' syntactic distribution complexity", journal = j-SCIENTOMETRICS, volume = "90", number = "2", pages = "483--498", month = feb, year = "2012", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-011-0546-z", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:38 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-011-0546-z", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Book{Wapner:2012:UEC, author = "Leonard M. Wapner", title = "Unexpected expectations: the curiosities of a mathematical crystal ball", publisher = pub-CRC, address = pub-CRC:adr, pages = "xvi + 204", year = "2012", ISBN = "1-56881-721-5 (hardback)", ISBN-13 = "978-1-56881-721-7 (hardback)", LCCN = "QA95 .W34 2012", bibdate = "Tue May 5 16:15:08 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib; z3950.loc.gov:7090/Voyager", abstract = "Mathematical expectation or expected value represents the long-term average numerical outcome to an experiment performed a large number of times. Routinely used in the physical sciences, business, and economics, mathematical expectation has also been used to calculate strategies in games of chance and even to justify the belief in God. How can this expression, which is trivial to calculate, have such broad applications and at the same time yield unexpected irresolvable paradoxes? In an easily accessible presentation, this book explores these puzzling and entertaining mysteries.", acknowledgement = ack-nhfb, author-dates = "1948--", subject = "Mathematical recreations", tableofcontents = "Dedication \\ Table of Contents \\ Acknowledgments \\ The Crystal Ball \\ 1. Looking Back \\ 2. The ABCs of E \\ 3. Doing the Right Thing \\ 4. Aversion Perversion \\ 5. And the Envelope Please! \\ 6. Parrondo's Paradox: You Can Win for Losing \\ 7. Imperfect Recall \\ 8. Non-zero-sum Games: The Inadequacy of Individual Rationality \\ 9. Newcomb's Paradox \\ 10. Benford's Law \\ Let the Mystery Be! \\ Bibliography", } @Article{Zea:2012:BEP, author = "Luz Milena Zea and Rodrigo B. Silva and Marcelo Bourguignon and Andrea M. Santos and Gauss M. Cordeiro", title = "The Beta Exponentiated {Pareto} Distribution with Application to Bladder Cancer Susceptibility", journal = j-INT-J-STAT-PROBAB, volume = "1", number = "2", pages = "8--??", month = "????", year = "2012", CODEN = "????", ISSN = "1927-7032 (print), 1927-7040 (electronic)", ISSN-L = "1927-7032", bibdate = "Tue Jun 9 14:40:16 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/intjstatprobab.bib", URL = "http://www.ccsenet.org/journal/index.php/ijsp/article/view/16301", acknowledgement = ack-nhfb, fjournal = "International Journal of Statistics and Probability", journal-URL = "http://www.ccsenet.org/journal/index.php/ijsp/issue/archive", } @Article{Zeng:2012:TMB, author = "Jianping Zeng and Jiangjiao Duan and Wenjun Cao and Chengrong Wu", title = "Topics modeling based on selective {Zipf} distribution", journal = j-EXPERT-SYST-APPL, volume = "39", number = "7", pages = "6541--6546", day = "1", month = jun, year = "2012", CODEN = "ESAPEH", DOI = "https://doi.org/10.1016/j.eswa.2011.12.051", ISSN = "0957-4174 (print), 1873-6793 (electronic)", ISSN-L = "0957-4174", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0957417411017222", acknowledgement = ack-nhfb, fjournal = "Expert Systems with Applications", journal-URL = "http://www.sciencedirect.com/science/journal/09574174", keywords = "Zipf's Law", } @Article{Abu-Dayyeh:2013:ESS, author = "Walid Abu-Dayyeh and Aissa Assrhani and Kamarulzaman Ibrahim", title = "Estimation of the shape and scale parameters of {Pareto} distribution using ranked set sampling", journal = j-STAT-PAPERS, volume = "54", number = "1", pages = "207--225", month = feb, year = "2013", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-011-0420-3", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:38 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-011-0420-3", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Alali:2013:BLA, author = "Fatima A. Alali and Silvia Romero", title = "{Benford's Law}: Analyzing a Decade of Financial Data", journal = "Journal of Emerging Technologies in Accounting", volume = "10", number = "1", pages = "1--39", month = dec, year = "2013", DOI = "https://doi.org/10.2308/jeta-50749", ISSN = "1554-1908 (print), 1558-7940 (electronic)", ISSN-L = "1554-1908", bibdate = "Thu Oct 13 08:07:00 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaajournals.org/doi/pdf/10.2308/jeta-50749", acknowledgement = ack-nhfb, } @Article{Andriotis:2013:JSD, author = "Panagiotis Andriotis and George Oikonomou and Theo Tryfonas", title = "{JPEG} steganography detection with {Benford's Law}", journal = "Digital Investigation", volume = "9", number = "3--4", pages = "246--257", year = "2013", DOI = "https://doi.org/10.1016/j.diin.2013.01.005", ISSN = "1742-2876 (print), 1873-202X (electronic)", ISSN-L = "1742-2876", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib; https://www.math.utah.edu/pub/tex/bib/datacompression.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1742287613000066", abstract = "In this paper we present a novel approach to the problem of steganography detection in {JPEG} images by applying a statistical attack. The method is based on the empirical Benford's Law and, more specifically, on its generalized form. We prove and extend the validity of the logarithmic rule in colour images and introduce a blind steganographic method which can flag a file as a suspicious stego-carrier. The proposed method achieves very high accuracy and speed and is based on the distributions of the first digits of the quantized Discrete Cosine Transform coefficients present in JPEGs. In order to validate and evaluate our algorithm, we developed steganographic tools which are able to analyse image files and we subsequently applied them on the popular Uncompressed Colour Image Database. Furthermore, we demonstrate that not only can our method detect steganography but, if certain criteria are met, it can also reveal which steganographic algorithm was used to embed data in a {JPEG} file.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Data hiding; Generalized Benford's Law; Quantized DCT coefficients; Quantized {DCT} coefficients; Steganalysis; Steganography detection", } @Misc{Anonymous:2013:NBL, author = "Anonymous", title = "Number 1 and {Benford's Law} --- Numberphile", howpublished = "Web video lecture.", day = "20", month = jan, year = "2013", bibdate = "Fri Oct 09 06:28:24 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.youtube.com/watch?v=XXjlR2OK1kM", acknowledgement = ack-nhfb, } @Article{Aron:2013:CFM, author = "Jacob Aron", title = "Crime-fighting maths law confirms planetary riches", journal = j-NEW-SCIENTIST, volume = "220", number = "2945", pages = "12-", year = "2013", CODEN = "NWSCAL", DOI = "https://doi.org/10.1016/S0262-4079(13)62775-X", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S026240791362775X", abstract = "The statistical tool called Benford's law has been shown to work for our catalogue of exoplanets, backing up predictions that the galaxy is brimming with alien worlds.", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law", } @Article{Banks:2013:BLM, author = "David G. Banks", title = "{Benford's Law} Made Easy: Common Software Eases use of Fraud Search Theorem", journal = "Fraud Magazine", volume = "??", number = "??", pages = "??--??", month = jan # "\slash " # feb, year = "2013", ISSN = "1553-6645", ISSN-L = "1553-6645", bibdate = "Sun Feb 17 08:11:01 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.fraud-magazine.com/article.aspx?id=4294968485", acknowledgement = ack-nhfb, fjournal = "Fraud Magazine. {A} Publication of the Association of Certified Fraud Examiners", } @Article{Birajdar:2013:DIF, author = "Gajanan K. Birajdar and Vijay H. Mankar", title = "Digital image forgery detection using passive techniques: A survey", journal = "Digital Investigation", volume = "10", number = "3", pages = "226--245", year = "2013", DOI = "https://doi.org/10.1016/j.diin.2013.04.007", ISSN = "1742-2876 (print), 1873-202X (electronic)", ISSN-L = "1742-2876", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1742287613000364", abstract = "Today manipulation of digital images has become easy due to powerful computers, advanced photo-editing software packages and high resolution capturing devices. Verifying the integrity of images and detecting traces of tampering without requiring extra prior knowledge of the image content or any embedded watermarks is an important research field. An attempt is made to survey the recent developments in the field of digital image forgery detection and complete bibliography is presented on blind methods for forgery detection. Blind or passive methods do not need any explicit priori information about the image. First, various image forgery detection techniques are classified and then its generalized structure is developed. An overview of passive image authentication is presented and the existing blind forgery detection techniques are reviewed. The present status of image forgery detection technique is discussed along with a recommendation for future research.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Image authentication; Image forensic; Image manipulation detection; Image tampering detection; Passive/blind image forgery detection", } @InCollection{Cali:2013:FA, author = "J. Cali", editor = "Jay A. Siegel and Pekka J. Saukko and Max M. Houck", booktitle = "Encyclopedia of Forensic Sciences", title = "Forensic Accounting", publisher = "Academic Press", address = "Waltham", pages = "423--431", year = "2013", DOI = "https://doi.org/10.1016/B978-0-12-382165-2.00218-X", ISBN = "0-12-382166-5", ISBN-13 = "978-0-12-382166-9", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/B978012382165200218X", abstract = "Forensic accounting is defined as the action of identifying, recording, settling, extracting, sorting, reporting, and verifying past financial data or other accounting activities for settling current or prospective legal disputes or using such past financial data for projecting future financial data to settle legal disputes. Forensic accountants practice a special area of accountancy that requires them to have knowledge of the courtroom, rules of evidence, and investigative techniques in addition to generally accepted accounting principles and generally accepted auditing standards. The practice of forensic accounting is used in criminal investigations to prosecute fraud, embezzlement, ponzi, and terrorist-financing schemes. While in civil litigation disputes, forensic accounting methods are employed to determine the value of economic damages related to insurance claims, lost profits, bankruptcy, qui-tam actions, and divorce. The ultimate role of the forensic accountant is to use their forensic accounting skills to prepare a written report and to provide expert testimony based on the findings in the written report that will help the judge and the members of the jury to better understand complex financial transactions.", acknowledgement = ack-nhfb, keywords = "Arson for profit; Bank Secrecy Act; Benford's Law; Business interruption claims; Civil litigation disputes; Currency transaction reports; Divorce; Economic damages; Financial motive; FinCEN; Forensic accounting; Forensic auditing; Fraud; Fraud examination; Fraud investigation; Fraud schemes; Hidden assets; Income from unknown sources; Income reconstruction; Insurance fraud; Life care plans; Lost profit computations; Money laundering; Mortgage fraud; Offshore accounts; Patriot Act; Ponzi scheme; Qui-tam actions; Securities fraud; Specified unlawful acts; Suspicious activity reports", } @Article{Deligny:2013:RRL, author = "Hugues Deligny and Paul Jolissaint", title = "Relations de r{\'e}currence lin{\'e}aires, primitivit{\'e} et loi de {Benford}. ({French}) [{Linear} recurrence relations, primitivity, and {Benford}'s law]", journal = j-ELEM-MATH, volume = "68", number = "1", pages = "9--21", year = "2013", DOI = "https://doi.org/10.4171/EM/213", ISSN = "0013-6018 (print), 1420-8962 (electronic)", ISSN-L = "0013-6018", MRclass = "11K36", MRnumber = "3016461", MRreviewer = "Simon Kristensen", bibdate = "Thu Feb 14 07:02:03 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Elemente der Mathematik", language = "French", } @Article{deVries:2013:CLN, author = "Pepijn de Vries and Albertinka J. Murk", title = "Compliance of {LC50} and {NOEC} data with {Benford's Law}: An indication of reliability?", journal = "Ecotoxicology and Environmental Safety", volume = "98", number = "0", pages = "171--178", year = "2013", DOI = "https://doi.org/10.1016/j.ecoenv.2013.09.002", ISSN = "0147-6513 (print), 1090-2414 (electronic)", ISSN-L = "0147-6513", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0147651313003692", abstract = "Reliability of research data is essential, especially when potentially far-reaching conclusions will be based on them. This is also, amongst others, the case for ecotoxicological data used in risk assessment. Currently, several approaches are available to classify the reliability of ecotoxicological data. The process of classification, such as using the Klimisch score, is time-consuming and focuses on the application of standardised protocols and the documentation of the study. The presence of irregularities and the integrity of the performed work, however, are not addressed. The present study shows that Benford's Law, based on the occurrence of first digits following a logarithmic scale, can be applied to ecotoxicity test data for identifying irregularities. This approach is already successfully applied in accounting. Benford's Law can be used as reliability indicator, in addition to existing reliability classifications. The law can be used to efficiently trace irregularities in large data sets of interpolated (no) effect concentrations such as LC50s (possibly the result of data manipulation), without having to evaluate the source of each individual record. Application of the law to systems in which large amounts of toxicity data are registered (e.g., European Commission Regulation concerning the Registration, Evaluation, Authorisation and Restriction of Chemicals) can therefore be valuable.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Data evaluation; LC50; NOEC; Quality assessment; Reliability; {LC50}; {NOEC}", } @Article{diGiovanni:2013:FET, author = "Julian di Giovanni and Andrei A. Levchenko", title = "Firm entry, trade, and welfare in {Zipf}'s world", journal = j-J-INT-ECON, volume = "89", number = "2", pages = "283--296", day = "15", month = mar, year = "2013", CODEN = "JIECBE", DOI = "https://doi.org/10.1016/j.jinteco.2012.08.002", ISSN = "0022-1996 (print), 1873-0353 (electronic)", ISSN-L = "0022-1996", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022199612001365", acknowledgement = ack-nhfb, fjournal = "Journal of International Economics", journal-URL = "http://www.sciencedirect.com/science/journal/09247963", keywords = "Zipf's Law", } @Article{Egghe:2013:FRB, author = "L. Egghe", title = "The functional relation between the impact factor and the uncitedness factor revisited", journal = j-J-INFORMETRICS, volume = "7", number = "1", pages = "183--189", year = "2013", DOI = "https://doi.org/10.1016/j.joi.2012.10.007", ISSN = "1751-1577 (print), 1875-5879 (electronic)", ISSN-L = "1751-1577", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1751157712000909", abstract = "We give a heuristic proof of the relation between the impact factor (IF) and the uncitedness factor (U), the fraction of the papers that are uncited: $ U = 1 / (1 + I F) $. This generalizes the proof of Hsu and Huang [Physica A 391, 2129 2134, 2012] who obtain the same result but based on the assumption of the validity of the Matthew-effect. This new informetric function opens the discussion on universal informetric laws, distribution dependent laws and parameter dependent laws of which examples from the informetrics literature are given.", acknowledgement = ack-nhfb, fjournal = "Journal of Informetrics", journal-URL = "http://www.sciencedirect.com/science/journal/17511577", keywords = "Benford's Law; Distribution dependent law; Impact factor; Parameter dependent law; Uncitedness factor; Universal informetric law", } @Article{Eliazar:2013:BLP, author = "Iddo I. Eliazar", title = "{Benford's Law}: A {Poisson} perspective", journal = j-PHYSICA-A, volume = "392", number = "16", pages = "3360--3373", year = "2013", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2013.03.057", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "62E10 (60G55 82C05)", MRnumber = "3069159", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437113002902", abstract = "Benford's Law is a counterintuitive statistical law asserting that the distribution of leading digits, taken from a large ensemble of positive numerical values that range over many orders of scale, is logarithmic rather than uniform (as intuition suggests). In this paper we explore Benford's Law from a Poisson perspective, considering ensembles of positive numerical values governed by Poisson-process statistics. We show that this Poisson setting naturally accommodates Benford's Law and: (i) establish a Poisson characterization and a Poisson multidigit-extension of Benford's Law; (ii) study a system-invariant leading-digit distribution which generalizes Benford's Law, and establish a Poisson characterization and a Poisson multidigit-extension of this distribution; (iii) explore the universal emergence of the system-invariant leading-digit distribution, couple this universal emergence to the universal emergence of the Weibull and Fr{\'e}chet extreme-value distributions, and distinguish the special role of Benford's Law in this universal emergence; (iv) study the continued-fractions counterpart of the system-invariant leading-digit distribution, and establish a Poisson characterization of this distribution; and (v) unveil the elemental connection between the system-invariant leading-digit distribution and its continued-fractions counterpart. This paper presents a panoramic Poisson approach to Benford's Law, to its system-invariant generalization, and to its continued-fractions counterpart.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Continued fractions; Extreme-value statistics; Invariance; Poisson limit theorems; Power-laws; Universality", } @Article{Fernandez:2013:SPC, author = "Arturo J. Fern{\'a}ndez", title = "Smallest {Pareto} confidence regions and applications", journal = j-COMPUT-STAT-DATA-ANAL, volume = "62", number = "??", pages = "11--25", month = jun, year = "2013", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:41 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947312004501", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @InCollection{Gangopadhyay:2013:EZL, author = "Kausik Gangopadhyay and Banasri Basu", title = "Evolution of {Zipf}'s law for {Indian} urban agglomerations via-{\`a}-vis {Chinese} urban agglomerations", crossref = "Abergel:2013:ESR", pages = "119--129", year = "2013", DOI = "https://doi.org/10.1007/978-88-470-2553-0_8", MRclass = "91B80", MRnumber = "2963609", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "New Econ. Windows", acknowledgement = ack-nhfb, } @Article{GomesdaSilva:2013:SAS, author = "Carlos {Gomes da Silva} and Pedro M. R. Carreira", title = "Selecting Audit Samples Using {Benford's Law}", journal = j-AUDITING, volume = "32", number = "2", pages = "53--65", month = may, year = "2013", DOI = "https://doi.org/10.2308/ajpt-50340", ISSN = "0278-0380 (print), 1558-7991 (electronic)", ISSN-L = "0278-0380", bibdate = "Thu Oct 13 08:05:18 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://aaajournals.org/doi/pdf/10.2308/ajpt-50340", acknowledgement = ack-nhfb, fjournal = "Auditing: A Journal of Practice \& Theory", } @TechReport{Grammatikos:2013:UBL, author = "T. Grammatikos and N. I. Papanikolaou", title = "Using {Benford's Law} to Detect Fraudulent Practices in Banking", type = "SSRN Scholarly Paper", number = "2352775", institution = "Social Science Research Network", address = "Rochester, NY, USA", year = "2013", bibdate = "Sat Sep 10 11:54:44 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @InProceedings{Haferkorn:2013:HVA, author = "Martin Haferkorn", editor = "Fethi Rabhi and Peter Gomber", booktitle = "{Enterprise applications and services in the finance industry: 6th International Workshop, FinanceCom 2012, Barcelona, Spain, June 10, 2012. Revised papers}", title = "Humans vs. Algorithms --- Who Follows {Newcomb--Benford's Law} Better with Their Order Volume?", chapter = "4", publisher = pub-SV, address = pub-SV:adr, pages = "61--70", year = "2013", DOI = "https://doi.org/10.1007/978-3-642-36219-4_4", ISBN = "3-642-36219-2", ISBN-13 = "978-3-642-36219-4", LCCN = "HG173 .I58 2012", bibdate = "Wed Feb 13 19:15:28 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4", acknowledgement = ack-nhfb, book-URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4", remark = "This may be the first publication to reference this bibliography. It examines trading patterns of several days on the German Stock Exchange (Deutsche B{\"o}rse), with a total volume of almost 10 million trades, split almost equally between human and algorithmic traders. It finds that the algorithmic trades follow Benford's Law closely, but the human trades do not. It points out that algorithmic trading could be manipulated to make it look more like human trades, so as not to alert competitors to its actions.", subject = "Financial services industry; Information technology; Congresses; Data processing", } @Article{Hofmarcher:2013:FSD, author = "P. Hofmarcher and K. Hornik", title = "First Significant Digits and the Credit Derivative Market During the Financial Crisis", journal = "Contemporary Economics", volume = "7", number = "2", pages = "21--29", month = "????", year = "2013", DOI = "https://doi.org/10.5709/ce.1897-9254.80", bibdate = "Sat Sep 10 12:11:42 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286063", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Hubert:2013:DID, author = "Mia Hubert and Goedele Dierckx and Dina Vanpaemel", title = "Detecting influential data points for the {Hill} estimator in {Pareto}-type distributions", journal = j-COMPUT-STAT-DATA-ANAL, volume = "65", number = "??", pages = "13--28", month = sep, year = "2013", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:43 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S016794731200285X", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Khosravani:2013:DBD, author = "Azar Khosravani and Constantin Rasinariu", title = "$n$-digit {Benford} distributed random variables", journal = j-ADV-APPL-STAT, volume = "36", number = "2", pages = "119--130", month = oct, year = "2013", CODEN = "????", ISSN = "0972-3617", ISSN-L = "0972-3617", MRclass = "60E05 (11K45)", MRnumber = "3134635", bibdate = "Wed Aug 16 09:06:43 MDT 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.pphmj.com/abstract/7887.htm", acknowledgement = ack-nhfb, fjournal = "Advances and Applications in Statistics", journal-URL = "http://www.pphmj.com/journals/contents/adas.htm", } @Article{Kossovsky:2013:RQO, author = "A. Ely Kossovsky", title = "On the Relative Quantities Occurring within Physical Data Sets", journal = "arxiv.org", month = may, year = "2013", bibdate = "Thu Oct 13 07:31:45 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://adsabs.harvard.edu/abs/2013arXiv1305.1893E", acknowledgement = ack-nhfb, keywords = "Mathematics - Statistics Theory", primaryclass = "math.ST", } @Article{Lu:2013:DZH, author = "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou", title = "Deviation of {Zipf}'s and {Heaps' Laws} in Human Languages with Limited Dictionary Sizes", journal = j-SCI-REP, volume = "3", number = "??", pages = "1--7", month = "????", year = "2013", CODEN = "SRCEC3", DOI = "https://doi.org/10.1038/srep01082", ISSN = "2045-2322", bibdate = "Tue Feb 26 07:39:15 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html", accepted = "21 December 2012", acknowledgement = ack-nhfb, articleno = "1082", fjournal = "Scientific Reports", journal-URL = "http://www.nature.com/srep/", onlinedate = "30 January 2013", received = "11 June 2012", } @InProceedings{Mebane:2013:SDI, author = "Walter R. {Mebane, Jr.} and T. Kent", editor = "????", booktitle = "{Proceedings of the 2013 Annual Meeting of the Midwest Political Science Association, Chicago, IL, April 11--14, 2013}", title = "Second Digit Implications of Voters' Strategies and Mobilizations in the {United States} during the 2000s", publisher = "????", address = "????", pages = "??--??", year = "2013", bibdate = "Sat Sep 10 14:33:23 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Michalski:2013:DCF, author = "T. Michalski and G. Stoltz", title = "Do Countries Falsify Economic Data Strategically? {Some} Evidence That They Might", journal = j-REV-ECON-STAT, volume = "95", number = "2", pages = "591--616", month = may, year = "2013", CODEN = "RECSA9", DOI = "https://doi.org/10.1162/REST_a_00274", ISSN = "0034-6535 (print), 1530-9142 (electronic)", ISSN-L = "0034-6535", bibdate = "Sat Sep 10 14:35:50 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.mitpressjournals.org/doi/abs/10.1162/REST_a_00274", acknowledgement = ack-nhfb, fjournal = "Review of Economics and Statistics", journal-URL = "http://www.jstor.org/journal/revieconstat; http://www.mitpressjournals.org/loi/rest", keywords = "Benford's Law", } @InProceedings{Milani:2013:AAB, author = "S. Milani and M. Tagliasacchi and S. Tubaro", booktitle = "2013 IEEE International Conference on Acoustics, Speech and Signal Processing", title = "Antiforensics attacks to {Benford's Law} for the detection of double compressed images", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "3053--3057", month = may, year = "2013", DOI = "https://doi.org/10.1109/ICASSP.2013.6638219", ISSN = "1520-6149", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "antiforensics attack strategy; Benford's law; data compression; Detectors; digit statistics; digital forensics; double image compression detectors; first digit law; Forensics; fraud detection methods; image coding; Image coding; Image reconstruction; object detection; PSNR; Quantization (signal); statistical analysis; Transform coding", } @Book{Newbold:2013:SBE, author = "Paul Newbold and William L. (William Lee) Carlson and Betty Thorne", title = "Statistics for Business and Economics", publisher = "Pearson Education", address = "Harlow, Essex, UK", edition = "Eighth", pages = "792", year = "2013", ISBN = "0-273-76706-2", ISBN-13 = "978-0-273-76706-0", LCCN = "HF1017 .N48 2013", bibdate = "Fri Mar 22 09:03:53 MDT 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-mjn # "\slash " # ack-nhfb, keywords = "Benford's Law", subject = "Commercial statistics; Economics; Statistical methods; Statistics", } @Article{Norris:2013:NRA, author = "Pippa Norris", title = "The new research agenda studying electoral integrity", journal = j-ELECT-STUDIES, volume = "32", number = "4", pages = "563--575", year = "2013", DOI = "https://doi.org/10.1016/j.electstud.2013.07.015", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Special Symposium: The new research agenda on electoral integrity", URL = "http://www.sciencedirect.com/science/article/pii/S0261379413001157", abstract = "A rapidly-growing research agenda shared by scholars and applied policy analysts is beginning to explore three questions: when do elections meet standards of electoral integrity? When do they fail to do so? And what can be done to mitigate these problems? To address these issues, Part 1 in this paper outlines the concept of electoral integrity, proposing a comprehensive and broad definition founded upon global norms and international conventions. Part 2 argues that several sub-fields contribute towards the study of electoral integrity, although commonly fragmented at present, including (i) public sector management; (ii) political culture; (iii) comparative institutions; and (iv) security studies. The emerging research agenda focused on electoral integrity, cutting across these conventional disciplinary boundaries, is characterized by its problem-oriented focus and global comparative framework, as well as by its use of pluralistic methods and analytical techniques. Part 3 outlines the contribution of papers in this symposium. The conclusion summarizes the key features of this new research agenda studying electoral integrity.", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Benford's Law; Corruption; Democracy and democratization; Elections; Electoral integrity; Fraud; Voting", } @Article{Ozer:2013:BLD, author = "G. Ozer and B. Babacan", title = "{Benford's Law} and Digital Analysis: Application on {Turkish} Banking Sector", journal = "Business and Economics Research Journal", volume = "4", number = "1", pages = "29--41", month = "", year = "2013", DOI = "", ISSN = "1309-2448", bibdate = "Sat Sep 10 15:29:55 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "", acknowledgement = ack-nhfb, journal-URL = "http://www.berjournal.com/", keywords = "Benford's Law", } @Article{Pain:2013:RSA, author = "Jean-Christophe Pain", title = "Regularities and symmetries in atomic structure and spectra", journal = "High Energy Density Physics", volume = "9", number = "3", pages = "392--401", month = sep, year = "2013", CODEN = "HEDPBW", DOI = "https://doi.org/10.1016/j.hedp.2013.04.007", ISSN = "1574-1818 (print), 1878-0563 (electronic)", ISSN-L = "1574-1818", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1574181813000475", abstract = "The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of levels and lines. In the past, much attention was paid to the distribution of energy levels (Wigner surmise, random-matrix model). However, information about the distribution of the lines (energy and strength) is lacking. Thirty years ago, Learner found empirically an unexpected law: the logarithm of the number of lines whose intensities lie between $^{2k}I_0$ and $^{2k + 1}I_0$, $ I_0$ being a reference intensity and $k$ an integer, is a decreasing linear function of $k$. In the present work, the fractal nature of such an intriguing regularity is outlined and a calculation of its fractal dimension is proposed. Other peculiarities are also presented, such as the fact that the distribution of line strengths follows Benford's law of anomalous numbers, the existence of additional selection rules (PH coupling), the symmetry with respect to a quarter of the subshell in the spin-adapted space (LL coupling) and the odd even staggering in the distribution of quantum numbers, pointed out by Bauche and Coss{\'e}.", acknowledgement = ack-nhfb, journal-URL = "http://www.sciencedirect.com/science/journal/15741818", keywords = "Atomic physics; Benford's Law; Fractals; Group theory; High-energy-density matter; Hot plasmas; Symmetries", } @Article{Phatarfod:2013:SAB, author = "Ravi Phatarfod", title = "Some aspects of the {Benford} law of leading significant digits", journal = j-MATH-SCI, volume = "38", number = "2", pages = "73--85", year = "2013", ISSN = "0312-3685 (print), 1475-6080 (electronic)", ISSN-L = "0312-3685", MRclass = "62P99 (11A63)", MRnumber = "3184679", bibdate = "Tue Jan 26 11:01:15 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://appliedprobability.org/content.aspx?Group=tms&Page=tmsabstracts38_2#one", acknowledgement = ack-nhfb, ajournal = "Math. Sci.", fjournal = "The Mathematical Scientist", journal-URL = "http://www.appliedprobability.org/content.aspx?Group=tms&Page=tms", } @Article{Piva:2013:OIF, author = "Alessandro Piva", title = "An Overview on Image Forensics", journal = "ISRN Signal Processing", volume = "2013", number = "??", pages = "496701", month = "????", year = "2013", DOI = "https://doi.org/10.1155/2013/496701", ISSN = "2090-5041 (print), 2090-505X (electronic)", ISSN-L = "2090-5041", bibdate = "Tue Feb 19 06:21:47 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.isrn.com/journals/sp/2013/496701/", accepted = "26 November 2012", acknowledgement = ack-nhfb, fjournal = "International Scholarly Research Network Signal Processing", journal-URL = "http://www.isrn.com/journals/sp/", keywords = "Benford's Law", pagecount = "22", received = "6 November 2012", } @Article{Rauch:2013:LME, author = "Bernhard Rauch and M. G{\"o}ttsche and Florian {El Mouaaouy}", title = "{LIBOR} Manipulation --- Empirical Analysis of Financial Market Benchmarks Using {Benford's Law}", journal = "Social Sciences Research Network", volume = "??", number = "??", pages = "26", day = "5", month = dec, year = "2013", DOI = "https://doi.org/10.2139/ssrn.2363895", bibdate = "Sat Sep 10 15:58:05 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2363895", acknowledgement = ack-nhfb, keywords = "Benford's law; collusion; financial institutions; inter-bank offered rates; manipulation; price-fixing", } @Article{Scollnik:2013:CTP, author = "David P. M. Scollnik", title = "Comments on two papers concerning estimation of the parameters of the {Pareto} distribution in the presence of outliers", journal = j-STAT-METHODOL, volume = "13", number = "??", pages = "1--11", month = jul, year = "2013", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:55 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312712000822", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Article{Slepkov:2013:BLT, author = "Aaron D. Slepkov and Kevin B. Ironside and David DiBattista", title = "{Benford's Law}: Textbook Exercises and Multiple-Choice Testbanks", journal = "arXiv.org", volume = "??", number = "??", pages = "??", day = "19", month = nov, year = "2013", bibdate = "Tue Jan 26 09:56:51 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1311.4787v1", abstract = "Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1\%, and the least common is 9, with an expected frequency of 4.6\%. The history and development of Benford's Law is inexorably linked to physics, yet there has been a dearth of physics-related Benford datasets reported in the literature. Currently, the most common application of Benford's Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford's Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford's Law, the testbank is nonetheless secure against such a Benford's attack for banal reasons.", acknowledgement = ack-nhfb, } @Article{Smith:2013:BNS, author = "Aaron Carl Smith", title = "{Benford--Newcomb} Subsequences for Fraud Detection", journal = "arXiv.org", volume = "??", number = "??", pages = "??", day = "22", month = jan, year = "2013", bibdate = "Tue Jan 26 10:01:46 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1301.6086v1", abstract = "Benford's law is frequently used to evaluate the likihood that data is misrepresentative. Typically statistical tests measure the likihood. Another method of employing Benford's law is to compare the frequency of leading digits to the probabilities of leading digits over a subset of the natural numbers. This paper proposes using the probabilities of leading digits from uniform, natural numbers to establish interval criteria for when to look more closely into the possibility of misrepresentative data.", acknowledgement = ack-nhfb, } @Article{Soo:2013:ZGG, author = "Kwok Tong Soo", title = "{Zipf}, {Gibrat} and geography: Evidence from {China}, {India} and {Brazil}", journal = j-PAP-REG-SCI, pages = "??--??", year = "2013", DOI = "https://doi.org/10.1111/j.1435-5957.2012.00477.x", ISSN = "1056-8190 (print), 1435-5957 (electronic)", ISSN-L = "1056-8190", bibdate = "Mon Feb 25 06:13:56 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Papers in Regional Science", keywords = "dynamic panel data models; Gibrat's Law; state populations; Zipf's Law", xxnote = "Online, but not yet in print with assigned page numbers, on 25 February 2013.", } @Article{Srivastava:2013:FD, author = "Tanya Kaushal Srivastava", title = "The First Digit $1$", journal = j-RESONANCE, volume = "18", number = "12", pages = "1073--1085", month = dec, year = "2013", CODEN = "RESOFE", DOI = "https://doi.org/10.1007/s12045-013-0135-y", ISSN = "0971-8044 (print), 0973-712X (electronic)", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s12045-013-0135-y", acknowledgement = ack-nhfb, fjournal = "Resonance", journal-URL = "http://link.springer.com/journal/12045", keywords = "Benford's Law", } @Article{Tavangar:2013:CGP, author = "Mahdi Tavangar and Marzieh Hashemi", title = "On characterizations of the generalized {Pareto} distributions based on progressively censored order statistics", journal = j-STAT-PAPERS, volume = "54", number = "2", pages = "381--390", month = may, year = "2013", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-012-0434-5", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Sun Feb 1 10:12:38 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-012-0434-5", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{vanZyl:2013:GPD, author = "J. Martin van Zyl", title = "The generalized {Pareto} distribution fitted to research outputs of countries", journal = j-SCIENTOMETRICS, volume = "94", number = "3", pages = "1099--1109", month = mar, year = "2013", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-012-0798-2", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:49 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-012-0798-2", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Wainer:2013:VRS, author = "Howard Wainer and Polina Harik and John Neter", title = "Visual Revelations: {Stigler}'s {Law of Eponymy} and {Marey}'s Train Schedule: Did {Serjev} Do It Before {Ibry}, and What About {Jules Petiet}?", journal = j-CHANCE, volume = "26", number = "1", pages = "53--56", year = "2013", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.2013.772394", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Tue Feb 3 09:42:07 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/chance.bib", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", } @Article{Wjcik:2013:HFI, author = "Micha{\l} Ryszard W{\'o}jcik", title = "How fast increasing powers of a continuous random variable converge to {Benford's Law}", journal = j-STAT-PROB-LETT, volume = "83", number = "12", pages = "2688--2692", year = "2013", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2013.09.003", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715213002927", abstract = "It is known that increasing powers of a continuous random variable converge in distribution to Benford's Law as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an elementary method, which is easier to apply and provides a better estimation in the widely studied case of a uniformly distributed random variable.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law; Fourier coefficients; Mantissa distribution; Significand distribution; Uniform distribution modulo 1", } @Article{Wojcik:2013:HFI, author = "Michal Ryszard W{\'o}jcik", title = "How fast increasing powers of a continuous random variable converge to {Benford's Law}", journal = j-STAT-PROB-LETT, volume = "83", number = "12", pages = "2688--2692", month = dec, year = "2013", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2013.09.003", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "60F15 (60E05)", MRnumber = "3118213", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715213002927", abstract = "It is known that increasing powers of a continuous random variable converge in distribution to {Benford's Law} as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an elementary method, which is easier to apply and provides a better estimation in the widely studied case of a uniformly distributed random variable.", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", keywords = "Benford's Law; Fourier coefficients; Mantissa distribution; Significand distribution; Uniform distribution modulo 1", } @Article{Yan:2013:CNE, author = "Su Yan and W. Scott Spangler and Ying Chen", title = "Chemical Name Extraction Based on Automatic Training Data Generation and Rich Feature Set", journal = j-TCBB, volume = "10", number = "5", pages = "1218--1233", month = sep, year = "2013", CODEN = "ITCBCY", DOI = "https://doi.org/10.1109/TCBB.2013.101", ISSN = "1545-5963 (print), 1557-9964 (electronic)", ISSN-L = "1545-5963", bibdate = "Thu Jan 9 15:34:03 MST 2014", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tcbb.bib", abstract = "The automation of extracting chemical names from text has significant value to biomedical and life science research. A major barrier in this task is the difficulty of getting a sizable and good quality data to train a reliable entity extraction model. Another difficulty is the selection of informative features of chemical names, since comprehensive domain knowledge on chemistry nomenclature is required. Leveraging random text generation techniques, we explore the idea of automatically creating training sets for the task of chemical name extraction. Assuming the availability of an incomplete list of chemical names, called a dictionary, we are able to generate well-controlled, random, yet realistic chemical-like training documents. We statistically analyze the construction of chemical names based on the incomplete dictionary, and propose a series of new features, without relying on any domain knowledge. Compared to state-of-the-art models learned from manually labeled data and domain knowledge, our solution shows better or comparable results in annotating real-world data with less human effort. Moreover, we report an interesting observation about the language for chemical names. That is, both the structural and semantic components of chemical names follow a Zipfian distribution, which resembles many natural languages.", acknowledgement = ack-nhfb, fjournal = "IEEE/ACM Transactions on Computational Biology and Bioinformatics", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J954", } @Article{Young:2013:ATL, author = "D. S. Young", title = "Approximate tolerance limits for {Zipf--Mandelbrot} distributions", journal = j-PHYSICA-A, volume = "392", number = "7", pages = "1702--1711", day = "1", month = apr, year = "2013", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2012.11.056", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Feb 27 07:32:55 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437112010497", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Zipf's Law", } @Article{Alexopoulos:2014:BLA, author = "Theodoros Alexopoulos and Stefanos Leontsinis", title = "{Benford}'s Law in Astronomy", journal = j-J-ASTROPHYS-ASTRON, volume = "35", number = "4", pages = "639--648", year = "2014", CODEN = "JASRD7", DOI = "https://doi.org/10.1007/s12036-014-9303-z", ISSN = "0250-6335 (print), 0973-7758 (electronic)", ISSN-L = "0250-6335", bibdate = "Wed Aug 12 10:02:04 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See follow-up \cite{Hill:2016:HLI}.", URL = "http://link.springer.com/article/10.1007/s12036-014-9303-z", acknowledgement = ack-nhfb, fjournal = "Journal of Astrophysics and Astronomy", journal-URL = "http://www.springerlink.com/content/0250-6335", keywords = "Benford's law; galaxies; significant digit.; stars; Universe", } @Article{Alexopoulos:2014:BLU, author = "Theodoros Alexopoulos and Stefanos Leontsinis", title = "{Benford's Law} and the {Universe}", journal = "arXiv.org", volume = "??", number = "??", pages = "6", day = "23", month = jan, year = "2014", bibdate = "Tue Jan 26 10:06:48 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1401.5794v2", abstract = "Benford's law predicts the occurrence of the nth digit of numbers in datasets originating from various sources of the world, ranging from financial data to atomic spectra. It is intriguing that although many features of Benford's law have been proven and analysed, it is still not fully mathematically understood. In this paper we investigate the distances of galaxies and stars by comparing the first, second and third significant digit probabilities with Benford's predictions. It is found that the distances of galaxies follow reasonably well the first digit law and the star distances agree very well with the first, second and third significant digit.", acknowledgement = ack-nhfb, } @Article{Alves:2014:BLA, author = "Alexandre Donizeti Alves and Horacio Hideki Yanasse and Nei Yoshihiro Soma", title = "{Benford's Law} and articles of scientific journals: comparison of {JCR\reg} and {Scopus} data", journal = j-SCIENTOMETRICS, volume = "98", number = "1", pages = "173--184", month = jan, year = "2014", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-013-1030-8", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:05:57 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/content/pdf/10.1007/s11192-013-1030-8.pdf", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", keywords = "Articles; Benford's Law; JCR; Scopus", } @Article{Aron:2014:LLN, author = "Jacob Aron", title = "Looking for life in numbers", journal = j-NEW-SCIENTIST, volume = "222", number = "2968", pages = "46--47", year = "2014", CODEN = "NWSCAL", DOI = "https://doi.org/10.1016/S0262-4079(14)60925-8", ISSN = "0262-4079 (print), 1364-8500 (electronic)", ISSN-L = "0262-4079", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0262407914609258", acknowledgement = ack-nhfb, fjournal = "New Scientist", journal-URL = "http://www.sciencedirect.com/science/journal/02624079", keywords = "Benford's Law", } @Article{Arshadi:2014:BLB, author = "Laleh Arshadi and Amir Hossein Jahangir", title = "{Benford's Law} behavior of {Internet} traffic", journal = j-J-NETW-COMPUT-APPL, volume = "40", number = "0", pages = "194--205", year = "2014", CODEN = "JNCAF3", DOI = "https://doi.org/10.1016/j.jnca.2013.09.007", ISSN = "1084-8045 (print), 1095-8592 (electronic)", ISSN-L = "1084-8045", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1084804513001951", abstract = "In this paper, we analyze the Internet traffic from a different point of view based on Benford's law, an empirical law that describes the distribution of leading digits in a collection of numbers met in naturally occurring phenomena. We claim that Benford's law holds for the inter-arrival times of TCP flows in case of normal traffic. Consequently, any type of anomalies affecting TCP flows, including intentional intrusions or unintended faults and network failures in general, can be detected by investigating the first-digit distributions of the inter-arrival times of TCP SYN packets. In this paper we apply our findings to the detection of intentional attacks, and leave other types of anomalies for future works. We support our claim with related researches that indicate the TCP flow inter-arrival times can be modeled by Weibull distribution with shape parameter less than 1, and show the relation between Weibull distributed data and Benford's law. Finally, we validate our findings on real traffic and achieve encouraging results.", acknowledgement = ack-nhfb, ajournal = "J. netw. comput. appl.", fjournal = "Journal of Network and Computer Applications", journal-URL = "http://www.sciencedirect.com/science/journal/10848045", keywords = "Anomaly detection; Benford's law; Benford's Law; Benford's law; Benford's Law; Computer network traffic analysis; Weibull distribution", } @Article{Ausloos:2014:BBL, author = "M. Ausloos and C. Herteliu and B. Ileanu", title = "Breakdown of {Benford's Law} for birth data", journal = "arXiv.org", volume = "??", number = "??", pages = "17", day = "6", month = oct, year = "2014", bibdate = "Tue Jan 26 09:59:08 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1410.1755v1", abstract = "Long birth time series for Romania are investigated from Benford's law point of view, distinguishing between families with a religious (Orthodox and Non-Orthodox) affiliation. The data extend from Jan. 01, 1905 till Dec. 31, 2001, i.e. over 97 years or 35\,429 days. The results point to a drastic breakdown of Benford's law. Some interpretation is proposed, based on the statistical aspects due to population sizes, rather than on human thought constraints when the law breakdown is usually expected. Benford's law breakdown clearly points to natural causes.", acknowledgement = ack-nhfb, } @Article{Ausloos:2014:ZMP, author = "Marcel Ausloos", title = "{Zipf--Mandelbrot--Pareto} model for co-authorship popularity", journal = j-SCIENTOMETRICS, volume = "101", number = "3", pages = "1565--1586", month = dec, year = "2014", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-014-1302-y", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:06:06 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-014-1302-y", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Beckett:2014:TPA, author = "Phil Beckett", title = "Taking a preventative approach towards the {Bribery Act}", journal = "Computer Fraud \& Security", volume = "2014", number = "6", pages = "16--18", year = "2014", DOI = "https://doi.org/10.1016/S1361-3723(14)70502-0", ISSN = "1361-3723 (print), 1873-7056 (electronic)", ISSN-L = "1361-3723", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1361372314705020", abstract = "The UK's Serious Fraud Office (SFO) recently tried to reinvigorate activity around the Bribery Act.1 It warned companies and banks that if they fail to prevent financial crime by their staff, they could face great fines and official blacklisting from European contracts. This proposed amendment put forward by the {SFO} would give the {UK} powers to take direct action against corporates, enabling it to levy US-style fines and brand them with assisted bribery. And so organisations need to ensure that awareness of and compliance with the Bribery Act is part of their risk analysis and mitigation activities and they should start by looking at their data.", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Zheng:2013:NSC, author = "Siqi Zheng", title = "Necessary and sufficient conditions for {Benford} sequences", journal = j-PI-MU-EPSILON-J, volume = "13", number = "9", pages = "553--561", year = "2013", CODEN = "PMEJBR", ISSN = "0031-952X", MRclass = "62E10", MRnumber = "3155505", bibdate = "Sat Dec 13 06:58:38 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Pi Mu Epsilon Journal", } @InCollection{Berger:2014:BSL, author = "Arno Berger and Gideon Eshun", editor = "Ziyad AlSharawi and Jim M. Cushing and Saber Elaydi", booktitle = "{Theory and Applications of Difference Equations and Discrete Dynamical Systems: ICDEA, Muscat, Oman, May 26--30, 2013}", title = "{Benford} Solutions of Linear Difference Equations", volume = "102", publisher = pub-SV, address = pub-SV:adr, bookpages = "xvi + 222", pages = "23--60", year = "2014", DOI = "https://doi.org/10.1007/978-3-662-44140-4_2", ISBN = "3-662-44139-X, 3-662-44140-3 (e-book)", ISBN-13 = "978-3-662-44139-8, 978-3-662-44140-4 (e-book)", LCCN = "QA218 .T446 2014", MRclass = "60-02 (11A63 11K06 60C05 60F05)", MRnumber = "3280199", bibdate = "Wed Aug 12 09:51:04 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Springer Proceedings in Mathematics \& Statistics", acknowledgement = ack-nhfb, } @Article{Berger:2014:CBL, author = "Arno Berger and Gideon Eshun", title = "A Characterization of {Benford's Law} in Discrete-Time Linear Systems", journal = j-J-DYN-DIFFER-EQU, volume = "??", number = "??", pages = "1--39", month = "????", year = "2014", CODEN = "JDDEEH", DOI = "https://doi.org/10.1007/s10884-014-9393-y", ISSN = "1040-7294 (print), 1572-9222 (electronic)", ISSN-L = "1040-7294", MRclass = "37A05, 37A45, 11J71, 62E20", bibdate = "Wed Aug 12 10:09:25 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of dynamics and differential equations", keywords = "$$\mathbb {Q}$$ Q -independence; 11J71; 37A05; 37A45; 62E20; Benford's sequence; Nonresonant set; Uniform distribution mod 1", } @Article{Best:2014:BBZ, author = "Andrew Best and Patrick Dynes and Xixi Edelsbrunner and Brian McDonald and Steven J. Miller and Kimsy Tor and Caroline Turnage-Butterbaugh and Madeleine Weinstein", title = "{Benford} Behavior of {Zeckendorf} Decompositions", journal = j-FIB-QUART, volume = "52", number = "5", pages = "35--??", month = dec, year = "2014", CODEN = "FIBQAU", DOI = "https://doi.org/10.1080/00150517.2014.12427855", ISSN = "0015-0517", ISSN-L = "0015-0517", MRclass = "11B39 (11B05)", MRnumber = "3479486", MRreviewer = "Martin Johann Stein", bibdate = "Mon Nov 25 10:05:44 MST 2019", bibsource = "http://www.fq.math.ca/52-5.html; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.fq.math.ca/Papers1/52-5/Best-Benford.pdf", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Bhole:2014:BDN, author = "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh", title = "{Benford} distributions in {NMR}", journal = "arXiv.org", volume = "??", number = "??", pages = "6", day = "27", month = jun, year = "2014", bibdate = "Tue Jan 26 10:03:00 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1406.7077v1", abstract = "Benford's Law is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of digit $1$, and decreasing occurrences to other larger digits. Here we report the Benford analysis of various NMR databases and draw several interesting inferences. We observe that, in general, NMR signals follow Benford distribution in time-domain as well as in frequency domain. Our survey included NMR signals of various nuclear species in a wide variety of molecules in different phases, namely liquid, liquid-crystalline, and solid. We also studied the dependence of Benford distribution on NMR parameters such as signal to noise ratio, number of scans, pulse angles, and apodization. In this process we also find that, under certain circumstances, the Benford analysis can distinguish a genuine spectrum from a visually identical simulated spectrum. Further we find that chemical-shift databases and amplitudes of certain radio frequency pulses generated using optimal control techniques also satisfy Benford's law to a good extent.", acknowledgement = ack-nhfb, } @Article{Cournane:2014:NAB, author = "S. Cournane and N. Sheehy and J. Cooke", title = "The novel application of {Benford}'s second order analysis for monitoring radiation output in interventional radiology", journal = "Physica Medica", volume = "30", number = "4", pages = "413--418", year = "2014", DOI = "https://doi.org/10.1016/j.ejmp.2013.11.004", ISSN = "1120-1797 (print), 1724-191X (electronic)", ISSN-L = "1120-1797", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1120179713004328", abstract = "Benford's law is an empirical observation which predicts the expected frequency of digits in naturally occurring datasets spanning multiple orders of magnitude, with the law having been most successfully applied as an audit tool in accountancy. This study investigated the sensitivity of the technique in identifying system output changes using simulated changes in interventional radiology Dose-Area-Product (DAP) data, with any deviations from Benford's distribution identified using z-statistics. The radiation output for interventional radiology X-ray equipment is monitored annually during quality control testing; however, for a considerable portion of the year an increased output of the system, potentially caused by engineering adjustments or spontaneous system faults may go unnoticed, leading to a potential increase in the radiation dose to patients. In normal operation recorded examination radiation outputs vary over multiple orders of magnitude rendering the application of normal statistics ineffective for detecting systematic changes in the output. In this work, the annual DAP datasets complied with Benford's first order law for first, second and combinations of the first and second digits. Further, a continuous rolling second order technique was devised for trending simulated changes over shorter timescales. This distribution analysis, the first employment of the method for radiation output trending, detected significant changes simulated on the original data, proving the technique useful in this case. The potential is demonstrated for implementation of this novel analysis for monitoring and identifying change in suitable datasets for the purpose of system process control.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Interventional radiology; Radiation dose", } @Article{Dunstan:2014:GSD, author = "D. J. Dunstan and A. J. Bushby", title = "Grain size dependence of the strength of metals: The {Hall--Petch} effect does not scale as the inverse square root of grain size", journal = j-INT-J-PLAST, volume = "53", number = "0", pages = "56--65", year = "2014", CODEN = "IJPLER", DOI = "https://doi.org/10.1016/j.ijplas.2013.07.004", ISSN = "0749-6419 (print), 1879-2154 (electronic)", ISSN-L = "0749-6419", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S074964191300140X", abstract = "The classic data in the literature for the grain size dependence of the strength in many metals are reviewed. The exponent $x$ relating strength to grain size $ d^{-x}$ is not often the eponymous inverse square-root relationship (known as the Hall--Petch effect), but is widely scattered from values as low as $ x = 0.2$ to values as high as $ x = 1$. These exponents for individual datasets are shown to be largely meaningless. For an ensemble of n selected datasets, the fit to the functional form $ \ln [d] / d + {\rm const}$ with $ n + 1$ free fitting parameters is found to be almost as good as the fit to $ 1 / \sqrt [d] + {\rm const}$ with $ 2 n$ fitting parameters (the Hall--Petch fit). The probability that the former is the preferable fit is high. Some data sets do not agree with the $ \ln [d] / d$ fit, but their deviation is readily explained on simple physical grounds. Moreover, even when they are included in the fit, statistical tests still show that the $ \ln [d] / d$ form is preferable by a wide margin. The conclusion is that the Hall--Petch effect is not another size effect sui generis but is the same size effect as that observed in epitaxial thin film growth and in micromechanical testing of small specimens. Consequently we propose that grain size strengthening of metals is driven by constraints on stress and dislocation curvature according to the space available.", acknowledgement = ack-nhfb, fjournal = "International Journal of Plasticity", journal-URL = "http://www.sciencedirect.com/science/journal/07496419", keywords = "Benford's Law; Dislocations; Grain boundaries; Metallic material; Polycrystalline material; Yield condition", } @TechReport{Edelsbrunner:2014:BLC, author = "X. Edelsbrunner and K. Huan and B. Mackall and S. J. Miller and J. Powell and C. Turnage-Butterbaugh and M. Weinstein", title = "{Benford's Law}, the {Cauchy} Distribution and Financial Data", type = "Report", institution = "????", address = "????", year = "2014", bibdate = "Sat Sep 10 11:09:53 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InProceedings{Ferariu:2014:PGP, author = "L. Ferariu and C. Cimpanu", booktitle = "{2014 18th International Conference System Theory, Control and Computing (ICSTCC)}", title = "{Pareto} genetic path planning hybridized with multi-objective {Dijkstra}'s algorithm", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "341--346", year = "2014", DOI = "https://doi.org/10.1109/ICSTCC.2014.6982439", bibdate = "Wed Mar 18 11:11:53 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6982439", acknowledgement = ack-nhfb, } @Article{Gonzalez-Alvarez:2014:POH, author = "David L. Gonz{\'a}lez-{\'A}lvarez and Miguel A. Vega-Rodr{\'\i}guez and {\'A}lvaro Rubio-Largo", title = "Parallelizing and optimizing a hybrid differential evolution with {Pareto} tournaments for discovering motifs in {DNA} sequences", journal = j-J-SUPERCOMPUTING, volume = "70", number = "2", pages = "880--905", month = nov, year = "2014", CODEN = "JOSUED", DOI = "https://doi.org/10.1007/s11227-014-1266-y", ISSN = "0920-8542 (print), 1573-0484 (electronic)", ISSN-L = "0920-8542", bibdate = "Fri Feb 13 12:13:17 MST 2015", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=70&issue=2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jsuper.bib", URL = "http://link.springer.com/article/10.1007/s11227-014-1266-y", acknowledgement = ack-nhfb, fjournal = "The Journal of Supercomputing", journal-URL = "http://link.springer.com/journal/11227", } @Article{Gray:2014:TGR, author = "Glen L. Gray and Roger S. Debreceny", title = "A taxonomy to guide research on the application of data mining to fraud detection in financial statement audits", journal = j-INT-J-ACCOUNT-INFO-SYS, volume = "15", number = "4", pages = "357--380", year = "2014", CODEN = "IJAIA7", DOI = "https://doi.org/10.1016/j.accinf.2014.05.006", ISSN = "1467-0895 (print), 1873-4723 (electronic)", ISSN-L = "1467-0895", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "2013 Research Symposium on Information Integrity \& Information Systems Assurance", URL = "http://www.sciencedirect.com/science/article/pii/S1467089514000323", abstract = "This paper explores the application of data mining techniques to fraud detection in the audit of financial statements and proposes a taxonomy to support and guide future research. Currently, the application of data mining to auditing is at an early stage of development and researchers take a scatter-shot approach, investigating patterns in financial statement disclosures, text in annual reports and MD\&As, and the nature of journal entries without appropriate guidance being drawn from lessons in known fraud patterns. To develop structure to research in data mining, we create a taxonomy that combines research on patterns of observed fraud schemes with an appreciation of areas that benefit from productive application of data mining. We encapsulate traditional views of data mining that operates primarily on quantitative data, such as financial statement and journal entry data. In addition, we draw on other forms of data mining, notably text and email mining.", acknowledgement = ack-nhfb, fjournal = "International Journal of Accounting Information Systems", keywords = "Auditing; Benford's Law; Data mining; Fraud", } @Article{Hackl:2014:CPP, author = "Franz Hackl and Michael E. Kummer and Rudolf Winter-Ebmer", title = "99 Cent: Price points in e-commerce", journal = "Information Economics and Policy", volume = "26", number = "0", pages = "12--27", year = "2014", DOI = "https://doi.org/10.1016/j.infoecopol.2013.10.001", ISSN = "0167-6245 (print), 1873-5975 (electronic)", ISSN-L = "0167-6245", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167624513000450", abstract = "Setting prices ending in nines is a common feature of many markets for consumer products. This prevalence has been explained either by a specific image of such price points or by the exploitation of rational inattention on the part of the consumers who want to economize on the cost of information processing. We use data from an Austrian price comparison site and find a remarkable prevalence of such price setting. Prices ending with nine are also sticky: price-setters change them with a significantly lower probability; rivals underbid these prices more seldom if they represent the cheapest price on the market, and we observe higher price jumps by price leaders for these price points. Finally, we explore the impact of these price points on the consumers demand.", acknowledgement = ack-nhfb, keywords = "Benford's Law; E-commerce; Focal prices; Price stability; Pricing behavior", } @Article{He:2014:EPD, author = "Hui He and Na Zhou and Ruiming Zhang", title = "On estimation for the {Pareto} distribution", journal = j-STAT-METHODOL, volume = "21", number = "??", pages = "49--58", month = nov, year = "2014", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:46:01 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312714000288", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Article{Holz:2014:QCG, author = "Carsten A. Holz", title = "The quality of {China}'s {GDP} statistics", journal = "China Economic Review", volume = "30", number = "0", pages = "309--338", year = "2014", DOI = "https://doi.org/10.1016/j.chieco.2014.06.009", ISSN = "1043-951X (print), 1873-7781 (electronic)", ISSN-L = "1043-951X", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1043951X14000753", abstract = "Since the 1998 wind of falsification and embellishment, Chinese official statistics on gross domestic product (GDP) have repeatedly come under scrutiny. This paper evaluates the quality of China's GDP statistics in four stages. First, it reviews past and ongoing suspicions of the quality of GDP data and examines the evidence. Second, it documents the institutional framework for data compilation and concludes on the implications for data quality. Third, it asks how the Chinese National Bureau of Statistics could possibly go about credibly falsifying GDP data without being found out. Fourth, it examines if the first- and second-digit distributions of official GDP data conform to established data regularities (Benford's Law). The findings are that the supposed evidence for GDP data falsification is not compelling, that the National Bureau of Statistics has much institutional scope for falsifying GDP data, and that certain manipulations of nominal and real data would be virtually undetectable. Official GDP data, however, exhibit few statistical anomalies (conform to Benford's Law) and the National Bureau of Statistics thus either makes no significant use of its scope to falsify data, or is aware of statistical data regularities when it falsifies data.", acknowledgement = ack-nhfb, keywords = "Accuracy of national statistics; Benford's Law; Compilation of {GDP} and sectoral value-added; National income accounting; National statistical system", } @Article{Hou:2014:PFD, author = "I-Hong Hou and Piyush Gupta", title = "Proportionally fair distributed resource allocation in multiband wireless systems", journal = j-IEEE-TRANS-NETWORKING, volume = "22", number = "6", pages = "1819--1830", month = dec, year = "2014", CODEN = "IEANEP", DOI = "https://doi.org/10.1109/TNET.2013.2284494", ISSN = "1063-6692 (print), 1558-2566 (electronic)", ISSN-L = "1063-6692", bibdate = "Thu Feb 12 18:29:37 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib", abstract = "A challenging problem in multiband multicell self-organized wireless systems, such as femtocells/picocells in cellular networks, multichannel Wi-Fi networks, and more recent wireless networks over TV white spaces, is of distributed resource allocation. This in general involves four components: channel selection, client association, channel access, and client scheduling. In this paper, we present a unified framework for jointly addressing the four components with the global system objective of maximizing the clients throughput in a proportionally fair manner. Our formulation allows a natural dissociation of the problem into two subparts. We show that the first part, involving channel access and client scheduling, is convex and derive a distributed adaptation procedure for achieving a Pareto-optimal solution. For the second part, involving channel selection and client association, we develop a Gibbs-sampler-based approach for local adaptation to achieve the global objective, as well as derive fast greedy algorithms from it that achieve good solutions often.", acknowledgement = ack-nhfb, fjournal = "IEEE\slash ACM Transactions on Networking", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J771", } @Article{Huang:2014:GSP, author = "Mu-Hsuan Huang and Wei-Tzu Huang and Cheng-Ching Chang and Dar-Zen Chen and Chang-Pin Lin", title = "The greater scattering phenomenon beyond {Bradford}'s law in patent citation", journal = j-J-ASSOC-INF-SCI-TECHNOL, volume = "65", number = "9", pages = "1917--1928", month = sep, year = "2014", CODEN = "????", DOI = "https://doi.org/10.1002/asi.23092", ISSN = "2330-1643 (print), 2330-1643 (electronic)", ISSN-L = "2330-1643", bibdate = "Fri Sep 11 12:15:14 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jaist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "8 Apr 2014", } @Article{Huettenberger:2014:DSM, author = "Lars Huettenberger and Christian Heine and Christoph Garth", title = "Decomposition and Simplification of Multivariate Data using {Pareto} Sets", journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH, volume = "20", number = "12", pages = "2684--2693", month = dec, year = "2014", CODEN = "ITVGEA", DOI = "https://doi.org/10.1109/TVCG.2014.2346447", ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306", ISSN-L = "1077-2626", bibdate = "Thu Feb 12 16:40:54 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib", URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html", abstract-URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Visualization and Computer Graphics", journal-URL = "http://www.computer.org/csdl/trans/tg/index.html", } @InProceedings{Iorliam:2014:DBI, author = "A. Iorliam and A. T. S. Ho and N. Poh and Y. Q. Shi", booktitle = "2014 International Workshop on Biometrics and Forensics (IWBF)", title = "Do biometric images follow {Benford's Law}?", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1--6", month = mar, year = "2014", DOI = "https://doi.org/10.1109/IWBF.2014.6914261", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "backend attack; Benford law; Benford's law; Biomedical imaging; biometric image manipulation; biometric images; biometric sample tampering; biometrics (access control); data compression; digital forensics; Discrete cosine transforms; double compressed face image; double compressed fingerprint image; EER; equal error rate; Face; Fingerprint recognition; forensic biometrics; forensics; image coding; Image coding; Image matching; malicious tampering detection; natural image tampering detection; security concern; sensor level tampering; single compressed face image; single compressed fingerprint image; spoofing; template contamination; Transform coding", } @Article{Jameson:2014:BLC, author = "Marie Jameson and Jesse Thomer and Lynelle Ye", title = "{Benford's Law} for Coefficients of Newforms", journal = "arxiv.org", volume = "??", number = "??", pages = "??--??", day = "7", month = jul, year = "2014", bibdate = "Sat Sep 10 12:26:03 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1407.1577", acknowledgement = ack-nhfb, keywords = "Benford's Law", } @Article{Kraus:2014:DWD, author = "Cornelia Kraus and Raul Valverde", title = "A Data Warehouse Design for the Detection of Fraud in the Supply Chain by Using the {Benford's Law}", journal = j-AM-J-APPL-SCI, volume = "11", number = "9", pages = "1507--1518", month = sep, year = "2014", CODEN = "AJASCJ", DOI = "https://doi.org/10.3844/ajassp.2014.1507.1518", ISSN = "1546-9239 (print), 1554-3641 (electronic)", ISSN-L = "1546-9239", bibdate = "Mon Jun 1 13:40:15 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Am. J. Appl. Sci.", fjournal = "American Journal of Applied Sciences", journal-URL = "https://thescipub.com/journals/ajas/archive", } @Article{Leemann:2014:SAS, author = "Lucas Leemann and Daniel Bochsler", title = "A systematic approach to study electoral fraud", journal = j-ELECT-STUDIES, volume = "35", number = "0", pages = "33--47", year = "2014", DOI = "https://doi.org/10.1016/j.electstud.2014.03.005", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0261379414000390", abstract = "Integrity of elections relies on fair procedures at different stages of the election process, and fraud can occur in many instances and different forms. This paper provides a general approach for the detection of fraud. While most existing contributions focus on a single instance and form of fraud, we propose a more encompassing approach, testing for several empirical implications of different possible forms of fraud. To illustrate this approach we rely on a case of electoral irregularities in one of the oldest democracies: In a Swiss referendum in 2011, one in twelve municipalities irregularly destroyed the ballots, rendering a recount impossible. We do not know whether this happened due to sloppiness, or to cover possible fraudulent actions. However, one of our statistical tests leads to results, which point to irregularities in some of the municipalities, which lost their ballots: they reported significantly fewer empty ballots than the other municipalities. Relying on several tests leads to the well known multiple comparisons problem. We show two strategies and illustrate strengths and weaknesses of each potential way to deal with multiple tests.", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Benford's Law; Electoral forensics; Electoral fraud; Referendums; Switzerland", } @Article{Lin:2014:CCE, author = "Fengyi Lin and Sheng-Fu Wu", title = "Comparison of cosmetic earnings management for the developed markets and emerging markets: Some empirical evidence from the {United States} and {Taiwan}", journal = "Economic Modelling", volume = "36", number = "0", pages = "466--473", year = "2014", DOI = "https://doi.org/10.1016/j.econmod.2013.10.002", ISSN = "0264-9993 (print), 1873-6122 (electronic)", ISSN-L = "0264-9993", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0264999313004288", abstract = "This study examines the effect of the implementation of corporate governance regulations on cosmetic earnings management in developed and emerging markets respectively. Using Benford's Law, the analysis employs 84,870 positive earnings observations for all publicly listed US and Taiwan companies from 1990 to 2011. The empirical results show that, regardless of developed markets and emerging markets, the phenomenon of cosmetic earnings management exists. In contrast to developed markets, corporate managers of emerging markets have stronger incentives to manipulate earnings. More importantly, it was found that the degree of earnings management is significantly less after implementing corporate governance regulations both in developed and emerging markets. This result suggests that the implementation of corporate governance regulations plays an important role in reducing the earnings manipulative behavior. The findings of the study add more evidence to the ongoing debate about the effectiveness of corporate governance regulations in preventing earnings management.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Corporate governance; Cosmetic earnings management", } @Article{Lin:2014:RAA, author = "Fengyi Lin and Chung-Min Wu and Tzu-Yi Fang and Jheng-Ci Wun", title = "The relations among accounting conservatism, institutional investors and earnings manipulation", journal = "Economic Modelling", volume = "37", number = "0", pages = "164--174", year = "2014", DOI = "https://doi.org/10.1016/j.econmod.2013.10.020", ISSN = "0264-9993 (print), 1873-6122 (electronic)", ISSN-L = "0264-9993", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0264999313004471", abstract = "Most scholars have indicated corporations using accounting conservatism to reduce earnings manipulation, although certain scholars believe that firms have more incentive to increase earnings manipulation. Institutional investors play an important external monitoring role, and affect firm's earnings manipulation. Previous studies adopted accruals as an earnings manipulation proxy to detect the relationship among accounting conservatism, institutional investor shareholdings, and earnings manipulation. We further investigate the relationship among accounting conservatism, institutional investor shareholdings, and earnings manipulation by using Benford's law. Our results indicate that firms with more conservative financial reporting have less probability of engaging in earnings-manipulative activities. We also find the negative association between earnings management and institutional investor shareholdings. However, if corporate financial statements tend toward conservatism, institutional investor shareholdings could increase managers' incentive to manage earnings. Our findings have important implications for investors to make investment decisions.", acknowledgement = ack-nhfb, keywords = "Accounting conservatism; Benford's law; Benford's Law; Benford's law; Benford's Law; Earnings management; Institutional investor shareholdings", } @Article{Lu:2014:ODE, author = "Lu Lu and Christine M. Anderson-Cook and Dennis K. J. Lin", title = "Optimal designed experiments using a {Pareto} front search for focused preference of multiple objectives", journal = j-COMPUT-STAT-DATA-ANAL, volume = "71", number = "??", pages = "1178--1192", month = mar, year = "2014", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:43:50 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947313001382", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Luca:2014:FDF, author = "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}", title = "On the first digits of the {Fibonacci} numbers and their {Euler} function", journal = "Uniform Distribution Theory", volume = "9", number = "1", pages = "21--25", year = "2014", ISSN = "1336-913X (print), 2309-5377 (electronic)", ISSN-L = "1336-913X", MRclass = "11B39 (11K36)", MRnumber = "3237073", MRreviewer = "Huaning Liu", bibdate = "Tue Jan 26 11:12:44 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "https://math.boku.ac.at/udt/vol09/no1/03LucaStanica.pdf", acknowledgement = ack-nhfb, ajournal = "Unif. Distrib. Theory", fjournal = "Uniform Distribution Theory", journal-URL = "https://doaj.org/toc/1336-913X", } @Article{MacDougall:2014:AIC, author = "Margaret MacDougall", title = "Assessing the Integrity of Clinical Data: When is Statistical Evidence Too Good to be True?", journal = "Topoi: An International Review of Philosophy", volume = "33", number = "2", pages = "323--337", month = oct, year = "2014", DOI = "https://doi.org/10.1007/s11245-013-9216-5", ISSN = "0167-7411 (print), 1572-8749 (electronic)", ISSN-L = "0167-7411", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11245-013-9216-5", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/11245", keywords = "Benford's Law", } @Article{Marden:2014:APO, author = "Jason R. Marden and H. Peyton Young and Lucy Y. Pao", title = "Achieving {Pareto} Optimality Through Distributed Learning", journal = j-SIAM-J-CONTROL-OPTIM, volume = "52", number = "5", pages = "2753--2770", month = "????", year = "2014", CODEN = "SJCODC", DOI = "https://doi.org/10.1137/110850694", ISSN = "0363-0129 (print), 1095-7138 (electronic)", ISSN-L = "0363-0129", bibdate = "Thu Feb 12 07:28:17 MST 2015", bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/52/5; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Control and Optimization", journal-URL = "http://epubs.siam.org/sicon", onlinedate = "January 2014", } @Book{Miller:2014:JFM, author = "Irwin Miller and Marylees Miller", title = "{John E. Freund}'s mathematical statistics with applications", publisher = "Pearson", address = "Boston, MA, USA", edition = "Eighth", pages = "xi + 529", year = "2014", ISBN = "0-321-80709-X (hardcover)", ISBN-13 = "978-0-321-80709-0 (hardcover)", LCCN = "QA276 .M4726 2014", bibdate = "Thu Oct 13 07:03:41 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, author-dates = "1928--", remark = "Revised edition of \cite{Miller:2004:JFM}.", subject = "Mathematical statistics", } @Article{Mir:2014:BLB, author = "T. A. Mir", title = "The {Benford Law} behavior of the religious activity data", journal = j-PHYSICA-A, volume = "408", number = "0", pages = "1--9", year = "2014", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2014.03.074", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437114002854", abstract = "An important aspect of religious association is that adherents, as part of their religious duty, carry out various activities. One religious group known for keeping the elaborate records of day-to-day activities of its members is the Jehovah's Witnesses (JWs) a worldwide Christian religious group. We analyse the historical records of the country-wide data associated with twelve different religious activities of {JWs} to see if there are any patterns in the distribution of the first digits as predicted by Benford's Law. This law states that the first digits of numbers in data sets are not uniformly distributed but often, not always, follow a logarithmic distribution such that the numbers beginning with smaller digits appear more frequently than those with larger ones. We find that the data on religious activities like peak publishers, pioneer publishers, baptizations, public meetings, congregations, bible studies, time spent in door-to-door contacts, attendances at the memorial services, total literature and individual magazines distributed, new subscriptions and back-calls received excellently conforms to Benford's Law.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Jehovah's Witnesses; Religious activities", } @Article{Mir:2014:BLP, author = "Tariq Ahmad Mir and Marcel Ausloos and Roy Cerqueti", title = "{Benford}'s law predicted digit distribution of aggregated income taxes: the surprising conformity of {Italian} cities and regions", journal = j-EUR-PHYS-J-B, volume = "87", number = "11", year = "2014", CODEN = "EPJBFY", DOI = "https://doi.org/10.1140/epjb/e2014-50525-2", ISSN = "1434-6028 (print), 1434-6036 (electronic)", ISSN-L = "1434-6028", bibdate = "Wed Aug 12 10:00:00 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, eid = "261", fjournal = "European Physical Journal B: Condensed Matter and Complex Systems", journal-URL = "http://link.springer.com/journal/10051", keywords = "Statistical and Nonlinear Physics", } @Article{Mitov:2014:EAP, author = "Kosto V. Mitov and Saralees Nadarajah", title = "Extremal and additive processes generated by {Pareto} distributed random vectors", journal = j-ESAIM-PROBAB-STATIST, volume = "18", number = "??", pages = "667--??", month = "????", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1051/ps/2014001", ISSN = "1292-8100 (print), 1262-3318 (electronic)", ISSN-L = "1262-3318", bibdate = "Mon Feb 9 06:54:48 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/esaim-probab-stat.bib", acknowledgement = ack-nhfb, fjournal = "ESAIM: Probability and Statistics", journal-URL = "http://www.edpsciences.org/ps/", } @Book{Oleksy:2014:DMB, author = "Marius Oleksy", title = "{Data Mining und Benford's Law als Controllinginstrumente}. ({German}) [{Data} mining and {Benford's Law} as controlling instruments]", volume = "45", publisher = "EHV Academicpress", address = "Bremen, Germany", pages = "220", year = "2014", ISBN = "3-86741-923-X (paperback), 3-86741-928-0", ISBN-13 = "978-3-86741-923-9 (paperback), 978-3-86741-928-4", LCCN = "????", bibdate = "Sat Jan 23 08:09:16 MST 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wismarer Schriften zu Management und Recht", URL = "http://deposit.d-nb.de/cgi-bin/dokserv?id=4627278\%26prov=M\%26dok\_var=1\%26dok\_ext=htm", acknowledgement = ack-nhfb, language = "German", tableofcontents = "1 Ziel und Abgrenzung der Arbeit / 16 \\ 1.1 Ziel / 18 \\ 1.2 Abgrenzung und die Hypothese / 18 \\ 2 Die Menge von Benford, die Benford Verteilung / 19 \\ 2.1 Untersuchungen der Benford-Verteilung / 20 \\ 2.2 Anwendungen des Benford-Gesetzes im Finanzbereich / 24 \\ 3 Datenursprung und Datenschutz / 25 \\ 3.1 Gesch{\"a}ftsmodell der DekaBank Luxembourg S.A. / 26 \\ 3.2 Systemarchitektur und die Datenquelle / 27 \\ 3.3 Datenschutz / 28 \\ 4 Orthodoxe Beweise der Verteilungskonformit{\"a}t / 30 \\ 4.1 Anpassungstests / 30 \\ 4.1.1 Nullhypothese und Fehlentscheidungen in der Statistik / 31 \\ 4.1.2 Normalverteilung / 33 \\ 4.1.3 Signifikanztests / 40 \\ 4.2 Auswahl der Anpassungstest / 50 \\ 5 Konzept des Frameworks f{\"u}r das Data Mining / 51 \\ 5.1 Einf{\"u}hrung in Data Mining / 51 \\ 5.2 Data Mining Phasen und Prozesse / 53 \\ 5.3 Biologische Grundlagen eines k{\"u}nstlichen Neurons / 61 \\ 5.4 K{\"u}nstliches Neuron / 62 \\ 5.5 Architektur des K{\"u}nstlichen Neuronalen Netzes / 84 \\ 5.6 Auswahl der Musterregeln / 94 \\ 5.7 Entwicklung eines Testszenarios / 102 \\ 5.8 Kriterien f{\"u}r Wissensextraktion / 104 \\ 5.9 Kriterien f{\"u}r den Testbetrieb / 107 \\ 6 Auswahl der Finanztransaktionen / 109 \\ 6.1 Finanztransaktionen / 109 \\ 6.2 Auswahl der Daten f{\"u}r die Untersuchung / 111 \\ 7 Modellentwurf der Datentransformation / 114 \\ 7.1 Import Datenmodell / 120 \\ 7.2 Target Datenmodell / 123 \\ 8 Datenstrukturen, Datenselection und Unwandlung / 128 \\ 8.1 Datenstrukturen des Initialen Datenmodells / 130 \\ 8.2 Datenstrukturen des Import Datenmodells / 133 \\ 8.3 Datenstrukturen des Target Datenmodells / 136 \\ 9. Data Mining / 140 \\ 9.1 Bewertung der Transaktionen / 141 \\ 9.2 Die Tests / 152 \\ 9.3 Interpretation der Ergebnisse / 155 \\ 9.4 Anwendung in der Praxis / 158 \\ Glossar / 166 \\ Literaturverzeichnis / 179 \\ Anh{\"a}nge / 181", } @Article{Olver:2014:MIM, author = "F. W. J. Olver", title = "Mathematics that has intrigued me", journal = j-ANAL-APPL, volume = "12", number = "4", pages = "341--354", year = "2014", DOI = "https://doi.org/10.1142/S0219530514500262", ISSN = "0219-5305 (print), 1793-6861 (electronic)", ISSN-L = "0219-5305", MRclass = "33-03 (01A70 39A06 65-03)", MRnumber = "3218916", bibdate = "Sun Nov 5 09:03:34 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Lecture delivered at Asymptotics and Applied Analysis, Conference in Honor of Frank W. J. Olver's 75th Birthday, January 10--14, 2000, San Diego State University, San Diego, California.", acknowledgement = ack-nhfb, ajournal = "Anal. Appl. (Singap.)", author-dates = "Frank William John Olver (15 December 1924--23 April 2013)", fjournal = "Analysis and Applications", journal-URL = "https://www.worldscientific.com/worldscinet/aa", remark = "This paper was completed after Frank Olver's death by his son, Peter J. Olver, from handwritten notes. It also contains a summary of Frank Olver's education and career. In the paper, Frank Olver discusses the application of Benford's Law to test data selection.", } @Article{Rane:2014:BLG, author = "Ameya Deepak Rane and Utkarsh Mishra and Anindya Biswas and Aditi Sen(De) and Ujjwal Sen", title = "{Benford's Law} gives better scaling exponents in phase transitions of quantum {$ X Y $} models", journal = j-PHYS-REV-E, volume = "90", number = "2", pages = "022144:1--022144:8", day = "29", month = aug, year = "2014", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.90.022144", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", bibdate = "Tue Jan 26 10:14:12 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.90.022144", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", numpages = "8", } @Article{Rauch:2014:DPM, author = "Bernhard Rauch and Max G{\"o}ttsche and Stephan Langenegger", title = "Detecting Problems in Military Expenditure Data Using Digital Analysis", journal = "Defence and Peace Economics", volume = "25", number = "2", pages = "97--111", month = "????", year = "2014", DOI = "https://doi.org/10.1080/10242694.2013.763438", bibdate = "Sat Sep 10 15:55:05 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/10242694.2013.763438", accepted = "07 Dec 2012", acknowledgement = ack-nhfb, journal-URL = "http://www.tandfonline.com/toc/gdpe20", keywords = "Benford's Law; digital analysis; forensic accounting,; military expenditure data", received = "24 May 2012", } @Article{Rauch:2014:DVS, author = "Bernhard Rauch and Max G{\"o}ttsche and Gernot Br{\"a}hler and Thomas Kronfeld", title = "Deficit versus Social Statistics: Empirical Evidence for the Effectiveness of {Benford's Law}", journal = j-APPL-ECON-LETT, volume = "21", number = "3", pages = "147--151", month = "????", year = "2014", DOI = "https://doi.org/10.1080/13504851.2013.844319", ISSN = "1350-4851 (print), 1466-4291 (electronic)", ISSN-L = "1350-4851", bibdate = "Sat Sep 10 15:51:42 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/13504851.2013.844319", acknowledgement = ack-nhfb, fjournal = "Applied Economics Letters", journal-URL = "http://www.tandfonline.com/toc/RAEL20", keywords = "Benford's Law", } @Article{Roukema:2014:FDA, author = "Boudewijn F. Roukema", title = "A first-digit anomaly in the {2009 Iranian Presidential} election", journal = j-J-APPL-STAT, volume = "41", number = "1", pages = "164--199", year = "2014", DOI = "https://doi.org/10.1080/02664763.2013.838664", ISSN = "0266-4763 (print), 1360-0532 (electronic)", ISSN-L = "0266-4763", MRclass = "Database Expansion Item", MRnumber = "3291207", bibdate = "Wed Mar 5 08:09:17 MST 2014", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/japplstat.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/cjas20", } @Article{Savanur:2014:LLA, author = "Kiran Savanur and S. Gayathri Devi and P. V. Konnur", title = "{Lotka's Law} and Authorship Distribution in the Journal of `{{\booktitle{Columbia Law Review}}}'", journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE, volume = "8", number = "1", pages = "193--208", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1080/09737766.2014.947840", ISSN = "0973-7766 (print), 2168-930X (electronic)", ISSN-L = "0973-7766", bibdate = "Thu Sep 10 17:47:12 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib", acknowledgement = ack-nhfb, fjournal = "Collnet Journal of Scientometrics and Information Management", journal-URL = "http://www.tandfonline.com/loi/tsim20", } @Article{Sjoberg:2014:AAS, author = "Fredrik M. Sjoberg", title = "Autocratic adaptation: The strategic use of transparency and the persistence of election fraud", journal = j-ELECT-STUDIES, volume = "33", number = "0", pages = "233--245", year = "2014", DOI = "https://doi.org/10.1016/j.electstud.2013.08.004", ISSN = "0261-3794 (print), 1873-6890 (electronic)", ISSN-L = "0261-3794", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0261379413001273", abstract = "Why would an autocrat want, or at least make it appear to want, to reduce election fraud? In recent years, non-democratic rulers have surprisingly begun to embrace fraud-reducing technologies, like web cameras or transparent ballot boxes. The reason for this is found in the relative ease by which one type of fraud can be replaced with another. With the help of new fraud identification techniques, I argue that the installation of web cameras in polling stations changes how fraud is conducted. Web cameras do not reduce fraud, but rather make certain blatant forms of fraud, like ballot box stuffing, more costly. Autocrats then substitute for other types of fraud, such as fabricating the vote count out of view of the cameras.", acknowledgement = ack-nhfb, fjournal = "Electoral Studies", keywords = "Autocracy; Benford's Law; Election fraud; Election monitoring; Fraud forensics; Web cameras; {ICT}", } @Article{Tripathi:2014:IEP, author = "Yogesh Mani Tripathi and Somesh Kumar and C. Petropoulos", title = "Improved estimators for parameters of a {Pareto} distribution with a restricted scale", journal = j-STAT-METHODOL, volume = "18", number = "??", pages = "1--13", month = may, year = "2014", CODEN = "????", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Fri Feb 6 07:45:59 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312713000749", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", } @Article{Wojcik:2014:CBL, author = "Micha{\l} Ryszard W{\'o}jcik", title = "A characterization of {Benford's Law} through generalized scale-invariance", journal = j-MATH-SOC-SCI, volume = "71", number = "??", pages = "1--5", month = sep, year = "2014", DOI = "https://doi.org/10.1016/j.mathsocsci.2014.03.006", ISSN = "0165-4896 (print), 1879-3118 (electronic)", ISSN-L = "0165-4896", MRclass = "60E05 (62E10)", MRnumber = "3249768", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0165489614000262", abstract = "If $X$ is uniformly distributed modulo $1$ and $Y$ is independent of $X$ then $ Y + X$ is also uniformly distributed modulo $1$. We prove a converse for any continuous random variable $Y$ (or a reasonable approximation to a continuous random variable) so that if $X$ and $ Y + X$ are equally distributed modulo $1$ and $Y$ is independent of $X$ then $X$ is uniformly distributed modulo $1$ (or approximates the uniform distribution equally reasonably). This translates into a characterization of Benford's Law through a generalization of scale-invariance: from multiplication by a constant to multiplication by an independent random variable.", acknowledgement = ack-nhfb, fjournal = "Mathematical Social Sciences", journal-URL = "http://www.sciencedirect.com/science/journal/01654896", keywords = "Benford's Law", } @Article{Xie:2014:GTK, author = "Min Xie and Laks V. S. Lakshmanan and Peter T. Wood", title = "Generating top-$k$ packages via preference elicitation", journal = j-PROC-VLDB-ENDOWMENT, volume = "7", number = "14", pages = "1941--1952", month = oct, year = "2014", CODEN = "????", ISSN = "2150-8097", ISSN-L = "2150-8097", bibdate = "Wed Feb 4 17:20:43 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/vldbe.bib", abstract = "There are several applications, such as play lists of songs or movies, and shopping carts, where users are interested in finding top-$k$ packages, consisting of sets of items. In response to this need, there has been a recent flurry of activity around extending classical recommender systems (RS), which are effective at recommending individual items, to recommend packages, or sets of items. The few recent proposals for package RS suffer from one of the following drawbacks: they either rely on hard constraints which may be difficult to be specified exactly by the user or on returning Pareto-optimal packages which are too numerous for the user to sift through. To overcome these limitations, we propose an alternative approach for finding personalized top-$k$ packages for users, by capturing users' preferences over packages using a linear utility function which the system learns. Instead of asking a user to specify this function explicitly, which is unrealistic, we explicitly model the uncertainty in the utility function and propose a preference elicitation-based framework for learning the utility function through feedback provided by the user. We propose several sampling-based methods which, given user feedback, can capture the updated utility function. We develop an efficient algorithm for generating top-$k$ packages using the learned utility function, where the rank ordering respects any of a variety of ranking semantics proposed in the literature. Through extensive experiments on both real and synthetic datasets, we demonstrate the efficiency and effectiveness of the proposed system for finding top-$k$ packages.", acknowledgement = ack-nhfb, fjournal = "Proceedings of the VLDB Endowment", journal-URL = "http://portal.acm.org/citation.cfm?id=J1174", } @Article{Yang:2014:RAE, author = "Z. K. Yang and D. M. Lin and M. Z. Xu", title = "The Re-applicability Explore of {Lotka's Law} in Patent Documents", journal = j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE, volume = "8", number = "1", pages = "183--191", year = "2014", CODEN = "????", DOI = "https://doi.org/10.1080/09737766.2014.916875", ISSN = "0973-7766 (print), 2168-930X (electronic)", ISSN-L = "0973-7766", bibdate = "Thu Sep 10 17:47:12 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib", acknowledgement = ack-nhfb, fjournal = "Collnet Journal of Scientometrics and Information Management", journal-URL = "http://www.tandfonline.com/loi/tsim20", } @Article{Zahran:2014:EAS, author = "Sammy Zahran and Terrence Iverson and Stephan Weiler and Anthony Underwood", title = "Evidence that the accuracy of self-reported lead emissions data improved: A puzzle and discussion", journal = j-J-RISK-UNCERT, volume = "49", number = "3", pages = "235--257", year = "2014", CODEN = "JRUNEN", DOI = "https://doi.org/10.1007/s11166-014-9204-1", ISSN = "0895-5646 (print), 1573-0476 (electronic)", ISSN-L = "0895-5646", bibdate = "Sat Sep 10 14:35:50 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Risk and Uncertainty", journal-URL = "http://link.springer.com/journal/11166", keywords = "Benford's Law", } @Article{Zomaya:2014:POC, author = "Albert Y. Zomaya", title = "{Pareto}-Optimal Cloud Bursting", journal = j-IEEE-TRANS-PAR-DIST-SYS, volume = "25", number = "10", pages = "2670--2682", month = oct, year = "2014", CODEN = "ITDSEO", ISSN = "1045-9219 (print), 1558-2183 (electronic)", ISSN-L = "1045-9219", bibdate = "Thu Feb 12 13:58:32 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib", URL = "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html", abstract-URL = "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Parallel and Distributed Systems", journal-URL = "http://www.computer.org/tpds/archives.htm", } @Article{Abushal:2015:EPP, author = "Tahani A. Abushal and Ahmed A. Soliman", title = "Estimating the {Pareto} parameters under progressive censoring data for constant-partially accelerated life tests", journal = j-J-STAT-COMPUT-SIMUL, volume = "85", number = "5", pages = "917--934", year = "2015", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949655.2013.853768", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Wed Feb 11 16:24:25 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", } @Article{Ausloos:2015:BBL, author = "M. Ausloos and C. Herteliu and B. Ileanu", title = "Breakdown of {Benford's Law} for birth data", journal = j-PHYSICA-A, volume = "419", number = "0", pages = "736--745", year = "2015", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2014.10.041", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437114008796", abstract = "Long birth time series for Romania are investigated from Benford's Law point of view, distinguishing between families with a religious (Orthodox and Non-Orthodox) affiliation. The data extend from Jan. 01, 1905 till Dec. 31, 2001, i.e. over 97 years or 35\,429 days. The results point to a drastic breakdown of Benford's Law. Some interpretation is proposed, based on the statistical aspects due to population sizes, rather than on human thought constraints when the law breakdown is usually expected. Benford's Law breakdown clearly points to natural causes.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Benford's Laws; Births; Non-Orthodoxes; Orthodoxes; Religious community; Time series", } @Book{Bahmann:2015:AMM, author = "Paul Bahmann", title = "{Eine Analyse von monet{\"a}ren, makro{\"o}konomischen Daten der BRD und DDR: Ziffernanalyse auf Grundlage des Benford's Law}. ({German}) [{An} analysis of monetary, macroeconomic data of the {FRG} and the {GDR}: numeric analysis on the basis of {Benford's Law}]", publisher = "AV Akademikerverlag", address = "Saarbr{\"u}cken, Germany", pages = "76", year = "2015", ISBN = "3-639-80882-7", ISBN-13 = "978-3-639-80882-7", LCCN = "????", bibdate = "Sat Jan 23 07:58:34 MST 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Balanzario:2015:BLM, author = "Eugenio P. Balanzario", title = "{Benford's Law} for mixtures", journal = j-COMMUN-STAT-THEORY-METH, volume = "44", number = "4", pages = "698--709", year = "2015", CODEN = "CSTMDC", DOI = "https://doi.org/10.1080/03610926.2012.752849", ISSN = "0361-0926 (print), 1532-415X (electronic)", ISSN-L = "0361-0926", MRclass = "60E05 (60G57)", MRnumber = "3315782", bibdate = "Tue Jan 26 11:02:38 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics. Theory and Methods", journal-URL = "http://www.tandfonline.com/loi/lsta20", } @Article{Beck:2015:PPI, author = "M{\'e}lanie Beck and Martin J. Gander", title = "On the positivity of {Poisson} integrators for the {Lotka--Volterra} equations", journal = j-BIT-NUM-MATH, volume = "55", number = "2", pages = "319--340", month = jun, year = "2015", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/s10543-014-0505-1", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Sat Aug 8 13:47:11 MDT 2015", bibsource = "http://link.springer.com/journal/10543/55/2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib", URL = "http://link.springer.com/article/10.1007/s10543-014-0505-1", acknowledgement = ack-nhfb, fjournal = "BIT Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", } @Book{Berger:2015:IBL, author = "Arno Berger and Theodore P. Hill", title = "An introduction to {Benford's Law}", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "viii + 248", year = "2015", DOI = "https://doi.org/10.1515/9781400866588", ISBN = "0-691-16306-5, 1-4008-6658-8 (e-book)", ISBN-13 = "978-0-691-16306-2, 978-1-4008-6658-8 (e-book)", LCCN = "QA273.6 .B474 2015", bibdate = "Fri Jan 22 12:19:25 MST 2016", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", URL = "http://site.ebrary.com/id/11040167; http://www.degruyter.com/viewbooktoc/product/465875", acknowledgement = ack-nhfb, subject = "Distribution; Probability measures", tableofcontents = "Preface / vii 1 Introduction / 1 \\ 1.1 History / 3 \\ 1.2 Empirical evidence / 4 \\ 1.3 Early explanations / 6 \\ 1.4 Mathematical framework / 7 \\ 2 Significant Digits and the Significand / 11 \\ 2.1 Significant digits / 11 \\ 2.2 The significand / 12 \\ 2.3 The significand s-algebra / 14 \\ 3 The Benford Property / 22 \\ 3.1 Benford sequences / 23 \\ 3.2 Benford functions / 28 \\ 3.3 Benford distributions and random variables / 29 \\ 4 The Uniform Distribution and Benford's Law / 43 \\ 4.1 Uniform distribution characterization of Benford's law / 43 \\ 4.2 Uniform distribution of sequences and functions / 46 \\ 4.3 Uniform distribution of random variables / 54 \\ 5 Scale-, Base-, and Sum-Invariance / 63 \\ 5.1 The scale-invariance property / 63 \\ 5.2 The base-invariance property / 74 \\ 5.3 The sum-invariance property / 80 \\ 6 Real-valued Deterministic Processes / 90 \\ 6.1 Iteration of functions / 90 \\ 6.2 Sequences with polynomial growth / 93 \\ 6.3 Sequences with exponential growth / 97 \\ 6.4 Sequences with super-exponential growth / 101 \\ 6.5 An application to Newton's method / 111 \\ 6.6 Time-varying systems / 116 \\ 6.7 Chaotic systems: Two examples / 124 \\ 6.8 Differential equations / 127 \\ 7 Multi-dimensional Linear Processes / 135 \\ 7.1 Linear processes, observables, and difference equations / 135 \\ 7.2 Nonnegative matrices / 139 \\ 7.3 General matrices / 145 \\ 7.4 An application to Markov chains / 162 \\ 7.5 Linear difference equations / 165 \\ 7.6 Linear differential equations / 170 \\ 8 Real-valued Random Processes / 180 \\ 8.1 Convergence of random variables to Benford's law / 180 \\ 8.2 Powers, products, and sums of random variables / 182 \\ 8.3 Mixtures of distributions / 202 \\ 8.4 Random maps / 213 \\ 9 Finitely Additive Probability and Benford's Law / 216 \\ 9.1 Finitely additive probabilities / 217 \\ 9.2 Finitely additive Benford probabilities / 219 \\ 10 Applications of Benford's Law / 223 \\ 10.1 Fraud detection / 224 \\ 10.2 Detection of natural phenomena / 225 \\ 10.3 Diagnostics and design / 226 \\ 10.4 Computations and Computer Science / 228 \\ 10.5 Pedagogical tool / 230 \\ List of Symbols / 231 \\ Bibliography / 234 \\ Index / 245", } @Article{Berger:2015:MLF, author = "Arno Berger", title = "Most linear flows on {$ R^d $} are {Benford}", journal = j-J-DIFFER-EQU, volume = "259", number = "5", pages = "1933--1957", year = "2015", CODEN = "JDEQAK", DOI = "https://doi.org/10.1016/j.jde.2015.03.016", ISSN = "0022-0396 (print), 1090-2732 (electronic)", ISSN-L = "0022-0396", MRclass = "60F99 (11J71 11K41 37A05 37A45 62E20)", MRnumber = "3349424", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022039615001527", abstract = "A necessary and sufficient condition (exponential nonresonance) is established for every signal obtained from a linear flow on $ R^d $ by means of a linear observable to either vanish identically or else exhibit a strong form of Benford's Law (logarithmic distribution of significant digits). The result extends and unifies all previously known (sufficient) conditions. Exponential nonresonance is shown to be typical for linear flows, both from a topological and a measure-theoretical point of view.", acknowledgement = ack-nhfb, fjournal = "Journal of Differential Equations", keywords = "(Continuous) uniform distribution mod 1; (Exponentially) nonresonant set; Benford function; Linear flow; Observable; Q -independence", } @InCollection{Berger:2015:SIM, author = "Arno Berger and T. P. Hill", title = "A short introduction to the mathematical theory of {Benford's Law}", crossref = "Miller:2015:BLT", pages = "23--67", year = "2015", DOI = "https://doi.org/10.1515/9781400866588", MRclass = "37A45 (11K06 60-02 60F15 60G57 62E10)", MRnumber = "3411057", bibdate = "Sat Mar 25 08:23:36 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Bermano:2015:DST, author = "Amit Bermano and Thabo Beeler and Yeara Kozlov and Derek Bradley and Bernd Bickel and Markus Gross", title = "Detailed spatio-temporal reconstruction of eyelids", journal = j-TOG, volume = "34", number = "4", pages = "44:1--44:??", month = aug, year = "2015", CODEN = "ATGRDF", DOI = "https://doi.org/10.1145/2766924", ISSN = "0730-0301 (print), 1557-7368 (electronic)", ISSN-L = "0730-0301", bibdate = "Tue Jul 28 17:22:44 MDT 2015", bibsource = "http://www.acm.org/pubs/contents/journals/tog/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tog.bib", abstract = "In recent years we have seen numerous improvements on 3D scanning and tracking of human faces, greatly advancing the creation of digital doubles for film and video games. However, despite the high-resolution quality of the reconstruction approaches available, current methods are unable to capture one of the most important regions of the face --- the eye region. In this work we present the first method for detailed spatio-temporal reconstruction of eyelids. Tracking and reconstructing eyelids is extremely challenging, as this region exhibits very complex and unique skin deformation where skin is folded under while opening the eye. Furthermore, eyelids are often only partially visible and obstructed due to self-occlusion and eyelashes. Our approach is to combine a geometric deformation model with image data, leveraging multi-view stereo, optical flow, contour tracking and wrinkle detection from local skin appearance. Our deformation model serves as a prior that enables reconstruction of eyelids even under strong self-occlusions caused by rolling and folding skin as the eye opens and closes. The output is a person-specific, time-varying eyelid reconstruction with anatomically plausible deformations. Our high-resolution detailed eyelids couple naturally with current facial performance capture approaches. As a result, our method can largely increase the fidelity of facial capture and the creation of digital doubles.", acknowledgement = ack-nhfb, articleno = "44", fjournal = "ACM Transactions on Graphics", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J778", } @Article{Berzunza:2015:YPR, author = "Gabriel Berzunza", title = "{Yule} processes with rare mutation and their applications to percolation on $b$-ary trees", journal = j-ELECTRON-J-PROBAB, volume = "20", number = "??", pages = "43:1--43:23", month = "????", year = "2015", CODEN = "????", ISSN = "1083-6489", ISSN-L = "1083-6489", bibdate = "Fri Aug 7 10:50:36 MDT 2015", bibsource = "http://ejp.ejpecp.org/index.php/ejp/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ejp.bib", URL = "http://ejp.ejpecp.org/article/view/3789", acknowledgement = ack-nhfb, fjournal = "Electronic Journal of Probability", journal-URL = "http://ejp.ejpecp.org/", } @Article{Bhole:2015:BAU, author = "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh", title = "{Benford} analysis: A useful paradigm for spectroscopic analysis", journal = j-CHEM-PHYS-LETT, volume = "639", number = "??", pages = "36--40", year = "2015", CODEN = "CHPLBC", DOI = "https://doi.org/10.1016/j.cplett.2015.08.061", ISSN = "0009-2614 (print), 1873-4448 (electronic)", ISSN-L = "0009-2614", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0009261415006582", abstract = "Benford's law is a statistical inference to predict the frequency of significant digits in naturally occurring numerical databases. In such databases this law predicts a higher occurrence of the digit $1$ in the most significant place and decreasing occurrences to other larger digits. Although counter-intuitive at first sight, Benford's law has seen applications in a wide variety of fields like physics, earth-science, biology, finance, etc. In this work, we have explored the use of Benford's law for various spectroscopic applications. Although, we use NMR signals as our databases, the methods described here may also be extended to other spectroscopic techniques. In particular, with the help of Benford analysis, we demonstrate emphasizing weak NMR signals and spectral corrections. We also explore a potential application of Benford analysis in the image-processing of MRI data.", acknowledgement = ack-nhfb, fjournal = "Chemical Physics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/00092614", } @Article{Biau:2015:FDF, author = "Damien Biau", title = "The first-digit frequencies in data of turbulent flows", journal = j-PHYSICA-A, volume = "440", number = "??", pages = "147--154", day = "15", month = dec, year = "2015", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2015.08.016", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "76F20 (82B05)", MRnumber = "3398896", bibdate = "Tue Jan 26 11:15:41 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Brunsch:2015:ISA, author = "Tobias Brunsch and Heiko R{\"o}glin", title = "Improved Smoothed Analysis of Multiobjective Optimization", journal = j-J-ACM, volume = "62", number = "1", pages = "4:1--4:??", month = feb, year = "2015", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/2699445", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Tue Mar 3 12:47:00 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", abstract = "We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the last decade. We consider problems in which d linear and one arbitrary objective function are to be optimized over a set $ S \subseteq \{ 0, 1 \}^n $ of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to $ O(n^{2 d} \phi^d) $, where $ \phi $ denotes the perturbation parameter. Additionally, we show that for any constant $c$ the $c$ th moment of the smoothed number of Pareto-optimal solutions is bounded by $ O((n^{2 d} \phi^d)^c)$. This improves the previously best known bounds significantly. Furthermore, we address the criticism that the perturbations in smoothed analysis destroy the zero-structure of problems by showing that the smoothed number of Pareto-optimal solutions remains polynomially bounded even for zero-preserving perturbations. This broadens the class of problems captured by smoothed analysis and it has consequences for nonlinear objective functions. One corollary of our result is that the smoothed number of Pareto-optimal solutions is polynomially bounded for polynomial objective functions. Our results also extend to integer optimization problems.", acknowledgement = ack-nhfb, articleno = "4", fjournal = "Journal of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Cacciari:2015:DMC, author = "I. Cacciari and P. Nieri and S. Siano", title = "{$3$D} Digital Microscopy for Characterizing Punchworks on Medieval Panel Paintings", journal = j-JOCCH, volume = "7", number = "4", pages = "19:1--19:??", month = feb, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2594443", ISSN = "1556-4673 (print), 1556-4711 (electronic)", ISSN-L = "1556-4673", bibdate = "Wed Feb 11 13:42:37 MST 2015", bibsource = "http://www.acm.org/pubs/contents/journals/jocch/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jocch.bib", abstract = "This article is devoted to a novel application of the micro-3D modeling based on shape from focus. A 3D portable digital microscope prototype has been used for the first time in order to analyze gold punchwork on medieval panel paintings. In general, the 3D domain provides a more flexible and complete characterization of these decorative elements than traditional photographic documentation. Low-magnification 3D digital microscopy is well suited for analyzing morphologies, depths, and profiles of different punch marks. Here, we used these parameters for interpreting the punching process and recognizing sliding and bouncing effects. The 3D reconstruction of the surface engraved also allowed identifying types of anomalies that could be useful as possible authentication markers. The advantages of the present approach with respect to the photographic documentation are of general valence and can be exploited in order to document, parameterize, and interpret a variety of engraving works on panel paintings and metal artifacts.", acknowledgement = ack-nhfb, articleno = "19", fjournal = "Journal on Computing and Cultural Heritage (JOCCH)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157", } @Article{Carrera:2015:TER, author = "C{\'e}sar Carrera", title = "Tracking exchange rate management in {Latin America}", journal = "Review of Financial Economics", volume = "25", number = "??", pages = "35--41", year = "2015", DOI = "https://doi.org/10.1016/j.rfe.2015.02.004", ISSN = "1058-3300 (print), 1873-5924 (electronic)", ISSN-L = "1058-3300", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Special Issue on Changing Dynamics in Financial Economics", URL = "http://www.sciencedirect.com/science/article/pii/S105833001500018X", abstract = "One way to track exchange-rate deviations from its long-run value is to examine numerical patterns in exchange rates to see if those patterns appear to have been subjected to some degree of policy management. We apply Benford's Law to exchange rates in Latin American countries, computing and comparing the distribution of exchange-rate observed values with those of Benford's Law. For most cases we find that the exchange rate for the US dollar does not satisfy Benford's Law, however this law holds when the euro is considered. This result may be explained by the fact that these countries are characterized for having different degrees of dollarization and intervention in the US dollar forex market while there is almost no policy intervention in the euro forex market. Our approach is an alternative view of how these characteristics play a role inducing deviations with respect to an implied equilibrium exchange rate.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Exchange rate; Forex; FX intervention; International reserves", } @Article{Chaves-Gonzalez:2015:DEP, author = "Jos{\'e} M. Chaves-Gonz{\'a}lez and Miguel A. P{\'e}rez-Toledano", title = "Differential evolution with {Pareto} tournament for the multi-objective next release problem", journal = j-APPL-MATH-COMP, volume = "252", number = "??", pages = "1--13", day = "1", month = feb, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Wed Feb 18 09:36:18 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300314016257", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Cuff:2015:WDB, author = "Victoria Cuff and Allison Lewis and Steven J. Miller", title = "The {Weibull} distribution and {Benford's Law}", journal = "Involve", volume = "8", number = "5", pages = "859--874", year = "2015", DOI = "https://doi.org/10.2140/involve.2015.8.859", ISSN = "1944-4176 (print), 1944-4184 (electronic)", ISSN-L = "1944-4176", MRclass = "60F05 (11K06 42A16 60E10 62E15 62P99)", MRnumber = "3404662", MRreviewer = "Nikolai Volodin", bibdate = "Tue Jan 26 11:03:29 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Involve. A Journal of Mathematics", journal-URL = "http://msp.org/involve/", } @Article{Dandurand:2015:DCP, author = "Brian Dandurand and Margaret M. Wiecek", title = "Distributed Computation of {Pareto} Sets", journal = j-SIAM-J-OPT, volume = "25", number = "2", pages = "1083--1109", month = "????", year = "2015", CODEN = "SJOPE8", DOI = "https://doi.org/10.1137/130929564", ISSN = "1052-6234 (print), 1095-7189 (electronic)", ISSN-L = "1052-6234", bibdate = "Sat Aug 8 07:33:46 MDT 2015", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/25/2; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/siamjopt.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Optimization", journal-URL = "http://epubs.siam.org/siopt", onlinedate = "January 2015", } @Article{delCastillo:2015:LIG, author = "Joan del Castillo and Isabel Serra", title = "Likelihood inference for generalized {Pareto} distribution", journal = j-COMPUT-STAT-DATA-ANAL, volume = "83", number = "??", pages = "116--128", month = mar, year = "2015", CODEN = "CSDADW", ISSN = "0167-9473 (print), 1872-7352 (electronic)", ISSN-L = "0167-9473", bibdate = "Fri Feb 6 11:44:05 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167947314003065", acknowledgement = ack-nhfb, fjournal = "Computational Statistics \& Data Analysis", journal-URL = "http://www.sciencedirect.com/science/journal/01679473", } @Article{Ferreira:2015:LPA, author = "Anselmo Ferreira and Luiz C. Navarro and Giuliano Pinheiro and Jefersson A. dos Santos and Anderson Rocha", title = "Laser printer attribution: Exploring new features and beyond", journal = "Forensic Science International", volume = "247", number = "0", pages = "105--125", year = "2015", DOI = "https://doi.org/10.1016/j.forsciint.2014.11.030", ISSN = "0379-0738 (print), 1872-6283 (electronic)", ISSN-L = "0379-0738", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib", note = "See also \cite{Jiang:2010:NMS}.", URL = "http://www.sciencedirect.com/science/article/pii/S0379073814005064", abstract = "With a huge amount of printed documents nowadays, identifying their source is useful for criminal investigations and also to authenticate digital copies of a document. In this paper, we propose novel techniques for laser printer attribution. Our solutions do not need very high resolution scanning of the investigated document and explore the multidirectional, multiscale and low-level gradient texture patterns yielded by printing devices. The main contributions of this work are: (1) the description of printed areas using multidirectional and multiscale co-occurring texture patterns; (2) description of texture on low-level gradient areas by a convolution texture gradient filter that emphasizes textures in specific transition areas and (3) the analysis of printer patterns in segments of interest, which we call frames, instead of whole documents or only printed letters. We show by experiments in a well documented dataset that the proposed methods outperform techniques described in the literature and present near-perfect classification accuracy being very promising for deployment in real-world forensic investigations.", acknowledgement = ack-nhfb, keywords = "Banding; Benford's Law; Printer forensics; Texture patterns", } @Article{Garrabrant:2015:ALU, author = "Scott Garrabrant and Siddharth Bhaskar and Abram Demski and Joanna Garrabrant and George Koleszarik and Evan Lloyd", title = "Asymptotic Logical Uncertainty and The {Benford} Test", journal = "CoRR", volume = "??", number = "??", pages = "??--??", month = "????", year = "2015", CODEN = "????", DOI = "https://doi.org/10.48550/arXiv.1510.03370", ISSN = "????", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1510.03370; https://dblp.org/db/journals/corr/corr1510.html#GarrabrantBDGKL15", abstract = "We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs ``true'' with probability $p$, we have that the sequence of probabilities that A assigns to these sentences converges to $p$.", acknowledgement = ack-nhfb, DBLP-key = "journals/corr/GarrabrantBDGKL15", DBLP-mdate = "2018-08-13", } @Article{Goegebeur:2015:ETI, author = "Yuri Goegebeur and Armelle Guillou and Michael Osmann", title = "An estimator for the tail index of an integrated conditional {Pareto--Weibull}-type model", journal = j-STAT-PROB-LETT, volume = "103", number = "??", pages = "8--16", month = aug, year = "2015", CODEN = "SPLTDC", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", bibdate = "Mon Jun 8 18:57:37 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715215001182", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", } @Article{Goel:2015:PCA, author = "Gagan Goel and Vahab Mirrokni and Renato Paes Leme", title = "Polyhedral Clinching Auctions and the {AdWords} Polytope", journal = j-J-ACM, volume = "62", number = "3", pages = "18:1--18:??", month = jun, year = "2015", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/2757277", ISSN = "0004-5411 (print), 1557-735X (electronic)", ISSN-L = "0004-5411", bibdate = "Fri Aug 7 10:12:49 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", abstract = "A central issue in applying auction theory in practice is the problem of dealing with budget-constrained agents. A desirable goal in practice is to design incentive compatible, individually rational, and Pareto optimal auctions while respecting the budget constraints. Achieving this goal is particularly challenging in the presence of nontrivial combinatorial constraints over the set of feasible allocations. Toward this goal and motivated by AdWords auctions, we present an auction for polymatroidal environments satisfying these properties. Our auction employs a novel clinching technique with a clean geometric description and only needs an oracle access to the submodular function defining the polymatroid. As a result, this auction not only simplifies and generalizes all previous results, it applies to several new applications including AdWords Auctions, bandwidth markets, and video on demand. In particular, our characterization of the AdWords auction as polymatroidal constraints might be of independent interest. This allows us to design the first mechanism for Ad Auctions taking into account simultaneously budgets, multiple keywords and multiple slots. We show that it is impossible to extend this result to generic polyhedral constraints. This also implies an impossibility result for multiunit auctions with decreasing marginal utilities in the presence of budget constraints.", acknowledgement = ack-nhfb, articleno = "18", fjournal = "Journal of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Gunasekera:2015:GIR, author = "Sumith Gunasekera", title = "Generalized inferences of {$ R = \Pr (X > Y) $} for {Pareto} distribution", journal = j-STAT-PAPERS, volume = "56", number = "2", pages = "333--351", month = may, year = "2015", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-014-0584-8", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Fri Apr 10 15:56:09 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/article/10.1007/s00362-014-0584-8", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Han:2015:PSS, author = "Qixing Han and Daqing Jiang", title = "Periodic solution for stochastic non-autonomous multispecies {Lotka--Volterra} mutualism type ecosystem", journal = j-APPL-MATH-COMP, volume = "262", number = "??", pages = "204--217", day = "1", month = jul, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Mon May 18 12:21:15 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300315005007", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Hu:2015:EES, author = "Yangzi Hu and Fuke Wu", title = "Exponential extinction of a stochastic {Lotka--Volterra} model with expectations in coefficients", journal = j-IMA-J-APPL-MATH, volume = "80", number = "4", pages = "1219--1234", month = aug, year = "2015", CODEN = "IJAMDM", DOI = "https://doi.org/10.1093/imamat/hxu050", ISSN = "0272-4960 (print), 1464-3634 (electronic)", ISSN-L = "0272-4960", bibdate = "Sat Jul 25 19:12:11 MDT 2015", bibsource = "http://imamat.oxfordjournals.org/contentcontent/80/4.toc; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/imajapplmath.bib", URL = "http://imamat.oxfordjournals.org/content/80/4/1219", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Applied Mathematics", journal-URL = "http://imamat.oxfordjournals.org/content/by/year", onlinedate = "October 23, 2014", } @Article{Hurlimann:2015:BLS, author = "Werner H{\"u}rlimann", title = "{Benford's Law} in Scientific Research", journal = j-INT-J-SCI-ENG-RESEARCH, volume = "6", number = "7", pages = "143--148", month = jul, year = "2015", ISSN = "2229-5518", ISSN-L = "2229-5518", bibdate = "Wed Jul 29 06:32:18 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.ijser.org/onlineResearchPaperViewer.aspx?Benfords-Law-in-Scientific-Research.pdf", abstract = "As departures from Benford's law have been observed in many scientific data sets, there is a theoretical need to understand such discrepancies. We argue that the use of parametric extensions to Benford's law is appropriate and demonstrate this for several first significant digit distributions taken from theoretical scientific laws or extracted from real-world data sets.", acknowledgement = ack-nhfb, fjournal = "International Journal of Scientific and Engineering Research", journal-URL = "http://www.ijser.org/", } @Article{Hurlimann:2015:FDT, author = "Werner H{\"u}rlimann", title = "A first digit theorem for powerful integer powers", journal = j-SPRINGERPLUS, volume = "4", number = "1", pages = "576:1--576:??", day = "6", month = oct, year = "2015", CODEN = "SPRIFB", DOI = "https://doi.org/10.1186/s40064-015-1370-3", ISSN = "2193-1801", ISSN-L = "2193-1801", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1186/s40064-015-1370-3", acknowledgement = ack-nhfb, fjournal = "SpringerPlus", journal-URL = "http://link.springer.com/journal/40064", keywords = "Benford's Law", } @Article{Hurlimann:2015:URU, author = "Werner H{\"u}rlimann", title = "On the uniform random upper bound family of first significant digit distributions", journal = j-J-INFORMETRICS, volume = "9", number = "2", pages = "349--358", year = "2015", DOI = "https://doi.org/10.1016/j.joi.2015.02.007", ISSN = "1751-1577 (print), 1875-5879 (electronic)", ISSN-L = "1751-1577", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1751157715000255", abstract = "The first significant digit patterns arising from a mixture of uniform distributions with a random upper bound are revisited. A closed-form formula for its first significant digit distribution (FSD) is obtained. The one-parameter model of Rodriguez is recovered for an extended truncated Pareto mixing distribution. Considering additionally the truncated Erlang, gamma and Burr mixing distributions, and the generalized Benford law, for which another probabilistic derivation is offered, we study the fitting capabilities of the FSD's for various Benford like data sets from scientific research. Based on the results, we propose the general use of a fine structure index for Benford's law in case the data is well fitted by the truncated Erlang member of the uniform random upper bound family of FSD's.", acknowledgement = ack-nhfb, fjournal = "Journal of Informetrics", journal-URL = "http://www.sciencedirect.com/science/journal/17511577", keywords = "Benford's law; Erlang distribution; Extended truncated Pareto; Simulation algorithm; Stigler's law; Uniform distribution", } @Article{Iafrate:2015:EDN, author = "Joseph R. Iafrate and Steven J. Miller and Frederick W. Strauch", title = "Equipartitions and a distribution for numbers: A statistical model for {Benford's Law}", journal = j-PHYS-REV-E, volume = "91", number = "6", pages = "062138:1--062138:6", month = jun, year = "2015", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/PhysRevE.91.062138", ISSN = "1539-3755 (print), 1550-2376 (electronic)", ISSN-L = "1539-3755", MRclass = "60E99 (82B05)", MRnumber = "3491369", bibdate = "Tue Jan 26 11:15:52 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.aps.org/doi/10.1103/PhysRevE.91.062138", acknowledgement = ack-nhfb, fjournal = "Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)", journal-URL = "http://pre.aps.org/browse", numpages = "6", } @Article{Khataei:2015:PPB, author = "Amirsam Khataei and Ali Arya", title = "Personalized presentation builder for persuasive communication", journal = j-COMMUN-DESIGN-Q-REVIEW, volume = "3", number = "3", pages = "25--32", month = may, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2792989.2792993", ISSN = "2166-1200 (print), 2166-1642 (electronic)", ISSN-L = "2166-1200", bibdate = "Wed Jun 17 19:00:11 MDT 2015", bibsource = "http://dl.acm.org/citation.cfm?id=J1351; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/commundesignqreview.bib", abstract = "Presentations are effective ways of communicating information, especially in the field of education, but they might not be equally or fully beneficial and persuasive to all users. Each member of the audience might be interested in a particular topic, come from a different background and profession, and have his or her own personality traits. In this conceptual paper, we first describe our persuasive personalization model; the Individualization Pyramid based on Yale Attitude Change Approach. The model consists of the following main sections: selecting contents by applying segmentation, adjusting comprehensibility of the text, tailoring the language of the text to fit with user's personality and recommending content that is associated with user's personal history within the related subjects. We then propose an enhanced version of our previously published presentation builder, which uses users' digital traces such as those on social media to personalize presentation content. Finally, we highlight the available tools and algorithms to assist us with developing the system.", acknowledgement = ack-nhfb, fjournal = "Communication Design Quarterly Review", journal-URL = "http://dl.acm.org/citation.cfm?id=J1351", } @Article{Khosravani:2015:DBC, author = "Azar Khosravani and Constantin Rasinariu", title = "$n$-digit {Benford} converges to {Benford}", journal = j-INT-J-MATH-MATH-SCI, pages = "Art. ID 123816, 4", year = "2015", DOI = "https://doi.org/10.1155/2015/123816", ISSN = "0161-1712 (print), 1687-0425 (electronic)", ISSN-L = "0161-1712", MRclass = "60F25 (11K45)", MRnumber = "3442627", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematics and Mathematical Sciences", journal-URL = "https://www.hindawi.com/journals/ijmms/", } @Book{Kossovsky:2015:BLT, author = "Alex Ely Kossovsky", title = "{Benford's Law}: theory, the general law of relative quantities, and forensic fraud detection applications", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xxi + 649", year = "2015", DOI = "https://doi.org/10.1142/9089", ISBN = "981-4583-68-5 (hardcover), 981-4583-69-3 (e-book)", ISBN-13 = "978-981-4583-68-8 (hardcover), 978-981-4583-69-5 (e-book)", LCCN = "HV8079.F7 K67 2015", bibdate = "Mon Feb 16 17:20:54 MST 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", abstract = "Contrary to common intuition that all digits should occur randomly with equal chances in real data, empirical examinations consistently show that not all digits are created equal, but rather that low digits such as {1, 2, 3} occur much more frequently than high digits such as {7, 8, 9} in almost all data types, such as those relating to geology, chemistry, astronomy, physics, and engineering, as well as in accounting, financial, econometrics, and demographics data sets. This intriguing digital phenomenon is known as Benford's Law. This book represents an attempt to give a comprehensive and in-depth account of all the theoretical aspects, results, causes and explanations of Benford's Law, with a strong emphasis on the connection to real-life data and the physical manifestation of the law. In addition to such a bird's eye view of the digital phenomenon, the conceptual distinctions between digits, numbers, and quantities are explored; leading to the key finding that the phenomenon is actually quantitative in nature; originating from the fact that in extreme generality, nature creates many small quantities but very few big quantities, corroborating the motto ``small is beautiful'', and that therefore all this is applicable just as well to data written in the ancient Roman, Mayan, Egyptian, and other digit-less civilizations. Fraudsters are typically not aware of this digital pattern and tend to invent numbers with approximately equal digital frequencies. The digital analyst can easily check reported data for compliance with this digital law, enabling the detection of tax evasion, Ponzi schemes, and other financial scams. The forensic fraud detection section in this book is written in a very concise and reader-friendly style; gathering all known methods and standards in the accounting and auditing industry; summarizing and fusing them into a singular coherent whole; and can be understood without deep knowledge in statistical theory or advanced mathematics. In addition, a digital algorithm is presented, enabling the auditor to detect fraud even when the sophisticated cheater is aware of the law and invents numbers accordingly. The algorithm employs a subtle inner digital pattern within the Benford's pattern itself. This newly discovered pattern is deemed to be nearly universal, being even more prevalent than the Benford phenomenon, as it is found in all random data sets, Benford as well as non-Benford types.", acknowledgement = ack-nhfb, subject = "Fraud investigation; Statistical methods; Fraud; Distribution (Probability theory); Forensic statistics; Forensic sciences", tableofcontents = "1. Benford's law \\ 2. Forensic digital analysis and fraud detection \\ 3. Data compliance tests \\ 4. Conceptual and mathematical foundations \\ 5. Benford's law in the physical sciences \\ 6. Topics in Benford's law \\ 7. The law of Relative quantities", } @Article{Kozubowski:2015:DTP, author = "Tomasz J. Kozubowski and Anna K. Panorska and Matthew L. Forister", title = "A discrete truncated {Pareto} distribution", journal = j-STAT-METHODOL, volume = "26", number = "??", pages = "135--150", month = sep, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1016/j.stamet.2015.04.002", ISSN = "1572-3127 (print), 1878-0954 (electronic)", ISSN-L = "1572-3127", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statmethodol.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1572312715000313", abstract = "We propose a new discrete distribution with finite support, which generalizes truncated Pareto and beta distributions as well as uniform and Benford's laws. Although our focus is on basic properties and stochastic representations, we also consider parameter estimation and include an illustration from ecology showing potential applications of this new stochastic model.", acknowledgement = ack-nhfb, fjournal = "Statistical Methodology", journal-URL = "http://www.sciencedirect.com/science/journal/15723127/", keywords = "Benford's Law; Beta distribution; Discrete Pareto; Ecology; First digit law; Heavy tail; Maximum likelihood estimation; Power law; Truncated geometric; Truncated Pareto", } @Article{Kramer:2015:MJE, author = "Walter Kr{\"a}mer", title = "{Miller, S. J. (ed.): \booktitle{Benford's law. Theory and applications}}", journal = j-STAT-PAPERS, volume = "56", number = "4", pages = "1251--1252", month = nov, year = "2015", CODEN = "STPAE4", DOI = "https://doi.org/10.1007/s00362-015-0717-8", ISSN = "0932-5026 (print), 1613-9798 (electronic)", ISSN-L = "0932-5026", bibdate = "Tue Nov 17 09:38:07 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://link.springer.com/accesspage/article/10.1007/s00362-015-0717-8", acknowledgement = ack-nhfb, fjournal = "Statistical Papers", journal-URL = "http://link.springer.com/journal/362", } @Article{Kudryashov:2015:APE, author = "Nikolay A. Kudryashov and Anastasia S. Zakharchenko", title = "Analytical properties and exact solutions of the {Lotka--Volterra} competition system", journal = j-APPL-MATH-COMP, volume = "254", number = "??", pages = "219--228", day = "1", month = mar, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Mon Feb 23 08:51:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300314017743", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Lafouge:2015:DTP, author = "Thierry Lafouge and Abdellatif Agouzal and Genevieve Lallich", title = "The deconstruction of a text: the permanence of the generalized {Zipf} law --- the inter-textual relationship between entropy and effort amount", journal = j-SCIENTOMETRICS, volume = "104", number = "1", pages = "193--217", month = jul, year = "2015", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-015-1600-z", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Wed Sep 2 12:06:12 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-015-1600-z", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @InCollection{Lee:2015:GBL, author = "Joanne Lee and Wendy K. Tam Cho and George Judge", title = "Generalizing {Benford's Law}", crossref = "Miller:2015:BLT", pages = "304--316", year = "2015", MRclass = "62P10", MRnumber = "3411066", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InCollection{Leemis:2015:BLG, author = "Lawrence Leemis", title = "{Benford's Law} geometry", crossref = "Miller:2015:BLT", pages = "109--118", year = "2015", MRclass = "62E17 (60E05)", MRnumber = "3411059", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Lewis:2015:SDA, author = "Peter R. Lewis and Lukas Esterle and Arjun Chandra and Bernhard Rinner and Jim Torresen and Xin Yao", title = "Static, Dynamic, and Adaptive Heterogeneity in Distributed Smart Camera Networks", journal = j-TAAS, volume = "10", number = "2", pages = "8:1--8:??", month = jun, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2764460", ISSN = "1556-4665 (print), 1556-4703 (electronic)", ISSN-L = "1556-4665", bibdate = "Wed Jun 10 08:01:03 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/taas.bib", abstract = "We study heterogeneity among nodes in self-organizing smart camera networks, which use strategies based on social and economic knowledge to target communication activity efficiently. We compare homogeneous configurations, when cameras use the same strategy, with heterogeneous configurations, when cameras use different strategies. Our first contribution is to establish that static heterogeneity leads to new outcomes that are more efficient than those possible with homogeneity. Next, two forms of dynamic heterogeneity are investigated: nonadaptive mixed strategies and adaptive strategies, which learn online. Our second contribution is to show that mixed strategies offer Pareto efficiency consistently comparable with the most efficient static heterogeneous configurations. Since the particular configuration required for high Pareto efficiency in a scenario will not be known in advance, our third contribution is to show how decentralized online learning can lead to more efficient outcomes than the homogeneous case. In some cases, outcomes from online learning were more efficient than all other evaluated configuration types. Our fourth contribution is to show that online learning typically leads to outcomes more evenly spread over the objective space. Our results provide insight into the relationship between static, dynamic, and adaptive heterogeneity, suggesting that all have a key role in achieving efficient self-organization.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Autonomous and Adaptive Systems (TAAS)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1010", } @Article{Li:2015:BBL, author = "Qinglei Li and Zuntao Fu and Naiming Yuan", title = "Beyond {Benford's Law}: Distinguishing Noise from Chaos", journal = j-PLOS-ONE, volume = "10", number = "6", pages = "e0129161:1--e0129161:11", day = "1", month = jun, year = "2015", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0129161", ISSN = "1932-6203", bibdate = "Wed Aug 12 08:58:10 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0129161", abstract = "Determinism and randomness are two inherent aspects of all physical processes. Time series from chaotic systems share several features identical with those generated from stochastic processes, which makes them almost undistinguishable. In this paper, a new method based on Benford's law is designed in order to distinguish noise from chaos by only information from the first digit of considered series. By applying this method to discrete data, we confirm that chaotic data indeed can be distinguished from noise data, quantitatively and clearly.", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", } @Article{Lin:2015:DES, author = "Cheng-Yen Lin and Chung-Wen Huang and Chi-Bang Kuan and Shi-Yu Huang and Jenq-Kuen Lee", title = "The Design and Experiments of a {SID}-Based Power-Aware Simulator for Embedded Multicore Systems", journal = j-TODAES, volume = "20", number = "2", pages = "22:1--22:??", month = feb, year = "2015", CODEN = "ATASFO", DOI = "https://doi.org/10.1145/2699834", ISSN = "1084-4309 (print), 1557-7309 (electronic)", ISSN-L = "1084-4309", bibdate = "Tue Mar 3 14:46:37 MST 2015", bibsource = "http://www.acm.org/pubs/contents/journals/todaes/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/todaes.bib", abstract = "Embedded multicore systems are playing increasingly important roles in the design of consumer electronics. The objective of such systems is to optimize both performance and power characteristics of mobile devices. However, currently there are no power metrics supporting popular application design platforms (such as SID) that application developers use to develop their applications. This hinders the ability of application developers to optimize power consumption. In this article we present the design and experiments of a SID-based power-aware simulation framework for embedded multicore systems. The proposed power estimation flow includes two phases: IP-level power modeling and power-aware system simulation. The first phase employs PowerMixer$^{IP}$ to construct the power model for the processor IP and other major IPs, while the second phase involves a power abstract interpretation method for summarizing the simulation trace, then, with a CPE module, estimating the power consumption based on the summarized trace information and the input of IP power models. In addition, a Manager component is devised to map each digital signal processor (DSP) component to a host thread and maintain the access to shared resources. The aim is to maintain the simulation performance as the number of simulated DSP components increases. A power-profiling API is also supported that developers of embedded software can use to tune the granularity of power-profiling for a specific code section of the target application. We demonstrate via case studies and experiments how application developers can use our SID-based power simulator for optimizing the power consumption of their applications. We characterize the power consumption of DSP applications with the DSPstone benchmark and discuss how compiler optimization levels with SIMD intrinsics influence the performance and power consumption. A histogram application and an augmented-reality application based on human-face-based RMS (recognition, mining, and synthesis) application are deployed as running examples on multicore systems to demonstrate how our power simulator can be used by developers in the optimization process to illustrate different views of power dissipations of applications.", acknowledgement = ack-nhfb, articleno = "22", fjournal = "ACM Transactions on Design Automation of Electronic Systems", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J776", } @Article{Liu:2015:ASN, author = "Qun Liu", title = "Analysis of a stochastic non-autonomous food-limited {Lotka--Volterra} cooperative model", journal = j-APPL-MATH-COMP, volume = "254", number = "??", pages = "1--8", day = "1", month = mar, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Mon Feb 23 08:51:11 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300314018037", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Liu:2015:DSD, author = "Qun Liu and Qingmei Chen", title = "Dynamics of stochastic delay {Lotka--Volterra} systems with impulsive toxicant input and {L{\'e}vy} noise in polluted environments", journal = j-APPL-MATH-COMP, volume = "256", number = "??", pages = "52--67", day = "1", month = apr, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Feb 27 06:15:38 MST 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300315000235", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Liu:2015:SPA, author = "Si Liu and Qiang Chen and Shuicheng Yan and Changsheng Xu and Hanqing Lu", title = "{Snap \& Play}: Auto-Generated Personalized Find-the-Difference Game", journal = j-TIST, volume = "5", number = "4", pages = "65:1--65:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2668109", ISSN = "2157-6904 (print), 2157-6912 (electronic)", ISSN-L = "2157-6904", bibdate = "Wed Feb 11 12:29:09 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tist.bib", abstract = "In this article, by taking a popular game, the Find-the-Difference (FiDi) game, as a concrete example, we explore how state-of-the-art image processing techniques can assist in developing a personalized, automatic, and dynamic game. Unlike the traditional FiDi game, where image pairs (source image and target image) with five different patches are manually produced by professional game developers, the proposed Personalized FiDi (P-FiDi) electronic game can be played in a fully automatic Snap \& Play mode. Snap means that players first take photos with their digital cameras. The newly captured photos are used as source images and fed into the P-FiDi system to autogenerate the counterpart target images for users to play. Four steps are adopted to autogenerate target images: enhancing the visual quality of source images, extracting some changeable patches from the source image, selecting the most suitable combination of changeable patches and difference styles for the image, and generating the differences on the target image with state-of-the-art image processing techniques. In addition, the P-FiDi game can be easily redesigned for the im-game advertising. Extensive experiments show that the P-FiDi electronic game is satisfying in terms of player experience, seamless advertisement, and technical feasibility.", acknowledgement = ack-nhfb, articleno = "65", fjournal = "ACM Transactions on Intelligent Systems and Technology (TIST)", journal-URL = "http://portal.acm.org/citation.cfm?id=J1318", } @Article{Llamocca:2015:DEP, author = "Daniel Llamocca and Marios Pattichis", title = "Dynamic Energy, Performance, and Accuracy Optimization and Management Using Automatically Generated Constraints for Separable {$2$D} {FIR} Filtering for Digital Video Processing", journal = j-TRETS, volume = "7", number = "4", pages = "4:1--4:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629623", ISSN = "1936-7406 (print), 1936-7414 (electronic)", ISSN-L = "1936-7406", bibdate = "Fri Feb 13 07:24:19 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/trets.bib", abstract = "There is strong interest in the development of dynamically reconfigurable systems that can meet real-time constraints on energy, performance, and accuracy. The generation of real-time constraints will significantly expand the applicability of dynamically reconfigurable systems to new domains, such as digital video processing. We develop a dynamically reconfigurable 2D FIR filtering system that can meet real-time constraints in energy, performance, and accuracy (EPA). The real-time constraints are automatically generated based on user input, image types associated with video communications, and video content. We first generate a set of Pareto-optimal realizations, described by their EPA values and associated 2D FIR hardware description bitstreams. Dynamic management is then achieved by selecting Pareto-optimal realizations that meet the automatically generated time-varying EPA constraints. We validate our approach using three different 2D Gaussian filters. Filter realizations are evaluated in terms of the required energy per frame, accuracy of the resulting image, and performance in frames per second. We demonstrate dynamic EPA management by applying a Difference of Gaussians (DOG) filter to standard video sequences. For video frame sizes that are equal to or larger than the VGA resolution, compared to a static implementation, our dynamic system provides significant reduction in the total energy consumption ({$>$30}\%).", acknowledgement = ack-nhfb, articleno = "4", fjournal = "ACM Transactions on Reconfigurable Technology and Systems (TRETS)", journal-URL = "http://portal.acm.org/toc.cfm?id=J1151", } @Article{LoBuglio:2015:WDT, author = "David {Lo Buglio} and Vanessa Lardinois and Livio {De Luca}", title = "What Do Thirty-One Columns Say about a {``Theoretical''} Thirty-Second?", journal = j-JOCCH, volume = "8", number = "1", pages = "6:1--6:??", month = feb, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2700425", ISSN = "1556-4673 (print), 1556-4711 (electronic)", ISSN-L = "1556-4673", bibdate = "Wed Feb 25 17:50:15 MST 2015", bibsource = "http://www.acm.org/pubs/contents/journals/jocch/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jocch.bib", abstract = "Over the past three decades, the introduction of digital technologies in the field of architectural documentation has profoundly changed tools and acquisition techniques. Most of the developments concern metrical and colorimetric characteristics of the objects studied. These developments, surrounding the practice of architectural survey, tend to respond primarily to the requirements of completeness. In this context, it seems necessary to assess the impact of these instruments on the cognitive value of architectural representation. With a strong technological presence, the study of the built heritage is facing a problem of ``information overload.'' Indeed, this strong technological presence fails to strengthen representation in its role as a vehicle of knowledge. Confronted with the intelligibility deficit, this article proposes an original approach for reading morphological features of an artifact by using a bottom-up approach: the meaning of elements (i.e., their semantic layouts) come from a statistical analysis of the major shape discontinuities of a collection of instances. The idea is to rely on data accumulation to render apparent high-level semantic structures from the comparative analysis of common low-level geometric features. The principles introduced are illustrated by the study of 31 columns of the cloister of the abbey of Saint-Michel-de-Cuxa. To summarize, the first objective is to understand how digital technologies can help us in the analysis of artistic and technical production of Romanesque columns. The second objective is to automatically identify the common semantic articulations of the entire collection to build a reference model for the future assessment of each artifact.", acknowledgement = ack-nhfb, articleno = "6", fjournal = "Journal on Computing and Cultural Heritage (JOCCH)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157", } @Article{Luo:2015:IAD, author = "Da Luo and Rui Yang and Jiwu Huang", title = "Identification of {AMR} decompressed audio", journal = j-DIGIT-SIGNAL-PROCESS, volume = "37", number = "0", pages = "85--91", year = "2015", CODEN = "DSPREJ", DOI = "https://doi.org/10.1016/j.dsp.2014.11.003", ISSN = "1051-2004 (print), 1095-4333 (electronic)", ISSN-L = "1051-2004", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1051200414003200", abstract = "More and more conversation recordings from phone calls are used as forensic evidence. To decide whether an unknown speech recording comes from mobile phone or not becomes an important issue in digital audio forensics. The communicating conversation recorded by mobile phones is encoded by Adaptive Multi-Rate (AMR) audio codec, which was adopted as the standard speech codec by 3GPP and widely used in {GSM} and UMTS. Therefore, {AMR} decompressed audio detection can be used to identify the source of the digital audio recording. Furthermore, it is helpful to locate the forgery position of the splicing {AMR} decompressed audio for forensic purposes. In this article, we focus on the identification of {AMR} decompressed audio, namely, given the waveform of an audio, we wish to identify whether it has been previously compressed by {AMR} codec or not. The artifacts introduced by the {AMR} codec will help to detect the source of the recordings. Based on our analysis, we find that the sample repetition rate of the {AMR} decompressed waveform is significantly greater than the regular waveform. Therefore, we employ the sample repetition rate as a feature to identify the {AMR} decompressed audio. The experimental results show that this feature is robust and effective.", acknowledgement = ack-nhfb, fjournal = "Digital Signal Processing", journal-URL = "https://www.sciencedirect.com/journal/digital-signal-processing", keywords = "Audio forensics; Benford's Law; Decompression audio identification; Sample repetition rate; {AMR}", } @Article{Manack:2015:LDL, author = "Corey Manack and Steven J. Miller", title = "Leading digit laws on linear {Lie} groups", journal = "Research in Number Theory", volume = "1", number = "1", pages = "22:1--22:19", month = dec, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1007/s40993-015-0024-4", ISSN = "2363-9555", ISSN-L = "2363-9555", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s40993-015-0024-4", acknowledgement = ack-nhfb, journal-URL = "http://link.springer.com/journal/40993", keywords = "Benford's Law; Digit laws; Haar measure; Matrix groups", } @Article{Masse:2015:FGS, author = "Bruno Mass{\'e} and Dominique Schneider", title = "Fast growing sequences of numbers and the first digit phenomenon", journal = j-INT-J-NUMBER-THEORY, volume = "11", number = "3", pages = "705--719", month = may, year = "2015", DOI = "https://doi.org/10.1142/S1793042115500384", ISSN = "1793-0421 (print), 1793-7310 (electronic)", ISSN-L = "1793-0421", MRclass = "11K31 (11K06)", MRnumber = "3327839", MRreviewer = "Steven Joel Miller", bibdate = "Tue Jan 26 11:14:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ijnt.bib", URL = "https://www.worldscientific.com/doi/10.1142/S1793042115500384", abstract = "We consider a large class of fast growing sequences of numbers $ U_n $ like the nth superfactorial, the $n$-th hyperfactorial and similar ones. We show that their mantissas are distributed following Benford's law in the sense of the natural density. We prove that this is also verified by, by and is passed down to all the sequences obtained by iterating this design process. We also consider the superprimorial numbers and the products of logarithms of integers.", acknowledgement = ack-nhfb, fjournal = "International Journal of Number Theory (IJNT)", journal-URL = "https://www.worldscientific.com/worldscinet/ijnt", } @Article{McCartney:2015:TSD, author = "Mark McCartney and David H. Glass", title = "A three-state dynamical model for religious affiliation", journal = j-PHYSICA-A, volume = "419", number = "0", pages = "145--152", year = "2015", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2014.09.052", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Wed Jan 28 10:08:12 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437114008206", abstract = "In the last century the western world has seen a rapid increase in the number of people describing themselves as affiliated with no religious group. We construct a set of models using coupled differential equations in which members of a society can be in one of three groups; religiously committed, religiously affiliated or religiously not affiliated. These models are then used to analyse post World War {II} census data for Northern Ireland.", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Benford's Law; Group behaviour; Nonlinear models; Religion", } @InCollection{Mebane:2015:CVC, author = "Walter R. {Mebane, Jr.}", title = "Can vote counts' digits and {Benford's Law} diagnose elections?", crossref = "Miller:2015:BLT", pages = "212--222", year = "2015", MRclass = "62P25 (91F10)", MRnumber = "3411063", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InCollection{Miller:2015:FAB, author = "Steven J. Miller", title = "{Fourier} analysis and {Benford's Law}", crossref = "Miller:2015:BLT", pages = "68--105", year = "2015", DOI = "https://doi.org/10.1515/9781400866595", MRclass = "60-02 (42B37 60B20 60F05 60J65 62G30 62N01 62N03)", MRnumber = "3411058", MRreviewer = "Rita Giuliano Antonini", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Miller:2015:HSOa, author = "Steven J. Miller", title = "How a Simple Observation from the 1800s about Patterns in Big Data Sets Can Fight Fraud", journal = "The Conversation", volume = "??", number = "??", pages = "??--??", day = "10", month = dec, year = "2015", bibdate = "Mon Dec 14 09:36:50 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://theconversation.com/how-a-simple-observation-from-the-1800s-about-patterns-in-big-data-sets-can-fight-fraud-42683", acknowledgement = ack-nhfb, } @Article{Miller:2015:HSOb, author = "Steven J. Miller", title = "How a Simple Observation from the 1800s about Patterns in Big Data Sets Can Fight Fraud", journal = j-SCI-COMPUT, volume = "??", number = "??", pages = "??--??", day = "10", month = dec, year = "2015", CODEN = "SCHRCU", ISSN = "1930-5753 (print), 1930-6156 (electronic)", ISSN-L = "1930-5753", bibdate = "Mon Dec 14 09:36:50 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.scientificcomputing.com/articles/2015/12/how-simple-observation-1800s-about-patterns-big-data-sets-can-fight-fraud", acknowledgement = ack-nhfb, fjournal = "Scientific Computing", journal-URL = "http://digital.scientificcomputing.com/scientificcomputing/", } @InCollection{Miller:2015:QIB, author = "Steven J. Miller", title = "A quick introduction to {Benford's Law}", crossref = "Miller:2015:BLT", pages = "3--22", year = "2015", DOI = "https://doi.org/10.1515/9781400866595", MRclass = "60-02 (60E05 62-02)", MRnumber = "3411056", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Mishra:2015:PGMa, author = "Nikita Mishra and Huazhe Zhang and John D. Lafferty and Henry Hoffmann", title = "A Probabilistic Graphical Model-based Approach for Minimizing Energy Under Performance Constraints", journal = j-COMP-ARCH-NEWS, volume = "43", number = "1", pages = "267--281", month = mar, year = "2015", CODEN = "CANED2", DOI = "https://doi.org/10.1145/2786763.2694373", ISSN = "0163-5964 (print), 1943-5851 (electronic)", ISSN-L = "0163-5964", bibdate = "Wed Jun 3 11:27:38 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigarch.bib", abstract = "In many deployments, computer systems are underutilized --- meaning that applications have performance requirements that demand less than full system capacity. Ideally, we would take advantage of this under-utilization by allocating system resources so that the performance requirements are met and energy is minimized. This optimization problem is complicated by the fact that the performance and power consumption of various system configurations are often application --- or even input --- dependent. Thus, practically, minimizing energy for a performance constraint requires fast, accurate estimations of application-dependent performance and power tradeoffs. This paper investigates machine learning techniques that enable energy savings by learning Pareto-optimal power and performance tradeoffs. Specifically, we propose LEO, a probabilistic graphical model-based learning system that provides accurate online estimates of an application's power and performance as a function of system configuration. We compare LEO to (1) offline learning, (2) online learning, (3) a heuristic approach, and (4) the true optimal solution. We find that LEO produces the most accurate estimates and near optimal energy savings.", acknowledgement = ack-nhfb, fjournal = "ACM SIGARCH Computer Architecture News", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J89", remark = "ASPLOS'15 conference proceedings.", } @Article{Mishra:2015:PGMb, author = "Nikita Mishra and Huazhe Zhang and John D. Lafferty and Henry Hoffmann", title = "A Probabilistic Graphical Model-based Approach for Minimizing Energy Under Performance Constraints", journal = j-SIGPLAN, volume = "50", number = "4", pages = "267--281", month = apr, year = "2015", CODEN = "SINODQ", DOI = "https://doi.org/10.1145/2775054.2694373", ISSN = "0362-1340 (print), 1523-2867 (print), 1558-1160 (electronic)", ISSN-L = "0362-1340", bibdate = "Tue May 12 17:41:19 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib", abstract = "In many deployments, computer systems are underutilized --- meaning that applications have performance requirements that demand less than full system capacity. Ideally, we would take advantage of this under-utilization by allocating system resources so that the performance requirements are met and energy is minimized. This optimization problem is complicated by the fact that the performance and power consumption of various system configurations are often application --- or even input --- dependent. Thus, practically, minimizing energy for a performance constraint requires fast, accurate estimations of application-dependent performance and power tradeoffs. This paper investigates machine learning techniques that enable energy savings by learning Pareto-optimal power and performance tradeoffs. Specifically, we propose LEO, a probabilistic graphical model-based learning system that provides accurate online estimates of an application's power and performance as a function of system configuration. We compare LEO to (1) offline learning, (2) online learning, (3) a heuristic approach, and (4) the true optimal solution. We find that LEO produces the most accurate estimates and near optimal energy savings.", acknowledgement = ack-nhfb, fjournal = "ACM SIGPLAN Notices", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J706", remark = "ASPLOS '15 conference proceedings.", } @InCollection{Nigrini:2015:DFE, author = "Mark Nigrini", title = "Detecting fraud and errors using {Benford's Law}", crossref = "Miller:2015:BLT", pages = "191--211", year = "2015", MRclass = "62P20", MRnumber = "3411062", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Noll:2015:FAO, author = "Tobias N{\"o}ll and Johannes K{\"o}hler and Gerd Reis and Didier Stricker", title = "Fully Automatic, Omnidirectional Acquisition of Geometry and Appearance in the Context of Cultural Heritage Preservation", journal = j-JOCCH, volume = "8", number = "1", pages = "2:1--2:??", month = feb, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629693", ISSN = "1556-4673 (print), 1556-4711 (electronic)", ISSN-L = "1556-4673", bibdate = "Wed Feb 25 17:50:15 MST 2015", bibsource = "http://www.acm.org/pubs/contents/journals/jocch/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jocch.bib", abstract = "Effective documentation and display of ancient objects is an essential task in the field of cultural heritage conservation. Digitization plays an important role in the process of creating, preserving, and accessing objects in digital space. Up to the present day, industrial scanners are used for this task, which focus mainly on the detailed reconstruction of the object's geometry only. However, particularly important for a faithful digital presentation of the object is the appearance information-that is, a description of the used materials and how they interact with incident light. Using the world's first full-spherical scanner, we propose a user-friendly reconstruction process that is specifically tailored to the needs of digitizing and representing cultural heritage artifacts. More precisely, our hardware specifically addresses the problem that invaluable or fragile artifacts may not be turned over during acquisition. Nevertheless, we can digitize the object completely, including its bottom. Further, by integrating appearance information into our digitization, we achieve a far more faithful digital replica with a quality comparable to a real picture of the object. But in contrast to a static picture, our representation allows one to interactively change the viewing and lighting directions freely. In addition, the results are very memory efficient, consuming only several megabytes per scanned object. In cooperation with museums and a private collector, we digitized several cultural heritage artifacts to demonstrate the feasibility of the proposed process.", acknowledgement = ack-nhfb, articleno = "2", fjournal = "Journal on Computing and Cultural Heritage (JOCCH)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157", } @Article{Obradovic:2015:GFT, author = "Marko Obradovi{\'c} and Milan Jovanovi{\'c} and Bojana Milosevi{\'c}", title = "Goodness-of-fit tests for {Pareto} distribution based on a characterization and their asymptotics", journal = j-STATISTICS, volume = "49", number = "5", pages = "1026--1041", year = "2015", CODEN = "MOSSD5", DOI = "https://doi.org/10.1080/02331888.2014.919297", ISSN = "0233-1888 (print), 1029-4910 (electronic)", ISSN-L = "0233-1888", bibdate = "Wed Aug 19 08:16:20 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statistics.bib", acknowledgement = ack-nhfb, fjournal = "Statistics: A Journal of Theoretical and Applied Statistics", journal-URL = "http://www.tandfonline.com/loi/gsta20", } @InCollection{Perez-Gonzalez:2015:ABL, author = "Fernando P{\'e}rez-Gonz{\'a}lez and Tu-Thach Quach and Chaouki T. Abdallah and Gregory L. Heileman and Steven J. Miller", title = "Application of {Benford's Law} to images", crossref = "Miller:2015:BLT", pages = "338--370", year = "2015", MRclass = "62H35", MRnumber = "3411068", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Raman:2015:CSC, author = "Raghu Raman and Smrithi Venkatasubramanian and Krishnashree Achuthan and Prema Nedungadi", title = "Computer Science {(CS)} Education in {Indian} Schools: Situation Analysis using {Darmstadt} Model", journal = j-TOCE, volume = "15", number = "2", pages = "7:1--7:??", month = may, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2716325", ISSN = "1946-6226", bibdate = "Tue May 12 06:10:11 MDT 2015", bibsource = "http://www.acm.org/pubs/toce; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/toce.bib", abstract = "Computer science (CS) and its enabling technologies are at the heart of this information age, yet its adoption as a core subject by senior secondary students in Indian schools is low and has not reached critical mass. Though there have been efforts to create core curriculum standards for subjects like Physics, Chemistry, Biology, and Math, CS seems to have been kept outside the purview of such efforts leading to its marginalization. As a first step, using the Darmstadt model from the ITiCSE working group that provides a systematic categorization approach to CS education in schools, we coded and analyzed the CS situation for the Indian schools. Next, we focused on the motivation category of the Darmstadt model and investigated behavioral intentions of secondary school students and teachers from 332 schools in India. Considering the CS subject as an educational innovation, using Rogers' Theory of Diffusion of Innovations, we propose a pedagogical framework for innovation attributes that can significantly predict-adoption of the CS subject among potential-adopter students and teachers. Data was analyzed to answer research questions about student and teacher intentions, influence of gender, school management, and school location in adopting CS. Interestingly, girls, urban students, teachers, and private schools were seen favoring the adoption of CS. An important issue that needed to be addressed, however, was the interchangeable use of terms like CS, Informatics, ICT, and digital literacy. Through our article, we offer a promising picture of the educational policy directives and the academic environment in India that is rapidly growing and embracing CS as a core subject of study in schools. We also analyze the factors that influence the adoption of CS by school students and teachers and conclude that there is a very positive response for CS among educators and students in India.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Computing Education", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1193", } @Article{Ribeiro:2015:MPE, author = "Marco Tulio Ribeiro and Nivio Ziviani and Edleno {Silva De Moura} and Itamar Hata and Anisio Lacerda and Adriano Veloso", title = "Multiobjective {Pareto}-Efficient Approaches for Recommender Systems", journal = j-TIST, volume = "5", number = "4", pages = "53:1--53:??", month = jan, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629350", ISSN = "2157-6904 (print), 2157-6912 (electronic)", ISSN-L = "2157-6904", bibdate = "Wed Feb 11 12:29:09 MST 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tist.bib", abstract = "Recommender systems are quickly becoming ubiquitous in applications such as e-commerce, social media channels, and content providers, among others, acting as an enabling mechanism designed to overcome the information overload problem by improving browsing and consumption experience. A typical task in many recommender systems is to output a ranked list of items, so that items placed higher in the rank are more likely to be interesting to the users. Interestingness measures include how accurate, novel, and diverse are the suggested items, and the objective is usually to produce ranked lists optimizing one of these measures. Suggesting items that are simultaneously accurate, novel, and diverse is much more challenging, since this may lead to a conflicting-objective problem, in which the attempt to improve a measure further may result in worsening other measures. In this article, we propose new approaches for multiobjective recommender systems based on the concept of Pareto efficiency-a state achieved when the system is devised in the most efficient manner in the sense that there is no way to improve one of the objectives without making any other objective worse off. Given that existing multiobjective recommendation algorithms differ in their level of accuracy, diversity, and novelty, we exploit the Pareto-efficiency concept in two distinct manners: (i) the aggregation of ranked lists produced by existing algorithms into a single one, which we call Pareto-efficient ranking, and (ii) the weighted combination of existing algorithms resulting in a hybrid one, which we call Pareto-efficient hybridization. Our evaluation involves two real application scenarios: music recommendation with implicit feedback (i.e., Last.fm) and movie recommendation with explicit feedback (i.e., MovieLens). We show that the proposed Pareto-efficient approaches are effective in suggesting items that are likely to be simultaneously accurate, diverse, and novel. We discuss scenarios where the system achieves high levels of diversity and novelty without compromising its accuracy. Further, comparison against multiobjective baselines reveals improvements in terms of accuracy (from 10.4\% to 10.9\%), novelty (from 5.7\% to 7.5\%), and diversity (from 1.6\% to 4.2\%).", acknowledgement = ack-nhfb, articleno = "53", fjournal = "ACM Transactions on Intelligent Systems and Technology (TIST)", journal-URL = "http://portal.acm.org/citation.cfm?id=J1318", } @InCollection{Roukema:2015:CBL, author = "Boudewijn F. Roukema", title = "Complementing {Benford's Law} for small {$N$}: a local bootstrap", crossref = "Miller:2015:BLT", pages = "223--232", year = "2015", MRclass = "62P25 (62G09)", MRnumber = "3411064", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Rubino:2015:ILB, author = "Irene Rubino and Claudia Barberis and Jetmir Xhembulla and Giovanni Malnati", title = "Integrating a Location-Based Mobile Game in the Museum Visit: Evaluating Visitors' Behaviour and Learning", journal = j-JOCCH, volume = "8", number = "3", pages = "15:1--15:??", month = may, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2724723", ISSN = "1556-4673 (print), 1556-4711 (electronic)", ISSN-L = "1556-4673", bibdate = "Tue May 12 07:01:13 MDT 2015", bibsource = "http://www.acm.org/pubs/contents/journals/jocch/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jocch.bib", abstract = "Location-based systems currently represent a suitable solution to enhance cultural experiences inside museums, as they can satisfy visitors' needs through the provision of contextualized contents and services. In this framework, a promising approach to captivate the attention of teenagers-a hard to please target audience-is represented by mobile serious games, such as playful activities aiming to primarily fulfil educational purposes. The use of a mobile digital tool during the visit definitely discloses new opportunities for contextual learning scenarios; however, so far, only a few studies have analysed the impact of different communication approaches on visitors' degree of exploration and acquisition of knowledge. This work aims to enrich this field of research, presenting the conceptual framework; the design principles; and the evaluation results of ``Gossip at palace,'' a location-based mobile game integrating a storytelling approach. The game was developed for an Italian historical residence to communicate its 18th-century history to teenagers, capitalizing on narrative and game mechanics to foster young visitors' motivations to explore the museum and facilitate their meaning-making process. Following a mixed-methods perspective, the article firstly describes to what extent the components of the application were appreciated by teenagers as well as by other visitor segments. Secondly, it provides an insight on the effectiveness of the game in facilitating the acquisition of historical knowledge by participants, enriched by considerations on the methods to be adopted when evaluating mobile learning in informal educational settings. Thirdly, players' degree of use of the digital game throughout the visit is compared to analogous patterns registered for people using a multimedia mobile guide in the same venue. On the one hand, the study pointed out that the game facilitated a wider exploration of the museum; on the other, it highlighted that players mainly gained a superficial knowledge of the proposed contents.", acknowledgement = ack-nhfb, articleno = "15", fjournal = "Journal on Computing and Cultural Heritage (JOCCH)", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1157", } @InCollection{Schurger:2015:LPB, author = "Klaus Sch{\"u}rger", title = "{L{\'e}vy} processes and {Benford's Law}", crossref = "Miller:2015:BLT", pages = "135--173", year = "2015", MRclass = "60G51 (60F10 60F15 62G10)", MRnumber = "3411061", MRreviewer = "Sreenivasan Ravi", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Serra:2015:POA, author = "Edoardo Serra and Sushil Jajodia and Andrea Pugliese and Antonino Rullo and V. S. Subrahmanian", title = "{Pareto}-Optimal Adversarial Defense of Enterprise Systems", journal = j-TISSEC, volume = "17", number = "3", pages = "11:1--11:??", month = mar, year = "2015", CODEN = "ATISBQ", DOI = "https://doi.org/10.1145/2699907", ISSN = "1094-9224 (print), 1557-7406 (electronic)", ISSN-L = "1094-9224", bibdate = "Fri Mar 27 17:03:46 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tissec.bib", abstract = "The National Vulnerability Database (NVD) maintained by the US National Institute of Standards and Technology provides valuable information about vulnerabilities in popular software, as well as any patches available to address these vulnerabilities. Most enterprise security managers today simply patch the most dangerous vulnerabilities-an adversary can thus easily compromise an enterprise by using less important vulnerabilities to penetrate an enterprise. In this article, we capture the vulnerabilities in an enterprise as a Vulnerability Dependency Graph (VDG) and show that attacks graphs can be expressed in them. We first ask the question: What set of vulnerabilities should an attacker exploit in order to maximize his expected impact? We show that this problem can be solved as an integer linear program. The defender would obviously like to minimize the impact of the worst-case attack mounted by the attacker-but the defender also has an obligation to ensure a high productivity within his enterprise. We propose an algorithm that finds a Pareto-optimal solution for the defender that allows him to simultaneously maximize productivity and minimize the cost of patching products on the enterprise network. We have implemented this framework and show that runtimes of our computations are all within acceptable time bounds even for large VDGs containing 30K edges and that the balance between productivity and impact of attacks is also acceptable.", acknowledgement = ack-nhfb, articleno = "11", fjournal = "ACM Transactions on Information and System Security", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J789", } @InProceedings{Singh:2015:ABL, author = "N. Singh and R. Bansal", booktitle = "Signal Processing and Communication {(ICSC), 2015} International Conference on", title = "Analysis of {Benford's Law} in digital image forensics", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "413--418", month = mar, year = "2015", DOI = "https://doi.org/10.1109/ICSPCom.2015.7150688", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford law; Benford's law; compression; data compression; data detection; data recovery; digital image forensics; Digital images; Discrete cosine transforms; Discrete wavelet transforms; Forensics; Image coding; image coding; image compression; image forensics; image registration; JPEG2000; Q-factor; tampering detection; Transform coding", } @Article{Slepkov:2015:BLT, author = "Aaron D. Slepkov and Kevin B. Ironside and David DiBattista", title = "{Benford's Law}: Textbook Exercises and Multiple-Choice Testbanks", journal = j-PLOS-ONE, volume = "10", number = "2", pages = "e0117972:1--e0117972:13", day = "17", month = feb, year = "2015", CODEN = "POLNCL", DOI = "https://doi.org/10.1371/journal.pone.0117972", ISSN = "1932-6203", bibdate = "Wed Aug 12 08:59:52 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0117972", abstract = "Benford's Law describes the finding that the distribution of leading (or leftmost) digits of innumerable datasets follows a well-defined logarithmic trend, rather than an intuitive uniformity. In practice this means that the most common leading digit is 1, with an expected frequency of 30.1\%, and the least common is 9, with an expected frequency of 4.6\%. Currently, the most common application of Benford's Law is in detecting number invention and tampering such as found in accounting-, tax-, and voter-fraud. We demonstrate that answers to end-of-chapter exercises in physics and chemistry textbooks conform to Benford's Law. Subsequently, we investigate whether this fact can be used to gain advantage over random guessing in multiple-choice tests, and find that while testbank answers in introductory physics closely conform to Benford's Law, the testbank is nonetheless secure against such a Benford's attack for banal reasons.", acknowledgement = ack-nhfb, fjournal = "PLoS One", journal-URL = "http://www.plosone.org/", } @Article{VanCaneghem:2015:NFSa, author = "Tom {Van Caneghem}", title = "{NPO} Financial Statement Quality: An Empirical Analysis Based on {Benford's Law}", journal = "VOLUNTAS: International Journal of Voluntary and Nonprofit Organizations", volume = "26", number = "1", pages = "1--24", month = feb, year = "2015", DOI = "https://doi.org/10.1007/s11266-015-9629-4", ISSN = "0957-8765 (print), 1573-7888 (electronic)", ISSN-L = "0957-8765", bibdate = "Wed Aug 12 10:03:53 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11266-015-9629-4", acknowledgement = ack-nhfb, journal-URL = "https://link.springer.com/journal/11266", keywords = "Benford's Law; Digital analysis; Financial reporting; Financial statements; Non-profit organizations", } @Article{VanCaneghem:2015:NFSb, author = "Tom {Van Caneghem}", title = "{NPO} Financial Statement Quality: An Empirical Analysis Based on {Benford's Law}", journal = "{VOLUNTAS}: International Journal of Voluntary and Nonprofit Organizations", volume = "27", number = "6", pages = "2685--2708", month = aug, year = "2015", DOI = "https://doi.org/10.1007/s11266-015-9629-4", ISSN = "0957-8765 (print), 1573-7888 (electronic)", ISSN-L = "0957-8765", bibdate = "Wed Jun 20 15:13:31 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "https://link.springer.com/journal/11266", } @Article{Wang:2015:SPW, author = "Xiaohuan Wang", title = "Stability of planar waves in a {Lotka--Volterra} system", journal = j-APPL-MATH-COMP, volume = "259", number = "??", pages = "313--326", day = "15", month = may, year = "2015", CODEN = "AMHCBQ", ISSN = "0096-3003 (print), 1873-5649 (electronic)", ISSN-L = "0096-3003", bibdate = "Fri Apr 24 18:27:24 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0096300315002398", acknowledgement = ack-nhfb, fjournal = "Applied Mathematics and Computation", journal-URL = "http://www.sciencedirect.com/science/journal/00963003/", } @Article{Whyman:2015:ICC, author = "G. Whyman and E. Shulzinger and Ed. Bormashenko", title = "Intuitive considerations clarifying the origin and applicability of the {Benford Law}", journal = "arXiv.org", volume = "??", number = "??", pages = "12", day = "25", month = oct, year = "2015", bibdate = "Tue Jan 26 09:53:36 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1510.07220v2", acknowledgement = ack-nhfb, } @Article{Woods:2015:PDP, author = "Louis Woods and Gustavo Alonso and Jens Teubner", title = "Parallelizing Data Processing on {FPGAs} with Shifter Lists", journal = j-TRETS, volume = "8", number = "2", pages = "7:1--7:??", month = apr, year = "2015", CODEN = "????", DOI = "https://doi.org/10.1145/2629551", ISSN = "1936-7406 (print), 1936-7414 (electronic)", ISSN-L = "1936-7406", bibdate = "Tue May 19 17:05:20 MDT 2015", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/trets.bib", abstract = "Parallelism is currently seen as a mechanism to minimize the impact of the power and heat dissipation problems encountered in modern hardware. Data parallelism-based on partitioning the data-and pipeline parallelism-based on partitioning the computation-are the two main approaches to leverage parallelism on a wide range of hardware platforms. Unfortunately, not all data processing problems are susceptible to either of those strategies. An example is the skyline operator [B{\"o}rzs{\"o}nyi et al. 2001], which computes the set of Pareto-optimal points within a multidimensional dataset. Existing approaches to parallelize the skyline operator are based on data parallelism. As a result, they suffer from a high overhead when merging intermediate results because of the lack of a global view of the problem inherent to partitioning the input data. In this article, we show how to combine pipeline with data parallelism on a Field-Programmable Gate Array (FPGA) for a more efficient utilization of the available hardware parallelism. As we show in our experiments, skyline computation using our proposed technique scales linearly with the number of processing elements, and the performance we achieve on a rather small FPGA is comparable to that of a 64-core high-end server running a state-of-the-art data parallel implementation of skyline [Park et al. 2009]. The proposed approach to parallelize the skyline operator can be generalized to a wider range of data processing problems. We demonstrate this through a novel, highly parallel data structure, a shifter list, that can be efficiently implemented on an FPGA. The resulting template is easy to parametrize to implement a variety of computationally intensive operators such as frequent items, n -closest pairs, or K-means.", acknowledgement = ack-nhfb, articleno = "7", fjournal = "ACM Transactions on Reconfigurable Technology and Systems (TRETS)", journal-URL = "http://portal.acm.org/toc.cfm?id=J1151", } @Article{Yang:2015:ERP, author = "Ziyun Yang and Xiaobo Dong", title = "Earnings roundup in private and public bank holding companies", journal = "Advances in Accounting", volume = "31", number = "1", pages = "96--99", year = "2015", DOI = "https://doi.org/10.1016/j.adiac.2015.03.004", ISSN = "0882-6110", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S088261101500005X", abstract = "In this study, we compare the relative tendencies of public versus private firms to round up earnings in a setting of the banking industry. This industry consists of a large number of public and private bank holding companies (BHCs) that face the same regulation environment. In both the full sample and the size-matched sample, we find evidence that public BHCs show a greater tendency to round up the second digit of earnings than do private BHCs. Our study contributes to the current debate on the financial reporting quality of public versus private firms by providing evidence supporting the opportunistic behavior hypothesis.", acknowledgement = ack-nhfb, keywords = "Benford's law; Earnings roundup; Reporting quality", } @Article{Zhao:2015:UCA, author = "Peng Zhao and Engui Fan", title = "A unified construction for the algebro-geometric quasiperiodic solutions of the {Lotka--Volterra} and relativistic {Lotka--Volterra} hierarchy", journal = j-J-MATH-PHYS, volume = "56", number = "4", pages = "043501", month = apr, year = "2015", CODEN = "JMAPAQ", DOI = "https://doi.org/10.1063/1.4916676", ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427", ISSN-L = "0022-2488", bibdate = "Tue Aug 4 09:20:02 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Mathematical Physics", journal-URL = "http://jmp.aip.org/", } @Article{Zornig:2015:ZLR, author = "Peter Z{\"o}rnig", title = "{Zipf}'s law for randomly generated frequencies: explicit tests for the goodness-of-fit", journal = j-J-STAT-COMPUT-SIMUL, volume = "85", number = "11", pages = "2202--2213", year = "2015", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949655.2014.925113", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Tue Jun 9 05:53:26 MDT 2015", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", } @Article{Alves:2016:ABI, author = "Alexandre Donizeti Alves and Horacio Hideki Yanasse and Nei Yoshihiro Soma", title = "An analysis of bibliometric indicators to {JCR} according to {Benford's Law}", journal = j-SCIENTOMETRICS, volume = "107", number = "3", pages = "1489--1499", month = jun, year = "2016", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-016-1908-3", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Mon May 16 16:03:17 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/content/pdf/10.1007/s11192-016-1908-3.pdf", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", keywords = "Journal Citation Reports (JCR)", } @Article{Amir:2016:SNE, author = "Ariel Amir and Mikhail Lemeshko and Tadashi Tokieda", title = "Surprises in Numerical Expressions of Physical Constants", journal = j-AMER-MATH-MONTHLY, volume = "123", number = "6", pages = "609--612", month = jun, year = "2016", CODEN = "AMMYAE", DOI = "https://doi.org/10.4169/amer.math.monthly.123.6.609", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jun 20 14:16:05 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.609", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", keywords = "Benford's Law; experimental mathematics", remark = "This paper looks at the probability that a particular numerical physical constant is generated by a simple expression involving a few mathematical constants. It also discusses Benford's Law.", } @Article{Ausloos:2016:QQP, author = "Marcel Ausloos and Olgica Nedic and Agata Fronczak and Piotr Fronczak", title = "Quantifying the quality of peer reviewers through {Zipf}'s law", journal = j-SCIENTOMETRICS, volume = "106", number = "1", pages = "347--368", month = jan, year = "2016", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-015-1704-5", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Sat Jan 16 07:09:36 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/article/10.1007/s11192-015-1704-5", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Ausloos:2016:RDC, author = "Marcel Ausloos and Rosella Castellano and Roy Cerqueti", title = "Regularities and discrepancies of credit default swaps: a data science approach through {Benford}'s law", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "90", pages = "8--17", month = sep, year = "2016", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2016.03.002", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", bibdate = "Tue May 22 16:45:20 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", } @Article{Berger:2016:CBL, author = "Arno Berger and Gideon Eshun", title = "A characterization of {Benford's Law} in discrete-time linear systems", journal = j-J-DYN-DIFFER-EQU, volume = "28", number = "2", pages = "431--469", year = "2016", CODEN = "JDDEEH", DOI = "https://doi.org/10.1007/s10884-014-9393-y", ISSN = "1040-7294 (print), 1572-9222 (electronic)", ISSN-L = "1040-7294", MRclass = "37A45 (11J71 37A05)", MRnumber = "3500397", MRreviewer = "Joseph Andrew Vandehey", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Dynamics and Differential Equations", } @Article{Bormashenko:2016:BLA, author = "Ed. Bormashenko and E. Shulzinger and G. Whyman and Ye. Bormashenko", title = "{Benford's Law}, its applicability and breakdown in the {IR} spectra of polymers", journal = j-PHYSICA-A, volume = "444", number = "??", pages = "524--529", year = "2016", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2015.10.090", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0378437115009498", abstract = "Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra is random. This observation may be explained by the fact that the value of transmittance $ T_r $ is restricted $ 0 < T_r < 1 $, due to the physical reasons, whereas the value of absorbance is not. Moreover, the transmittance and absorbance $A$ are interrelated by the logarithmic dependence $ A = \log T_r$. This observation supplies the idea that the Benford law is valid in the situations, when logarithmic dependencies take place. Amalgamation of spectral data obtained for various polymers brings the distribution of the leading digits in the absorbance domain into proximity to the Benford Law.", acknowledgement = ack-nhfb, fjournal = "Physica A", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", keywords = "Absorbance; Benford's Law; Infrared spectra of polymers; Transmittance", } @Article{Chen:2016:LBS, author = "Evan Chen and Peter S. Park and Ashvin A. Swaminathan", title = "On logarithmically {Benford} sequences", journal = j-PROC-AM-MATH-SOC, volume = "144", number = "11", pages = "4599--4608", year = "2016", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/proc/13112", ISSN = "0002-9939 (print), 1088-6826 (electronic)", ISSN-L = "0002-9939", MRclass = "11F11 (11N05)", MRnumber = "3544512", MRreviewer = "Ping Xi", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @Article{Friar:2016:UBL, author = "J. L. Friar and T. Goldman and J. P{\'e}rez-Mercader", title = "Ubiquity of {Benford's Law} and emergence of the reciprocal distribution", journal = j-PHYS-LET-A, volume = "380", number = "22--23", pages = "1895--1899", year = "2016", CODEN = "PYLAAG", DOI = "https://doi.org/10.1016/j.physleta.2016.03.045", ISSN = "0375-9601 (print), 1873-2429 (electronic)", ISSN-L = "0375-9601", MRclass = "60E05 (94A15)", MRnumber = "3489018", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physics Letters. A", journal-URL = "http://www.sciencedirect.com/science/journal/03759601", } @InCollection{Frunza:2016:CBL, author = "Marius-Christian Frunza", editor = "Marius-Christian Frunza", booktitle = "Solving Modern Crime in Financial Markets", title = "{Benford's Law}", chapter = "2K", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, bookpages = "528", pages = "233--245", year = "2016", DOI = "https://doi.org/10.1016/B978-0-12-804494-0.00017-6", ISBN = "0-12-804494-2 (hardcover), 0-12-804532-9 (e-book)", ISBN-13 = "978-0-12-804494-0 (hardcover), 978-0-12-804532-9 (e-book)", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/B9780128044940000176", abstract = "Since the seminal work published by Nigrini in 1992, Benford's Law has been employed as a forensic accounting tool that is currently used as evidence in many courts. The application to cases of fraud on financial markets is still new, but successful applications have been illustrated, in particular in the case of the LIBOR manipulation. The field of application for Benford's Law in the financial markets is growing as many data sets can be the target of manipulation or misrepresentation. Therefore, the test assessing conformity with Benford's Law can emphasize fictitious figures resulting from manual handling of data in areas like fund performance metrics, benchmarks, and index values or prices of niche commodity markets.", acknowledgement = ack-nhfb, keywords = "Chi-square test; Digit manipulation; First digit; Second digit", } @InCollection{Garrabrant:2016:ALU, author = "Scott Garrabrant and Tsvi Benson-Tilsen and Siddharth Bhaskar and Abram Demski and Joanna Garrabrant and George Koleszarik and Evan Lloyd", booktitle = "Artificial General Intelligence ({AGI 2016})", title = "Asymptotic Logical Uncertainty and the {Benford} Test", volume = "9782", publisher = "Springer International Publishing", address = "Cham, Switzerland", pages = "202--211", year = "2016", DOI = "https://doi.org/10.1007/978-3-319-41649-6_20", ISBN = "3-319-41648-0 (print), 3-319-41649-9 (e-book)", ISBN-13 = "978-3-319-41648-9 (print), 978-3-319-41649-6 (e-book)", bibdate = "Wed Jun 20 15:26:46 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @Article{Goodman:2016:PPB, author = "William Goodman", title = "The promises and pitfalls of {Benford}'s law", journal = j-SIGNIF, volume = "13", number = "3", pages = "38--41", month = jun, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1111/j.1740-9713.2016.00919.x", ISSN = "1740-9705 (print), 1740-9713 (electronic)", ISSN-L = "1740-9705", bibdate = "Thu Aug 13 12:04:02 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/significance.bib", acknowledgement = ack-nhfb, ajournal = "Signif.", fjournal = "Significance", journal-URL = "https://rss.onlinelibrary.wiley.com/journal/17409713", onlinedate = "06 June 2016", } @Book{Guttag:2016:ICP, author = "John Guttag", title = "Introduction to Computation and Programming Using {Python}: with Application to Understanding Data", publisher = pub-MIT, address = pub-MIT:adr, edition = "Second", pages = "xvii + 447", year = "2016", ISBN = "0-262-52962-9 (paperback), 0-262-33738-X (e-book)", ISBN-13 = "978-0-262-52962-4 (paperback), 978-0-262-33738-0 (e-book)", LCCN = "QA76.73.P98 G88 2016", bibdate = "Tue Jun 5 11:01:20 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/python.bib; z3950.loc.gov:7090/Voyager", abstract = "This book introduces students with little or no prior programming experience to the art of computational problem solving using Python and various Python libraries, including PyLab. It provides students with skills that will enable them to make productive use of computational techniques, including some of the tools and techniques of data science for using computation to model and interpret data. The book is based on an MIT course (which became the most popular course offered through MIT's OpenCourseWare) and was developed for use not only in a conventional classroom but in a massive open online course (MOOC). This new edition has been updated for Python 3, reorganized to make it easier to use for courses that cover only a subset of the material, and offers additional material including five new chapters. Students are introduced to Python and the basics of programming in the context of such computational concepts and techniques as exhaustive enumeration, bisection search, and efficient approximation algorithms. Although it covers such traditional topics as computational complexity and simple algorithms, the book focuses on a wide range of topics not found in most introductory texts, including information visualization, simulations to model randomness, computational techniques to understand data, and statistical techniques that inform (and misinform) as well as two related but relatively advanced topics: optimization problems and dynamic programming. This edition offers expanded material on statistics and machine learning and new chapters on Frequentist and Bayesian statistics.", acknowledgement = ack-nhfb, subject = "Python (Computer program language); Textbooks; Computer programming", tableofcontents = "Preface \\ 1. Introduction \\ 2: Introduction to Python: The basic elements of Python \\ Objects, expressions, and numerical types \\ Variables and assignment \\ Python IDE's \\ Branching programs \\ Strings and input \\ Input \\ A digression about character encoding \\ Iteration \\ 3: Some simple numerical programs: Exhaustive enumeration \\ For loops \\ Approximate solutions and bisection search \\ Few words about using floats \\ Newton--Raphson \\ 4: Functions, scoping, and abstraction: Functions and scoping \\ Function definitions \\ Keyword arguments and default values \\ Scoping \\ Specifications \\ Recursion \\ Fibonacci numbers \\ Palindromes \\ Global variables \\ Modules \\ Files \\ 5: Structured types, mutability, and higher-order functions: Tuples \\ Sequences and multiple assignment \\ Ranges \\ Lists and mutability \\ Cloning \\ List comprehension \\ Functions as objects \\ Strings, tuples, ranges, and lists \\ Dictionaries \\ 6: Testing and debugging: Testing \\ Black-box testing \\ Glass-box testing \\ Conducting tests \\ Debugging \\ Learning to debug \\ Designing the experiment \\ When the going gets tough \\ When you have found ``the'' bug \\ 7: Exceptions and assertions: Handling exceptions \\ Exceptions as a control flow mechanism \\ Assertions \\ 8: Classes and object-oriented programming: Abstract data types and classes \\ Designing programs using abstract data types \\ Using classes to keep track of students and faculty \\ Inheritance \\ Multiple levels of inheritance \\ Substitution principle \\ Encapsulation and information hiding \\ Generators \\ Mortgages, an extended example \\ 9: A simplistic introduction to algorithmic complexity: Thinking about computational complexity \\ Asymptotic notation \\ Some important complexity classes \\ Constant complexity \\ Logarithmic complexity \\ Linear complexity \\ Log-linear complexity \\ Polynomial complexity \\ Exponential complexity \\ Comparisons of complexity classes \\ 10: Some simple algorithms and data structures: Search algorithms \\ Linear search and using indirection to access elements \\ Binary search and exploiting assumptions \\ Sorting algorithms \\ Merge sort \\ Exploiting functions as parameters \\ Sorting in Python \\ Hash tables \\ 11: Plotting and more about classes: Plotting using PyLab \\ Plotting mortgages, an extended example \\ 12: Knapsack and graph optimization problems: Knapsack problems \\ Greedy algorithms \\ Optimal solution to the 0/1 Knapsack problem \\ Graph optimization problems \\ Some classic graph-theoretic problems \\ Shortest path: depth-first search and breadth-first search \\ 13: Dynamic programming: Fibonacci sequences, revisited \\ Dynamic programming and the 0/1 Knapsack problem \\ Dynamic programming and divide-and-conquer \\ 14: Random walks and more about data visualization: Random walks \\ The drunkard's walk \\ Biased random walks \\ Treacherous fields \\ 15: Stochastic programs, probability, and distributions: Stochastic programs \\ Calculating simple probabilities \\ Inferential statistics \\ Distributions \\ Probability distributions \\ Normal distributions \\ Continuous and discrete uniform distributions \\ Binomial and multinomial distributions \\ Exponential and geometric distributions \\ Benford's distribution \\ Hashing and collisions \\ How often does the better team win? \\ 16: Monte Carlo stimulation: Pascal's problem \\ Pass or don't pass? \\ Using table lookup to improve performance \\ Finding pi \\ Some closing remarks about simulation models \\ 17: Sampling and confidence intervals: Sampling the Boston Marathon \\ Central limit theorem \\ Standard error of the mean \\ 18: Understanding experimental data: The behavior of springs \\ Using linear regression to find a fit \\ The behavior of projectiles \\ Coefficient of determination \\ Using a computational model \\ Fitting exponentially distributed data \\ When theory is missing \\ 19: Randomized trials and hypothesis checking: Checking significance \\ Beware of P-values \\ One-tail and one-sample tests \\ Significant or not? \\ Which N? \\ Multiple hypotheses \\ 20: Conditional probability and Bayesian statistics: Conditional probabilities \\ Bayes' theorem \\ Bayesian updating \\ 21: Lies, damned lies, and statistics: Garbage in garbage out (GIGO) \\ Tests are imperfect \\ Pictures can be deceiving \\ Cum hoc ergo propter hoc \\ Statistical measures don't tell the whole story \\ Sampling bias \\ Context matters \\ Beware of extrapolation \\ Texas sharpshooter fallacy \\ Percentages can confuse \\ Statistically significant differences can be insignificant \\ Regressive fallacy \\ Just beware \\ 22: A quick look at machine learning: Feature vectors \\ Distance metrics \\ 23: Clustering: Class cluster \\ K-means clustering \\ A contrived example \\ A less contrived example \\ 24: Classification methods: Evaluating classifiers \\ Predicting the gender of runners \\ K-nearest neighbors \\ Regression-based classifiers \\ Surviving the Titanic \\ Wrapping up \\ Python 3.5 quick reference", } @Article{Hill:2016:HLI, author = "Theodore P. Hill and Ronald F. Fox", title = "{Hubble's Law} Implies {Benford's Law} for Distances to Galaxies", journal = j-J-ASTROPHYS-ASTRON, volume = "37", number = "1", pages = "??--??", month = feb, year = "2016", CODEN = "JASRD7", DOI = "https://doi.org/10.1007/s12036-016-9373-1", ISSN = "0250-6335 (print), 0973-7758 (electronic)", ISSN-L = "0250-6335", bibdate = "Wed Jun 20 15:21:17 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "See \cite{Alexopoulos:2014:BLA}.", acknowledgement = ack-nhfb, fjournal = "Journal of Astrophysics and Astronomy", journal-URL = "http://www.springerlink.com/content/0250-6335", pagecount = "4", } @Article{Hoppe:2016:BLD, author = "Fred M. Hoppe", title = "{Benford's Law} and distractors in multiple choice exams", journal = j-INT-J-MATH-EDU-SCI-TECH, volume = "47", number = "4", pages = "606--612", year = "2016", CODEN = "IJMEBM", DOI = "https://doi.org/10.1080/0020739X.2015.1091515", ISSN = "0020-739x (print), 1464-5211 (electronic)", ISSN-L = "0020-739X", MRclass = "60C05", MRnumber = "3484057", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Mathematical Education in Science and Technology", journal-URL = "http://www.tandfonline.com/loi/tmes20", } @Article{Jameson:2016:BLC, author = "Marie Jameson and Jesse Thorner and Lynnelle Ye", title = "{Benford's Law} for coefficients of newforms", journal = j-INT-J-NUMBER-THEORY, volume = "12", number = "2", pages = "483--494", month = mar, year = "2016", DOI = "https://doi.org/10.1142/S1793042116500299", ISSN = "1793-0421 (print), 1793-7310 (electronic)", ISSN-L = "1793-0421", MRclass = "11F11 (11F30 11K06)", MRnumber = "3461444", MRreviewer = "Bingrong Huang", bibdate = "Sat Mar 25 08:28:06 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/ijnt.bib", URL = "https://www.worldscientific.com/doi/10.1142/S1793042116500299", abstract = "Let $ f(z) = \sum_{n = 1}^\infty \lambda_f(n) e^P{2 \pi i n z} \in S_k^{\mathrm {new}}(\Gamma_0 (N)) $ be a newform of even weight $ k \geq 2 $ on $ \Gamma_0 (N) $ without complex multiplication. Let $P$ denote the set of all primes. We prove that the sequence $ \{ \lambda_f(p) \}_{p \in P}$ does not satisfy Benford s Law in any integer base $ b \geq 2$. However, given a base $ b \geq 2$ and a string of digits $S$ in base $b$, the set $ A_{\lambda_f}(b, S) \coloneq \{ p \mathrm {prime : the first digits of } \lambda_f(p) \mathrm {in base} b \mathrm {are given by} S \} $ has logarithmic density equal to $ \log_b(1 + S^{ 1})$. Thus, $ \{ \lambda_f(p) \}_{p \in P}$ follows Benford's Law with respect to logarithmic density. Both results rely on the now-proven Sato -Tate Conjecture.", acknowledgement = ack-nhfb, fjournal = "International Journal of Number Theory (IJNT)", journal-URL = "https://www.worldscientific.com/worldscinet/ijnt", } @Article{Karthik:2016:ETS, author = "Deepak Karthik and Gil Stelzer and Sivan Gershanov and Danny Baranes and Mali Salmon-Divon", title = "Elucidating tissue specific genes using the {Benford} distribution", journal = "{BMC} Genomics", volume = "17", number = "1", month = aug, year = "2016", DOI = "https://doi.org/10.1186/s12864-016-2921-x", ISSN = "1471-2164", ISSN-L = "1471-2164", bibdate = "Wed Jun 20 15:15:23 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, journal-URL = "https://link.springer.com/journal/12864", } @Article{Li:2016:QNS, author = "Qinglei Li and Zuntao Fu", title = "Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by {Benford}'s law", journal = j-COMM-NONLIN-SCI-NUM-SIM, volume = "33", number = "??", pages = "91--98", month = apr, year = "2016", DOI = "https://doi.org/10.1016/j.cnsns.2015.09.006", ISSN = "1007-5704 (print), 1878-7274 (electronic)", ISSN-L = "1007-5704", MRclass = "86A10 (62M10)", MRnumber = "3417171", bibdate = "Tue Jan 26 11:05:08 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Commun. Nonlinear Sci. Numer. Simul.", fjournal = "Communications in Nonlinear Science and Numerical Simulation", journal-URL = "http://www.sciencedirect.com/science/journal/10075704", } @Article{Mir:2016:CAC, author = "Tariq Ahmad Mir", title = "Citations to articles citing {Benford}'s law: a {Benford} analysis", journal = "CoRR", volume = "abs/1602.01205", number = "??", pages = "??--??", month = "????", year = "2016", CODEN = "????", DOI = "https://doi.org/10.48550/arXiv.1602.01205", ISSN = "????", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://arxiv.org/abs/1602.01205; https://dblp.org/db/journals/corr/corr1602.html#Mir16", abstract = "The occurrence of first significant digits of numbers in large data is often governed by a logarithmically decreasing distribution called Benford's law (BL), reported first by S. Newcomb (SN) and many decades later independently by F. Benford (FB). Due to its counter-intuitiveness the law was ignored for decades as a mere curious observation. However, an indication of its remarkable resurgence is the huge swell in the number of citations received by the papers of SN/FB. The law has come a long way, from obscurity to now being a regular subject of books, peer reviewed papers, patents, blogs and news. Here, we use Google Scholar (GS) to collect the data on the number of citations received by the articles citing the original paper of SN/FB and then investigate whether the leading digits of this citations data are distributed according to the law they discovered. We find that the citations data of literature on BL is in remarkable agreement with the predictions of the law.", acknowledgement = ack-nhfb, DBLP-key = "journals/corr/Mir16", DBLP-mdate = "2018-08-13", } @Article{Mir:2016:LDD, author = "T. A. Mir", title = "The leading digit distribution of the worldwide illicit financial flows", journal = j-QUAL-QUANT, volume = "50", number = "1", pages = "271--281", month = jan, year = "2016", CODEN = "QQEJAV", DOI = "https://doi.org/10.1007/s11135-014-0147-z", ISSN = "0033-5177 (print), 1573-7845 (electronic)", ISSN-L = "0033-5177", bibdate = "Tue Jan 26 07:28:33 MST 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://link.springer.com/article/10.1007/s11135-014-0147-z", acknowledgement = ack-nhfb, fjournal = "Quality \& Quantity", journal-URL = "http://www.springer.com/social+sciences/journal/11135", keywords = "Benford's Law", } @InProceedings{Neubert:2016:IPP, author = "T. Neubert and M. Hildebrandt and J. Dittmann", booktitle = "2016 First International Workshop on Sensing, Processing and Learning for Intelligent Machines {(SPLINE)}", title = "Image pre-processing detection: Evaluation of {Benford's Law}, spatial and frequency domain feature performance", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "1--5", month = jul, year = "2016", DOI = "https://doi.org/10.1109/SPLIM.2016.7528405", bibdate = "Sat Sep 10 11:43:16 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "Benford's law; Computer science; data integrity; Data models; Feature extraction; frequency domain feature performance; Frequency-domain analysis; image data integrity; image filtering; image forensics; image preprocessing blind detection; image preprocessing filters; learning (artificial intelligence); Pattern recognition; sensor intrinsic preprocessing; spatial domain feature performance; statistical analysis; statistical pattern recognition; supervised learning; Transform coding", } @Article{Sheng:2016:DCA, author = "Guorui Sheng and Tao Li and Qingtang Su and Beijing Chen and Yi Tang", title = "Detection of content-aware image resizing based on {Benford}'s law", journal = j-SOFT-COMP, volume = "21", number = "19", pages = "5693--5701", month = apr, year = "2016", DOI = "https://doi.org/10.1007/s00500-016-2146-6", ISSN = "1432-7643 (print), 1433-7479 (electronic)", ISSN-L = "1432-7643", bibdate = "Wed Jun 20 15:03:09 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Soft computing: newsletter of the {Canadian Society for Fuzzy Information and Neural Systems}", } @Article{Sheng:2016:DSC, author = "Guorui Sheng and Tiegang Gao", title = "Detection of Seam-Carving Image Based on {Benford's Law} for Forensic Applications", journal = "International Journal of Digital Crime and Forensics", volume = "8", number = "1", pages = "51--61", month = "????", year = "2016", CODEN = "????", DOI = "https://doi.org/10.4018/IJDCF.2016010104", ISSN = "1941-6210 (print), 1941-6229 (electronic)", ISSN-L = "1941-6210", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/ijdcf/ijdcf8.html#ShengG16", acknowledgement = ack-nhfb, ajournal = "Int. J. Digit. Crime Forensics", DBLP-key = "journals/ijdcf/ShengG16", DBLP-mdate = "2020-08-12", fjournal = "International Journal of Digital Crime and Forensics", journal-URL = "https://www.igi-global.com/gateway/journal/1112", } @Article{Stoerk:2016:SCB, author = "Thomas Stoerk", title = "Statistical corruption in {Beijing}'s air quality data has likely ended in 2012", journal = j-ATMOS-ENV, volume = "127", number = "??", pages = "365--371", year = "2016", CODEN = "ATENBP", DOI = "https://doi.org/10.1016/j.atmosenv.2015.12.055", ISSN = "1352-2310 (print), 1873-2844 (electronic)", ISSN-L = "1352-2310", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1352231015306336", abstract = "This research documents changes in likely misreporting in official air quality data from Beijing for the years 2008--2013. It is shown that, consistent with prior research, the official Chinese data report suspiciously few observations that exceed the politically important Blue Sky Day threshold, a particular air pollution level used to evaluate local officials, and an excess of observations just below that threshold. Similar data, measured by the US Embassy in Beijing, do not show this irregularity. To document likely misreporting, this analysis proposes a new way of comparing air quality data via Benford's Law, a statistical regularity known to fit air pollution data. Using this method to compare the official data to the US Embassy data for the first time, I find that the Chinese data fit Benford's Law poorly until a change in air quality measurements at the end of 2012. From 2013 onwards, the Chinese data fit Benford's Law closely. The US Embassy data, by contrast, exhibit no variation over time in the fit with Benford's Law, implying that the underlying pollution processes remain unchanged. These findings suggest that misreporting of air quality data for Beijing has likely ended in 2012. Additionally, I use aerosol optical density data to show the general applicability of this method of detecting likely misreporting in air pollution data.", acknowledgement = ack-nhfb, fjournal = "Atmospheric Environment", keywords = "Air pollution; Air quality data; Beijing; Benford's Law; Misreporting; PM10; PM2.5", } @Article{Whyman:2016:ICC, author = "G. Whyman and E. Shulzinger and Ed. Bormashenko", title = "Intuitive considerations clarifying the origin and applicability of the {Benford Law}", journal = "Results in Physics", volume = "6", number = "??", pages = "3--6", year = "2016", DOI = "https://doi.org/10.1016/j.rinp.2015.11.010", ISSN = "2211-3797", bibdate = "Tue Jan 26 09:03:59 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "http://www.sciencedirect.com/science/article/pii/S2211379715000728", abstract = "The diverse applications of the Benford law attract investigators working in various fields of physics, biology and sociology. At the same time, the groundings of the Benford law remain obscure. Our paper demonstrates that the Benford law arises from the positional (place-value) notation accepted for representing various sets of data. An alternative to Benford formulae to predict the distribution of digits in statistical data is derived. Application of these formulae to the statistical analysis of infrared spectra of polymers is presented. Violations of the Benford Law are discussed.", acknowledgement = ack-nhfb, keywords = "Benford's Law; Infrared spectra; Leading digit phenomenon; Positional notation; Statistical data", } @Article{Yang:2016:WSZ, author = "Yue Yang and Jianwen Zhu", title = "Write Skew and {Zipf} Distribution: Evidence and Implications", journal = j-TOS, volume = "12", number = "4", pages = "21:1--21:??", month = aug, year = "2016", CODEN = "????", DOI = "https://doi.org/10.1145/2908557", ISSN = "1553-3077 (print), 1553-3093 (electronic)", ISSN-L = "1553-3077", bibdate = "Sat Mar 25 07:00:07 MDT 2017", bibsource = "http://www.acm.org/pubs/contents/journals/tos/; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tos.bib", abstract = "Understanding workload characteristics is essential to storage systems design and performance optimization. With the emergence of flash memory as a new viable storage medium, the new design concern of flash endurance arises, necessitating a revisit of workload characteristics, in particular, of the write behavior. Inspired by Web caching studies where a Zipf-like access pattern is commonly found, we hypothesize that write count distribution at the block level may also follow Zipf's Law. To validate this hypothesis, we study 48 block I/O traces collected from a wide variety of real and benchmark applications. Through extensive analysis, we demonstrate that the Zipf-like pattern indeed widely exists in write traffic provided its disguises are removed by statistical processing. This finding implies that write skew in a large class of applications could be analytically expressed and, thus, facilitates design tradeoff explorations adaptive to workload characteristics.", acknowledgement = ack-nhfb, articleno = "21", fjournal = "ACM Transactions on Storage", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J960", } @Article{Berger:2017:WLB, author = "Arno Berger and Theodore P. Hill", title = "What is \ldots{} {Benford's Law}?", journal = j-NAMS, volume = "64", number = "2", pages = "132--134", month = feb, year = "2017", CODEN = "AMNOAN", DOI = "https://doi.org/10.1090/noti1477", ISSN = "0002-9920 (print), 1088-9477 (electronic)", ISSN-L = "0002-9920", MRclass = "60C05 (60E05)", MRnumber = "3587717", bibdate = "Mon Jan 30 16:18:54 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/nams2010.bib", URL = "http://www.ams.org/publications/journals/notices/201702/rnoti-p132.pdf", acknowledgement = ack-nhfb, ajournal = "Notices Amer. Math. Soc.", fjournal = "Notices of the American Mathematical Society", journal-URL = "http://www.ams.org/notices/", } @InCollection{Best:2017:BBG, author = "Andrew Best and Patrick Dynes and Xixi Edelsbrunner and Brian McDonald and Steven J. Miller and Kimsy Tor and Caroline Turnage-Butterbaugh and Madeleine Weinstein", editor = "M. Nathanson", booktitle = "Springer Proceedings in Mathematics \& Statistics", title = "{Benford} Behavior of Generalized {Zeckendorf} Decompositions", publisher = "Springer International Publishing", address = "Cham, Switzerland", pages = "25--37", year = "2017", DOI = "https://doi.org/10.1007/978-3-319-68032-3_3", ISBN = "3-319-68032-3; 3-319-68030-7", ISBN-13 = "978-3-319-68032-3; 978-3-319-68030-9", MRclass = "11B39 (11B05 11K06 60F05 62E20)", MRnumber = "3754894", MRreviewer = "Vilius Stakenas", bibdate = "Wed Jun 20 15:07:06 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Corazza:2017:LET, author = "Marco Corazza and Andrea Ellero and Alberto Zorzi", title = "L'importanza di Essere ``{UNO}'' (ovvero la legge di {Benford}). ({Italian}) [The importance of Being ``one'' (i.e., the {Benford} law)]", journal = "Lettera Matematica Pristem", volume = "103", number = "1", pages = "31--38", month = dec, year = "2017", DOI = "https://doi.org/10.1007/s10031-017-0051-5", ISSN = "1593-5884 (print), 1970-6820 (electronic)", ISSN-L = "1593-5884", bibdate = "Wed Jun 20 15:01:02 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Daniels:2017:BLQ, author = "Jeremy Daniels and Samantha-Jo Caetano and Dirk Huyer and Andrew Stephen and John Fernandes and Alice Lytwyn and Fred M. Hoppe", title = "{Benford's Law} for Quality Assurance of Manner of Death Counts in Small and Large Databases", journal = "Journal of Forensic Sciences", volume = "62", number = "5", pages = "1326--1331", month = jun, year = "2017", DOI = "https://doi.org/10.1111/1556-4029.13437", ISSN = "0022-1198 (print), 1556-4029 (electronic)", ISSN-L = "0022-1198", bibdate = "Wed Jun 20 14:41:06 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Fellman:2017:BP, author = "Johan Fellman", title = "{Benford} paradox", journal = j-ARKHIMEDES, volume = "??", number = "4", pages = "26--33", year = "2017", CODEN = "AKMDA5", ISSN = "0004-1920", MRclass = "60E99", MRnumber = "3931184", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Arkhimedes", } @Article{Hullemann:2017:ABL, author = "S. H{\"u}llemann and G. Sch{\"u}pfer and J. Mauch", title = "Application of {Benford}'s law: a valuable tool for detecting scientific papers with fabricated data?", journal = "Der Anaesthesist", volume = "66", number = "10", pages = "795--802", month = jun, year = "2017", DOI = "https://doi.org/10.1007/s00101-017-0333-1", ISSN = "0003-2417 (print), 1432-055X (electronic)", ISSN-L = "0003-2417", bibdate = "Wed Jun 20 14:24:42 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @InCollection{Iorliam:2017:UBL, author = "Aamo Iorliam and Anthony T. S. Ho and Adrian Waller and Xi Zhao", editor = "Y. Shi and H. Kim and F. Perez-Gonzalez and F. Liu", booktitle = "Digital Forensics and Watermarking {(IWDW 2016)}", title = "Using {Benford's Law} Divergence and Neural Networks for Classification and Source Identification of Biometric Images", volume = "10082", publisher = "Springer International Publishing", address = "Cham, Switzerland", pages = "88--105", year = "2017", DOI = "https://doi.org/10.1007/978-3-319-53465-7_7", bibdate = "Wed Jun 20 15:08:25 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @InCollection{Klepac:2017:CDS, author = "Goran Klepac", editor = "A. Sangaiah and A. Thangavelu and Sundaram V. Meenakshi", booktitle = "Cognitive Computing for Big Data Systems Over {IoT}", title = "Cognitive Data Science Automatic Fraud Detection Solution, Based on {Benford's Law}, Fuzzy Logic with Elements of Machine Learning", publisher = "Springer International Publishing", address = "Cham, Switzerland", pages = "79--95", month = dec, year = "2017", DOI = "https://doi.org/10.1007/978-3-319-70688-7_4", ISBN = "3-319-70687-X (print), 3-319-70688-8 (electronic)", ISBN-13 = "978-3-319-70687-0 (print), 978-3-319-70688-7 (electronic)", bibdate = "Wed Jun 20 14:57:48 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Lecture Notes on Data Engineering and Communications Technologies", acknowledgement = ack-nhfb, } @InCollection{Mochty:2017:ABL, author = "Ludwig Mochty", editor = "B. Kaluza and K. Braun and H. Beschorner and B. Rolfes", booktitle = "Betriebswirtschaftliche Fragen zu Steuern, Finanzierung, Banken und Management", title = "{Die Achillesferse des Benford's Law: KMUs}. ({German}) [{The} {Achilles} heel of {Benford's Law}: {SMEs}]", publisher = "Springer Fachmedien Wiesbaden", address = "Wiesbaden, Germany", pages = "39--55", year = "2017", DOI = "https://doi.org/10.1007/978-3-658-16730-1_3", bibdate = "Wed Jun 20 15:11:20 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Misc{Oransky:2017:TCT, author = "Ivar Oransky", title = "Two in 100 clinical trials in eight major journals likely contain inaccurate data: Study", howpublished = "Web site article.", day = "5", month = jun, year = "2017", bibdate = "Wed Jun 20 14:31:24 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://retractionwatch.com/2017/06/05/two-100-clinical-trials-eight-major-journals-likely-contain-inaccurate-data-study/", acknowledgement = ack-nhfb, } @Article{Shukla:2017:BDE, author = "Abhishek Shukla and Ankit Kumar Pandey and Anirban Pathak", title = "{Benford}'s Distribution in Extrasolar World: Do the Exoplanets Follow {Benford}'s Distribution?", journal = j-J-ASTROPHYS-ASTRON, volume = "38", number = "1", month = mar, year = "2017", CODEN = "JASRD7", DOI = "https://doi.org/10.1007/s12036-017-9427-z", ISSN = "0250-6335 (print), 0973-7758 (electronic)", ISSN-L = "0250-6335", bibdate = "Wed Jun 20 15:05:03 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Astrophysics and Astronomy", journal-URL = "http://www.springerlink.com/content/0250-6335", } @Article{Tseng:2017:MBL, author = "Hsiang-chi Tseng and Wei-neng Huang and Ding-wei Huang", title = "Modified {Benford's Law} for two-exponent distributions", journal = j-SCIENTOMETRICS, volume = "110", number = "3", pages = "1403--1413", month = mar, year = "2017", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-016-2217-6", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Tue Feb 21 09:16:43 MST 2017", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib", URL = "http://link.springer.com/accesspage/article/10.1007/s11192-016-2217-6", acknowledgement = ack-nhfb, fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Barabesi:2018:GFT, author = "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli and Domenico Perrotta", title = "Goodness-of-Fit Testing for the {Newcomb--Benford Law} With Application to the Detection of Customs Fraud", journal = j-J-BUS-ECON-STAT, volume = "36", number = "2", pages = "346--358", year = "2018", DOI = "https://doi.org/10.1080/07350015.2016.1172014", ISSN = "0735-0015 (print), 1537-2707 (electronic)", ISSN-L = "0735-0015", MRclass = "62G10", MRnumber = "3790219", bibdate = "Mon Jun 15 17:20:33 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jbuseconstat.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/07350015.2016.1172014", acknowledgement = ack-nhfb, fjournal = "Journal of Business \& Economic Statistics", journal-URL = "https://amstat.tandfonline.com/loi/ubes20", onlinedate = "28 Apr 2017", } @Article{Becker:2018:BLC, author = "Thealexa Becker and David Burt and Taylor C. Corcoran and Alec Greaves-Tunnell and Joseph R. Iafrate and Joy Jing and Steven J. Miller and Jaclyn D. Porfilio and Ryan Ronan and Jirapat Samranvedhya and Frederick W. Strauch and Blaine Talbut", title = "{Benford}'s law and continuous dependent random variables", journal = j-ANN-PHYS, volume = "388", pages = "350--381", year = "2018", CODEN = "APNYA6", DOI = "https://doi.org/10.1016/j.aop.2017.11.013", ISSN = "0003-4916 (print), 1096-035x (electronic)", ISSN-L = "0003-4916", MRclass = "60A10 (11K06 60E10)", MRnumber = "3759655", MRreviewer = "Ad Ridder", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annals of Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00034916", } @Article{Berger:2018:BFA, author = "Arno Berger and Chuang Xu", title = "Best Finite Approximations of {Benford's Law}", journal = j-J-THEOR-PROBAB, volume = "??", number = "??", pages = "??--??", month = apr, year = "2018", CODEN = "JTPREO", DOI = "https://doi.org/10.1007/s10959-018-0827-z", ISSN = "0894-9840 (print), 1572-9230 (electronic)", ISSN-L = "0894-9840", bibdate = "Wed Jun 20 14:46:04 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Probability", journal-URL = "http://link.springer.com/journal/10959", xxnote = "Check; not yet assigned volume / number / pages data.", } @Article{Berger:2018:SUR, author = "Arno Berger and Isaac Twelves", title = "On the significands of uniform random variables", journal = j-J-APPL-PROBAB, volume = "55", number = "2", pages = "353--367", month = jun, year = "2018", CODEN = "JPRBAM", DOI = "https://doi.org/10.1017/jpr.2018.23", ISSN = "0021-9002 (print), 1475-6072 (electronic)", ISSN-L = "0021-9002", bibdate = "Sat Mar 16 09:23:51 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/japplprobab.bib", URL = "https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-the-significands-of-uniform-random-variables/0D08D0EEC38F52E431CF41290651603A", abstract = "For all $ \alpha > 0 $ and real random variables $X$, we establish sharp bounds for the smallest and the largest deviation of $ \alpha X$ from the logarithmic distribution also known as Benford's law. In the case of uniform $X$, the value of the smallest possible deviation is determined explicitly. Our elementary calculation puts into perspective the recurring claims that a random variable conforms to Benford's law, at least approximately, whenever it has large spread.", acknowledgement = ack-nhfb, ajournal = "J. Appl. Probab.", fjournal = "Journal of Applied Probability", journal-URL = "https://www.cambridge.org/core/journals/journal-of-applied-probability", onlinedate = "26 July 2018", } @Article{Corazza:2018:IBO, author = "Marco Corazza and Andrea Ellero and Alberto Zorzi", title = "The importance of being ``one'' (or {Benford}'s law)", journal = "Lettera Matematica", volume = "6", number = "1", pages = "33--39", day = "01", month = mar, year = "2018", DOI = "https://doi.org/10.1007/s40329-018-0218-4", ISSN = "2281-5937 (print), 2281-6917 (electronic)", ISSN-L = "2281-6917", MRclass = "60E05 (62P99)", MRnumber = "3775303", bibdate = "Wed Jun 20 14:53:18 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Translated from the Italian.", acknowledgement = ack-nhfb, keywords = "Benford's law; First significant digit; Power sequences; Tax evasion; Vote rigging", } @Article{Ferrer-i-Cancho:2018:OZM, author = "Ramon Ferrer-i-Cancho and Michael S. Vitevitch", title = "The origins of {Zipf}'s meaning-frequency law", journal = j-J-ASSOC-INF-SCI-TECHNOL, volume = "69", number = "11", pages = "1369--1379", month = nov, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1002/asi.24057", ISSN = "2330-1643 (print), 2330-1643 (electronic)", ISSN-L = "2330-1643", bibdate = "Thu Mar 28 08:58:20 MDT 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jaist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "30 July 2018", } @Article{Hartmann:2018:AVK, author = "Sandro Hartmann and Daniel Brinkert", title = "{Aufdeckung von Versicherungsbetrug bei Kfz-Sch{\"a}den mit Hilfe des Benford-Tests}. ({German}) [{Detection} of insurance fraud for vehicle damage using the {Benford} test]", journal = "{Zeitschrift f{\"u}r die gesamte Versicherungswissenschaft}", volume = "107", number = "1", pages = "41--59", month = jan, year = "2018", DOI = "https://doi.org/10.1007/s12297-017-0396-8", ISSN = "0044-2585 (print), 1865-9748 (electronic)", ISSN-L = "0044-2585", bibdate = "Wed Jun 20 14:52:07 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Book{Holt:2018:WEW, author = "Jim Holt", title = "When {Einstein} walked with {G{\"o}del}: excursions to the edge of thought", publisher = pub-FARRAR, address = pub-FARRAR:adr, pages = "xi + 368", year = "2018", ISBN = "0-374-14670-5 (hardcover), 0-374-71784-2 (e-book)", ISBN-13 = "978-0-374-14670-2 (hardcover), 978-0-374-71784-1 (e-book)", LCCN = "PS3608.O4943595 A6 2018", bibdate = "Fri May 18 13:58:57 MDT 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib; https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib; https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", abstract = "A collection of essays on philosophy, mathematics, and science, and the people who pursue them.", acknowledgement = ack-nhfb, author-dates = "1954--", remark = "Chapter 8 discusses the influence of Zipf's Law on Mandelbrot's discovery of fractals.", shorttableofcontents = "Part I: The moving image of eternity \\ Part II: Numbers in the brain, in platonic heaven, and in society \\ Part III: Mathematics, pure and impure \\ Part IV: Higher dimensions, abstract maps \\ Part V: Infinity, large and small \\ Part VI: Heroism, tragedy, and the computer age \\ Part VII: The cosmos reconsidered \\ Part VIII: Quick studies: A selection of shorter essays \\ Part IX: God, sainthood, truth and bullshit", tableofcontents = "Part I: The moving image of eternity \\ 1: When Einstein walked with G{\"o}del \\ 2: Time --- the grand illusion? \\ Part II: Numbers in the brain, in platonic heaven, and in society \\ 3: Numbers guy: the neuroscience of math \\ 4: The Riemann Zeta conjecture and the laughter of the primes \\ 5: Sir Francis Galton, the father of statistics\ldots{}and eugenics \\ Part III: Mathematics, pure and impure \\ 6: A mathematical romance \\ 7: The avatars of higher mathematics \\ 8: Beno{\^\i}t Mandelbrot and the discovery of fractals \\ Part IV: Higher dimensions, abstract maps \\ 9: Geometrical creatures \\ 10: A comedy of colors \\ Part V: Infinity, large and small \\ 11: Infinite visions: Georg Cantor v. David Foster Wallace \\ 12: Worshipping infinity: why the Russians do and the French don't \\ 13: The dangerous idea of the infinitesimal \\ Part VI: Heroism, tragedy, and the computer age \\ 14: The Ada perplex: was Byron's daughter the first coder? \\ 15: Alan Turing in life, logic, and death \\ 16: Dr. Strangelove makes a thinking machine \\ 17: Smarter, happier, more productive \\ Part VII: The cosmos reconsidered \\ 18: The string theory wars: is beauty truth? \\ 19: Einstein, ``Spooky action,'' and the reality of space \\ 20: How will the Universe end? \\ Part VII: Quick studies: a selection of shorter essays \\ Little big man \\ Doom soon \\ Death: bad? \\ The looking-glass war \\ Astrology and the demarcation problem \\ G{\"o}del takes on the U.S. Constitution \\ The law of least action \\ Emmy Noether's beautiful theorem \\ Is logic coercive? \\ Newcomb's problem and the paradox of choice \\ The right not to exist \\ Can't anyone get Heisenberg right? \\ Overconfidence and the Monty Hall problem \\ The cruel law of eponymy \\ The mind of a rock \\ Part IX: God, sainthood, truth, and bullshit \\ 21: Dawkins and the deity \\ 22: On moral sainthood \\ 23: Truth and reference: a philosophical feud \\ 24: Say anything \\ Further Reading \\ Acknowledgments \\ Index", } @InCollection{Humenberger:2018:BGW, author = "Hans Humenberger", editor = "Hans-Stefan Siller and Gilbert Greefrath and Werner Blum", booktitle = "Neue Materialien f{\"u}r einen realit{\"a}tsbezogenen Mathematikunterricht 4: 25 Jahre {ISTRON-Gruppe} - eine Best-of-Auswahl aus der {ISTRON-Schriftenreihe}", title = "{Das Benford-Gesetz`` --- warum ist die Eins als f{\"u}hrende Ziffer von Zahlen bevorzugt?}. ({German}) [{The} ``{Benford Law}'' --- why is one preferred as the leading digit of numbers?]", chapter = "12", publisher = "Springer Fachmedien Wiesbaden", address = "Wiesbaden", pages = "161--176", year = "2018", DOI = "https://doi.org/10.1007/978-3-658-17599-3_12", ISBN = "3-658-17599-0", ISBN-13 = "978-3-658-17599-3", bibdate = "Wed Jun 20 14:56:18 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, language = "German", } @Article{Lacasa:2018:NBL, author = "Lucas Lacasa", title = "{Newcomb--Benford} law helps customs officers to detect fraud in international trade", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "116", number = "1", pages = "11--13", month = dec, year = "2018", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.1819470116", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", bibdate = "Wed Aug 28 15:42:44 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.pnas.org/cgi/doi/10.1073/pnas.1819470116", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/content/by/year", } @Article{Lee:2018:PIB, author = "Edward D. Lee", title = "Partisan Intuition Belies Strong, Institutional Consensus and Wide {Zipf's Law} for Voting Blocs in {US Supreme Court}", journal = j-J-STAT-PHYS, volume = "173", number = "6", pages = "1722--1733", month = dec, year = "2018", CODEN = "JSTPSB", DOI = "https://doi.org/10.1007/s10955-018-2156-0", ISSN = "0022-4715 (print), 1572-9613 (electronic)", ISSN-L = "0022-4715", bibdate = "Fri Mar 1 07:23:36 MST 2019", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jstatphys2010.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Physics", journal-URL = "http://link.springer.com/journal/10955", } @Article{Mir:2018:BLS, author = "Tariq Ahmad Mir and Marcel Ausloos", title = "{Benford}'s law: a ``sleeping beauty'' sleeping in the dirty pages of logarithmic tables", journal = j-J-ASSOC-INF-SCI-TECHNOL, volume = "69", number = "3", pages = "349--358", month = mar, year = "2018", CODEN = "????", DOI = "https://doi.org/10.1002/asi.23845", ISSN = "2330-1643 (print), 2330-1643 (electronic)", ISSN-L = "2330-1643", bibdate = "Tue May 22 14:36:54 MDT 2018", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jaist.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the Association for Information Science and Technology", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643", onlinedate = "17 September 2017", } @Article{Riccioni:2018:RPF, author = "Jessica Riccioni and Roy Cerqueti", title = "Regular paths in financial markets: investigating the {Benford}'s law", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "107", pages = "186--194", year = "2018", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2018.01.008", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", MRclass = "91B24", MRnumber = "3759502", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", } @Article{Aleksandrova:2019:BLD, author = "Elena B. Aleksandrova and Daria S. Lavrova and A. V. Yarmak", title = "{Benford's Law} in the Detection of {DoS} Attacks on Industrial Systems", journal = j-AUTO-CTL-COMP-SCI, volume = "53", number = "8", pages = "954--962", month = "????", year = "2019", CODEN = "ACCSCE", DOI = "https://doi.org/10.3103/S0146411619080030", ISSN = "0146-4116 (print), 1558-108X (electronic)", ISSN-L = "0146-4116", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/accs/accs53.html#AleksandrovaLY19", acknowledgement = ack-nhfb, ajournal = "Autom. Control. Comput. Sci.", DBLP-key = "journals/accs/AleksandrovaLY19", DBLP-mdate = "2021-10-14", fjournal = "Automatic Control and Computer Sciences", } @Article{Benjamin:2019:LSB, author = "Arthur T. Benjamin", title = "The long and the short of {Benford}'s law", journal = "Math Horizons", volume = "26", number = "4", pages = "8--9", year = "2019", DOI = "https://doi.org/10.1080/10724117.2019.1568086", ISSN = "1072-4117", MRclass = "60E05", MRnumber = "3925688", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Math Horiz.", fjournal = "Math Horizons", } @Article{Berger:2019:BFA, author = "Arno Berger and Chuang Xu", title = "Best Finite Approximations of {Benford's Law}", journal = j-J-THEOR-PROBAB, volume = "32", number = "3", pages = "1525--1553", month = sep, year = "2019", CODEN = "JTPREO", DOI = "https://doi.org/10.1007/s10959-018-0827-z", ISSN = "0894-9840 (print), 1572-9230 (electronic)", ISSN-L = "0894-9840", MRclass = "60B10 (60E15 62E15)", MRnumber = "3979679", bibdate = "Tue Jul 9 09:42:45 MDT 2019", bibsource = "http://link.springer.com/journal/10959/32/3; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Theoretical Probability", journal-URL = "http://link.springer.com/journal/10959", } @Article{Cai:2019:LBL, author = "Zhaodong Cai and A. J. Hildebrand and Junxian Li", title = "A local {Benford Law} for a class of arithmetic sequences", journal = j-INT-J-NUMBER-THEORY, volume = "15", number = "3", pages = "613--638", month = apr, year = "2019", DOI = "https://doi.org/10.1142/S1793042119500325", ISSN = "1793-0421 (print), 1793-7310 (electronic)", ISSN-L = "1793-0421", MRclass = "11K31 (11B05 11K06 11N05)", MRnumber = "3925756", MRreviewer = "Vilius Stakenas", bibdate = "Tue Jul 21 10:35:38 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib; https://www.math.utah.edu/pub/tex/bib/ijnt.bib", URL = "https://www.worldscientific.com/doi/10.1142/S1793042119500325", abstract = "It is well known that sequences such as the Fibonacci numbers and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by $ P(d) = \log_{10} (1 + 1 / d) $, $ d = 1, 2, \ldots, 9 $. In this paper, we investigate leading digit distributions of arithmetic sequences from a local point of view. We call a sequence locally Benford distributed of order $k$ if, roughly speaking, $k$-tuples of consecutive leading digits behave like $k$ independent Benford-distributed digits. This notion refines that of a Benford distributed sequence, and it provides a way to quantify the extent to which the Benford distribution persists at the local level. Surprisingly, most sequences known to satisfy Benford's Law have rather poor local distribution properties. In our main result we establish, for a large class of arithmetic sequences, a ``best-possible'' local Benford Law; that is, we determine the maximal value k such that the sequence is locally Benford distributed of order k. The result applies, in particular, to sequences of the form $ \{ a^n \} $, $ \{ a^{n^d} \} $, and $ \{ n^\beta a^{n^\alpha } \} $, as well as the sequence of factorials $ \{ n! \} $ and similar iterated product sequences.", acknowledgement = ack-nhfb, fjournal = "International Journal of Number Theory (IJNT)", journal-URL = "https://www.worldscientific.com/worldscinet/ijnt", } @Article{Cerioli:2019:NBL, author = "Andrea Cerioli and Lucio Barabesi and Andrea Cerasa and Mario Menegatti and Domenico Perrotta", title = "{Newcomb--Benford} law and the detection of frauds in international trade", journal = j-PROC-NATL-ACAD-SCI-USA, volume = "116", number = "1", pages = "106--115", year = "2019", CODEN = "PNASA6", DOI = "https://doi.org/10.1073/pnas.1806617115", ISSN = "0027-8424 (print), 1091-6490 (electronic)", ISSN-L = "0027-8424", MRclass = "91B60 (62P99 91B24)", MRnumber = "3900205", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the National Academy of Sciences of the United States of America", journal-URL = "http://www.pnas.org/content/by/year", } @Article{Durst:2019:BLB, author = "Rebecca F. Durst and Steven J. Miller", title = "{Benford}'s law beyond independence: tracking {Benford} behavior in copula models", journal = "Involve", volume = "12", number = "7", pages = "1193--1218", year = "2019", DOI = "https://doi.org/10.2140/involve.2019.12.1193", ISSN = "1944-4176", MRclass = "60E99", MRnumber = "4023347", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Involve. A Journal of Mathematics", } @Article{Ruankong:2019:CTB, author = "Pongpol Ruankong and Songkiat Sumetkijakan", title = "Chains of truncated beta distributions and {Benford}'s law", journal = "Unif. Distrib. Theory", volume = "14", number = "2", pages = "27--32", year = "2019", ISSN = "1336-913X (print), 2309-5377 (electronic)", ISSN-L = "1336-913X", MRclass = "60A10", MRnumber = "4063899", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Uniform Distribution Theory", } @Article{Zunini:2019:BL, author = "Mar{\'{}\i}a Caputi Zunini", title = "{Benford}'s law", journal = "Publ. Mat. Urug.", volume = "17", pages = "285--290", year = "2019", ISSN = "0797-1443", MRclass = "62E99", MRnumber = "4018784", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Publicaciones Matem\'{a}ticas del Uruguay", } @Article{Barabesi:2020:GBL, author = "Lucio Barabesi and Luca Pratelli", title = "On the {Generalized Benford law}", journal = j-STAT-PROB-LETT, volume = "160", number = "??", pages = "Article 108702", month = may, year = "2020", CODEN = "SPLTDC", DOI = "https://doi.org/10.1016/j.spl.2020.108702", ISSN = "0167-7152 (print), 1879-2103 (electronic)", ISSN-L = "0167-7152", MRclass = "60E05 (60F05 62E15)", MRnumber = "4058264", bibdate = "Mon Aug 3 15:37:29 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/statproblett2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167715220300055", acknowledgement = ack-nhfb, fjournal = "Statistics \& Probability Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01677152", } @Article{Cai:2020:SAB, author = "Zhaodong Cai and Matthew Faust and A. J. Hildebrand and Junxian Li and Yuan Zhang", title = "The surprising accuracy of {Benford}'s law in mathematics", journal = j-AMER-MATH-MONTHLY, volume = "127", number = "3", pages = "217--237", year = "2020", CODEN = "AMMYAE", DOI = "https://doi.org/10.1080/00029890.2020.1690387", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "11K31 (11K38 11Y55 60F99)", MRnumber = "4067893", MRreviewer = "Russell Jay Hendel", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "http://www.jstor.org/journals/00029890.html", } @Article{DAlessandro:2020:BLM, author = "Angelo D'Alessandro", title = "{Benford}'s law and metabolomics: a tale of numbers and blood", journal = "Transfusion and Apheresis Science", volume = "59", number = "6", pages = "103019", month = dec, year = "2020", DOI = "https://doi.org/10.1016/j.transci.2020.103019", ISSN = "1473-0502 (print), 1878-1683 (electronic)", ISSN-L = "1473-0502", bibdate = "Thu May 20 15:42:53 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{DaSilva:2020:BBS, author = "St{\'e}phane Blondeau {Da Silva}", title = "{Benford} or Not {Benford}: a Systematic But Not Always Well-Founded Use of an Elegant Law in Experimental Fields", journal = j-COMMUN-MATH-STAT, volume = "8", number = "2", pages = "167--201", month = jun, year = "2020", CODEN = "????", DOI = "https://doi.org/10.1007/s40304-018-00172-1", ISSN = "2194-6701 (print), 2194-671X (electronic)", ISSN-L = "2194-6701", MRclass = "60E05", MRnumber = "4102358", bibdate = "Fri Jul 24 15:51:38 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communmathstat.bib", URL = "http://link.springer.com/article/10.1007/s40304-018-00172-1", acknowledgement = ack-nhfb, fjournal = "Communications in Mathematics and Statistics", journal-URL = "http://link.springer.com/journal/40304", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", bibdate = "Sat Dec 13 07:24:49 2025", acknowledgement = ack-nhfb, } @Article{daSilva:2020:VNB, author = "A. J. da Silva and S. Floquet and D. O. C. Santos and R. F. Lima", title = "On the validation of the {Newcomb--Benford} law and the {Weibull} distribution in neuromuscular transmission", journal = j-PHYSICA-A, volume = "553", pages = "124606, 15", year = "2020", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2020.124606", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "92C42 (62P10 92C37)", MRnumber = "4096745", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Durst:2020:IGD, author = "R. F. Durst and C. Huynh and A. Lott and S. J. Miller and E. A. Palsson and W. Touw and G. Vriend", title = "The inverse gamma distribution and {Benford}'s law", journal = "PUMP J. Undergrad. Res.", volume = "3", pages = "95--109", year = "2020", DOI = "https://doi.org/10.46787/pump.v3i0.2409", ISSN = "2765-8724", MRclass = "60F05 (42A16 60E10 62E15)", MRnumber = "4143770", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "The PUMP Journal of Undergraduate Research", } @Article{Ectors:2020:ZPL, author = "Wim Ectors and Bruno Kochan and Davy Janssens and Tom Bellemans and Geert Wets", title = "{Zipf}'s power law in activity schedules and the effect of aggregation", journal = j-FUT-GEN-COMP-SYS, volume = "107", number = "??", pages = "1014--1025", month = jun, year = "2020", CODEN = "FGSEVI", DOI = "https://doi.org/10.1016/j.future.2018.04.095", ISSN = "0167-739X (print), 1872-7115 (electronic)", ISSN-L = "0167-739X", bibdate = "Fri Jun 19 07:44:14 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/futgencompsys.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167739X17321891", acknowledgement = ack-nhfb, fjournal = "Future Generation Computer Systems", journal-URL = "http://www.sciencedirect.com/science/journal/0167739X", } @Article{Fang:2020:SCP, author = "Guojun Fang and Qihong Chen", title = "Several common probability distributions obey {Benford}'s law", journal = j-PHYSICA-A, volume = "540", pages = "123129, 8", year = "2020", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2019.123129", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "60E05", MRnumber = "4041619", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A. Statistical Mechanics and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Huang:2020:TFL, author = "Yasheng Huang and Zhiyong Niu and Clair Yang", title = "Testing firm-level data quality in {China} against {Benford}'s law", journal = j-ECONOM-LETT, volume = "192", pages = "109182, 4", year = "2020", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/j.econlet.2020.109182", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "91G70", MRnumber = "4095772", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", } @Article{Kazemitabar:2020:MCD, author = "Jalil Kazemitabar and Javad Kazemitabar", title = "Measuring the conformity of distributions to {Benford's Law}", journal = j-COMMUN-STAT-THEORY-METH, volume = "49", number = "14", pages = "3530--3536", year = "2020", CODEN = "CSTMDC", DOI = "https://doi.org/10.1080/03610926.2019.1590599", ISSN = "0361-0926 (print), 1532-415X (electronic)", ISSN-L = "0361-0926", MRclass = "60E05", MRnumber = "4107617", bibdate = "Fri Jul 24 10:15:17 MDT 2020", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/03610926.2019.1590599", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics: Theory and Methods", journal-URL = "http://www.tandfonline.com/loi/lsta20", onlinedate = "28 Mar 2019", } @Article{Koch:2020:BLC, author = "Christoffer Koch and Ken Okamura", title = "{Benford's Law} and {COVID-19} reporting", journal = j-ECONOM-LETT, volume = "196", pages = "109573", month = nov, year = "2020", CODEN = "ECLEDS", DOI = "https://doi.org/10.1016/j.econlet.2020.109573", ISSN = "0165-1765 (print), 1873-7374 (electronic)", ISSN-L = "0165-1765", MRclass = "92B10 (92D30)", MRnumber = "4150786", bibdate = "Thu May 20 15:46:14 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Economics Letters", journal-URL = "http://www.sciencedirect.com/science/journal/01651765", } @Article{Lee:2020:CFC, author = "Kang-Bok Lee and Sumin Han and Yeasung Jeong", title = "{COVID-19}, flattening the curve, and {Benford}'s law", journal = j-PHYSICA-A, volume = "559", pages = "125090", month = dec, year = "2020", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2020.125090", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", MRclass = "92D30 (62P10)", MRnumber = "4138406", bibdate = "Thu May 20 15:48:54 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @InProceedings{Lindstrom:2020:VRC, author = "Peter Lindstrom", title = "Variable-Radix Coding of the Reals", crossref = "Cornea:2020:ISC", pages = "111--116", month = jun, year = "2020", DOI = "https://doi.org/10.1109/ARITH48897.2020.00024", ISSN = "2576-2265", bibdate = "Wed Jul 7 06:24:52 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", abstract = "Recently proposed real number systems like Posits and Elias codes make use of tapered accuracy resulting from variable-length coding of exponents and significands. Several quite different interpretations of these number systems have been provided, though most often these rely on some combination of fixed- and variable-length codes for exponent and significand. We provide a new perspective on these number systems that unifies known representations while suggesting new ones. Our framework is based on multibit radix representations that encode the exponent in unary, the leading nonzero digit in a variable-length code, and the remaining digits in fixed-length binary code. We show how Posits, the various Elias codes, and IEEE 754 like representations can be expressed in this framework. Moreover, we show that Posits and the Elias and codes represent the leading digit using the canonical Huffman code for a probability distribution given by Benford's law, which governs the probability of leading digits. We further show that Posits correspond to the use of a fixed radix while Elias and codes are based on simple sequences of increasing radix. Our approach provides for an intuitive and uniform framework for representing numbers that reveals a visual mapping between codewords and the binary representation of real numbers obscured by prior frameworks. This new interpretation suggests a generalization of Posits and other number systems and provides simple rules for designing information-theoretically optimal codes.", acknowledgement = ack-nhfb, keywords = "Benford's law; Binary codes; Digital arithmetic; Elias codes; Encoding; floating point; Huffman code; Indexes; posits; Probability distribution; Proposals; real number systems; tapered accuracy; Visualization", } @Article{Ma:2020:ERD, author = "Chengcheng Ma and Baoyuan Wu and Shibiao Xu and Yanbo Fan and Yong Zhang and Xiaopeng Zhang and Zhifeng Li", title = "Effective and Robust Detection of Adversarial Examples via {Benford--Fourier} Coefficients", journal = "CoRR", volume = "??", number = "??", pages = "??--??", month = "????", year = "2020", CODEN = "????", DOI = "https://doi.org/10.48550/arXiv.2005.05552", ISSN = "????", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://arxiv.org/abs/2005.05552 [;] db/journals/corr/corr2005.html#abs-2005-05552", abstract = "Adversarial examples have been well known as a serious threat to deep neural networks (DNNs). In this work, we study the detection of adversarial examples, based on the assumption that the output and internal responses of one DNN model for both adversarial and benign examples follow the generalized Gaussian distribution (GGD), but with different parameters (i.e., shape factor, mean, and variance). GGD is a general distribution family to cover many popular distributions (e.g., Laplacian, Gaussian, or uniform). It is more likely to approximate the intrinsic distributions of internal responses than any specific distribution. Besides, since the shape factor is more robust to different databases rather than the other two parameters, we propose to construct discriminative features via the shape factor for adversarial detection, employing the magnitude of Benford-Fourier coefficients (MBF), which can be easily estimated using responses. Finally, a support vector machine is trained as the adversarial detector through leveraging the MBF features. Extensive experiments in terms of image classification demonstrate that the proposed detector is much more effective and robust on detecting adversarial examples of different crafting methods and different sources, compared to state-of-the-art adversarial detection methods.", acknowledgement = ack-nhfb, DBLP-key = "journals/corr/abs-2005-05552", DBLP-mdate = "2022-04-22", } @Article{Volcic:2020:UDB, author = "Aljo{\v{s}}a Vol{\v{c}}i{\v{c}}", title = "Uniform distribution, {Benford}'s law and scale-invariance", journal = j-BOLL-UNIONE-MAT-ITAL, volume = "13", number = "4", pages = "539--543", year = "2020", CODEN = "BLUMAM", DOI = "https://doi.org/10.1007/s40574-020-00245-6", ISSN = "1972-6724", MRclass = "60A10 (28D05)", MRnumber = "4172954", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Bollettino dell'Unione Matematica Italiana", } @Article{Barabesi:2021:FBL, author = "Lucio Barabesi and Andrea Cerioli and Domenico Perrotta", title = "Forum on {Benford}'s law and statistical methods for the detection of frauds [{Editorial}]", journal = "Stat. Methods Appl.", volume = "30", number = "3", pages = "767--778", year = "2021", DOI = "https://doi.org/10.1007/s10260-021-00588-0", ISSN = "1613-981X (print), 1618-2510 (electronic)", ISSN-L = "1613-981X", MRclass = "Expansion", MRnumber = "4308363", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistical Methods \& Applications. Journal of the Italian Statistical Society", } @Article{Berger:2021:MBL, author = "Arno Berger and Theodore P. Hill", title = "The mathematics of {Benford}'s law: a primer", journal = "Stat. Methods Appl.", volume = "30", number = "3", pages = "779--795", year = "2021", DOI = "https://doi.org/10.1007/s10260-020-00532-8", ISSN = "1613-981X (print), 1618-2510 (electronic)", ISSN-L = "1613-981X", MRclass = "Expansion", MRnumber = "4308364", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistical Methods \& Applications. Journal of the Italian Statistical Society", } @Article{Cerqueti:2021:DVS, author = "Roy Cerqueti and Mario Maggi", title = "Data validity and statistical conformity with {Benford's Law}", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "144", pages = "Paper No. 110740, 7", year = "2021", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2021.110740", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", MRclass = "62R07", MRnumber = "4220694", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Chaos, Solitons \& Fractals", } @Article{daSilvaAzevedo:2021:BLB, author = "Caio {da Silva Azevedo} and Rodrigo Franco Gon{\c{c}}alves and Vagner Luiz Gava and Mauro {de Mesquita Spinola}", title = "A {Benford's Law} based methodology for fraud detection in social welfare programs: {Bolsa Familia} analysis", journal = j-PHYSICA-A, volume = "567", pages = "125626", month = apr, year = "2021", CODEN = "PHYADX", DOI = "https://doi.org/10.1016/j.physa.2020.125626", ISSN = "0378-4371 (print), 1873-2119 (electronic)", ISSN-L = "0378-4371", bibdate = "Thu May 20 15:52:27 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Physica A", journal-URL = "http://www.sciencedirect.com/science/journal/03784371", } @Article{Farris:2021:RRB, author = "Madeleine Farris and Noah Luntzlara and Steven J. Miller and Lily Shao and Mengxi Wang", title = "Recurrence relations and {Benford}'s law", journal = "Stat. Methods Appl.", volume = "30", number = "3", pages = "797--817", year = "2021", DOI = "https://doi.org/10.1007/s10260-020-00547-1", ISSN = "1613-981X (print), 1618-2510 (electronic)", ISSN-L = "1613-981X", MRclass = "11K06 (60F05 65Q30)", MRnumber = "4308365", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistical Methods \& Applications. Journal of the Italian Statistical Society", } @Article{Galveas:2021:FAS, author = "Daniel Galv{\^e}as and Fernando Barros and Carlos Alessandro Fuzo", title = "A forensic analysis of {SARS-CoV-2} cases and {COVID-19} mortality misreporting in the {Brazilian} population", journal = "Public Health", month = may, year = "2021", CODEN = "PUHEAE", DOI = "https://doi.org/10.1016/j.puhe.2021.05.010", ISSN = "0033-3506 (print), 1476-5616 (electronic)", ISSN-L = "0033-3506", bibdate = "Thu May 20 15:54:19 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Article{Jianu:2021:RFI, author = "Ionel Jianu and Iulia Jianu", title = "Reliability of Financial Information from the Perspective of {Benford's Law}", journal = j-ENTROPY, volume = "23", number = "5", pages = "557--??", month = may, year = "2021", CODEN = "ENTRFG", DOI = "https://doi.org/10.3390/e23050557", ISSN = "????", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/entropy/entropy23.html#JianuJ21", acknowledgement = ack-nhfb, DBLP-key = "journals/entropy/JianuJ21", DBLP-mdate = "2021-06-01", fjournal = "Entropy", journal-URL = "https://www.mdpi.com/journal/entropy/", } @Article{Marchand:2021:BLC, author = "Chase Marchand and Dalton Maahs", title = "{Benford's Law} and {COVID-19} Data", journal = j-CHANCE, volume = "34", number = "2", pages = "31--38", year = "2021", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.2021.1915031", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Mon May 17 16:10:57 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/chance.bib", acknowledgement = ack-nhfb, fjournal = "Chance: a magazine for people interested in the analysis of data", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", onlinedate = "26 Apr 2021", } @Article{Mocnik:2021:BLG, author = "Franz-Benjamin Mocnik", title = "{Benford}'s law and geographical information --- the example of {OpenStreetMap}", journal = "International Journal of Geographical Information Science", volume = "35", number = "9", pages = "1746--1772", month = "????", year = "2021", CODEN = "????", DOI = "https://doi.org/10.1080/13658816.2020.1829627", ISSN = "1365-8816 (print), 1365-8824 (electronic)", ISSN-L = "1365-8816", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/gis/gis35.html#Mocnik21", acknowledgement = ack-nhfb, ajournal = "Int. J. Geogr. Inf. Sci.", DBLP-key = "journals/gis/Mocnik21", DBLP-mdate = "2021-09-16", fjournal = "International Journal of Geographical Information Science", } @Article{Mumic:2021:MTD, author = "Nermina Mumic and Peter Filzmoser", title = "A multivariate test for detecting fraud based on {Benford}'s law, with application to music streaming data", journal = "Stat. Methods Appl.", volume = "30", number = "3", pages = "819--840", year = "2021", DOI = "https://doi.org/10.1007/s10260-021-00582-6", ISSN = "1613-981X (print), 1618-2510 (electronic)", ISSN-L = "1613-981X", MRclass = "Expansion", MRnumber = "4308366", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Statistical Methods \& Applications. Journal of the Italian Statistical Society", } @InCollection{Neves:2021:ABL, author = "Gilberto A. Neves and Catarina S. Nunes and Paula Odete Fernandes", booktitle = "Optimization, Learning Algorithms and Applications: First International Conference, {OL2A 2021}, Bragan{\c{c}}a, Portugal, July 19--21, 2021, Revised Selected Papers", title = "Application of {Benford}'s law to the tourism demand: the case of the {Island of Sal, Cape Verde}", volume = "1488", publisher = pub-SV-CHAM, address = pub-SV-CHAM:adr, pages = "587--598", year = "2021", DOI = "https://doi.org/10.1007/978-3-030-91885-9_43", ISBN = "3-030-91884-X; 3-030-91885-8", ISBN-13 = "978-3-030-91884-2; 978-3-030-91885-9", MRnumber = "4432720", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Commun. Comput. Inf. Sci.", acknowledgement = ack-nhfb, } @Article{Tosic:2021:UBL, author = "Aleksandar To{\v{s}}i{\'c} and Jernej Vi{\v{c}}i{\v{c}}", title = "Use of {Benford}'s law on academic publishing networks", journal = j-J-INFORMETRICS, volume = "15", number = "3", pages = "Article 101163", month = aug, year = "2021", CODEN = "????", DOI = "https://doi.org/10.1016/j.joi.2021.101163", ISSN = "1751-1577 (print), 1875-5879 (electronic)", ISSN-L = "1751-1577", bibdate = "Thu May 20 15:50:31 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jinformetrics.bib", URL = "http://www.sciencedirect.com/science/article/pii/S1751157721000341", acknowledgement = ack-nhfb, fjournal = "Journal of Informetrics", journal-URL = "http://www.sciencedirect.com/science/journal/17511577/", } @Article{Wase:2021:BLB, author = "Viktor Wase", title = "{Benford's Law} in the {Beale} ciphers", journal = j-CRYPTOLOGIA, volume = "45", number = "3", pages = "282--286", year = "2021", CODEN = "CRYPE6", DOI = "https://doi.org/10.1080/01611194.2020.1821409", ISSN = "0161-1194 (print), 1558-1586 (electronic)", ISSN-L = "0161-1194", bibdate = "Wed Jun 9 08:58:59 MDT 2021", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptologia.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/01611194.2020.1821409", acknowledgement = ack-nhfb, fjournal = "Cryptologia", journal-URL = "https://www.tandfonline.com/loi/ucry20", } @Article{Barabesi:2022:CTB, author = "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli and Domenico Perrotta", title = "On Characterizations and Tests of {Benford's Law}", journal = j-J-AM-STAT-ASSOC, volume = "117", number = "540", pages = "1887--1903", year = "2022", CODEN = "JSTNAL", DOI = "https://doi.org/10.1080/01621459.2021.1891927", ISSN = "0162-1459 (print), 1537-274X (electronic)", ISSN-L = "0162-1459", bibdate = "Wed Mar 22 07:55:40 MDT 2023", bibsource = "http://www.tandfonline.com/toc/uasa20/117/540; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jamstatassoc2020.bib", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", journal-URL = "http://www.tandfonline.com/loi/uasa20", onlinedate = "06 Apr 2021", } @Article{Cangiotti:2022:BLN, author = "Nicol{\`o} Cangiotti and Mattia Sensi", title = "{Benford}'s law: a number-theoretical perspective", journal = "Palestine Journal of Mathematics", volume = "11", number = "3", pages = "379--385", year = "2022", ISSN = "2219-5688", ISSN-L = "2219-5688", MRclass = "62E10 (11K06 11K16 62A99)", MRnumber = "4447060", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Palest. J. Math.", fjournal = "Palestine Journal of Mathematics", } @Article{Chen:2022:ASU, author = "Tianyi Chen and Charalampos E. Tsourakakis", title = "{AntiBenford} Subgraphs: Unsupervised Anomaly Detection in Financial Networks", journal = "CoRR", volume = "??", number = "??", pages = "??--??", month = "????", year = "2022", CODEN = "????", DOI = "https://doi.org/10.48550/arXiv.2205.13426", ISSN = "????", bibdate = "Wed Mar 29 09:27:49 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/corr/corr2205.html#abs-2205-13426", acknowledgement = ack-nhfb, DBLP-key = "journals/corr/abs-2205-13426", DBLP-mdate = "2022-10-02", } @Article{Groharing:2022:BLC, author = "Brooks Groharing and David McCune", title = "{Benford's Law} and County-Level Votes in {US} {Presidential} Elections", journal = j-CHANCE, volume = "35", number = "2", pages = "4--10", year = "2022", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.2022.2066408", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Sat Jun 4 14:19:58 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/chance.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066408", acknowledgement = ack-nhfb, fjournal = "Chance", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", } @Article{Mbona:2022:FSU, author = "Innocent Mbona and Jan H. P. Eloff", title = "Feature selection using {Benford}'s law to support detection of malicious social media bots", journal = j-INFO-SCI, volume = "582", pages = "369--381", month = jan, year = "2022", CODEN = "ISIJBC", DOI = "https://doi.org/10.1016/j.ins.2021.09.038", ISSN = "0020-0255 (print), 1872-6291 (electronic)", ISSN-L = "0020-0255", MRclass = "62H25 (91D30)", MRnumber = "4318332", bibdate = "Tue Feb 22 14:31:21 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://dblp.org/db/journals/isci/isci582.html#MbonaE22", acknowledgement = ack-nhfb, DBLP-key = "journals/isci/MbonaE22", DBLP-mdate = "2021-12-01", fjournal = "Information Sciences. An International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/00200255", } @Article{Miraglia:2022:AIC, author = "Jorge E. Miraglia and Maria Silvia Gravielle", title = "Atomic ionization, capture, and stopping cross sections by ion impact examined with the {Benford law}", journal = j-ADV-QUANTUM-CHEM, volume = "85", pages = "??--??", year = "2022", CODEN = "AQCHA9", DOI = "https://doi.org/10.1016/bs.aiq.2022.04.006", ISSN = "0065-3276", ISSN-L = "0065-3276", bibdate = "Wed Sep 21 07:26:09 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.sciencedirect.com/science/article/pii/S0065327622000107", acknowledgement = ack-nhfb, ajournal = "Adv. Quantum Chem.", fjournal = "Advances in Quantum Chemistry", journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276/", } @InCollection{Nelson:2022:BLM, author = "Sybil Prince Nelson and Brian Wickman and Jack Null and Eric Gazin", booktitle = "Mathematics and computation in music", title = "{Benford}'s law and music note frequencies", volume = "13267", publisher = pub-SV-CHAM, address = pub-SV-CHAM:adr, pages = "383--389", year = "2022", DOI = "https://doi.org/10.1007/978-3-031-07015-0_34", ISBN = "3-031-07014-3; 3-031-07015-1", ISBN-13 = "978-3-031-07014-3; 978-3-031-07015-0", MRclass = "00A65", MRnumber = "4485599", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = ser-LNCS, acknowledgement = ack-nhfb, } @Article{Pollack:2022:DSB, author = "Paul Pollack and Akash Singha Roy", title = "{Dirichlet}, {Sierpi{\'n}ski}, and {Benford}", journal = j-J-NUMBER-THEORY, volume = "239", number = "??", pages = "352--364", month = oct, year = "2022", CODEN = "JNUTA9", DOI = "https://doi.org/10.1016/j.jnt.2021.12.010", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Fri Jun 3 11:42:55 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022314X22000099", acknowledgement = ack-nhfb, ajournal = "J. Number Theory", fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", } @Article{DaSilva:2022:AOB, author = "St{\'e}phane Blondeau {Da Silva}", title = "An alternative to the oversimplifying {Benford}'s law in experimental fields", journal = j-SANKHYA-B, volume = "84", number = "2", pages = "778--808", year = "2022", CODEN = "SANBBV", DOI = "https://doi.org/10.1007/s13571-022-00287-0", ISSN = "0976-8386 (print), 0976-8394 (electronic)", ISSN-L = "0976-8394", MRclass = "99-01", MRnumber = "4502751", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Sankhya B. The Indian Journal of Statistics", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", bibdate = "Sat Dec 13 07:24:49 2025", acknowledgement = ack-nhfb, } @Article{Velleman:2022:ECD, author = "Paul Velleman and Howard Wainer", title = "Exploring {COVID} Data with {Benford}'s and {Zipf}'s Laws", journal = j-CHANCE, volume = "35", number = "2", pages = "11--15", year = "2022", CODEN = "CNDCE4", DOI = "https://doi.org/10.1080/09332480.2022.2066410", ISSN = "0933-2480 (print), 1867-2280 (electronic)", ISSN-L = "0933-2480", bibdate = "Sat Jun 4 14:19:58 MDT 2022", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/chance.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066410", acknowledgement = ack-nhfb, fjournal = "Chance", journal-URL = "http://chance.amstat.org/; http://link.springer.com/journal/144; http://www.tandfonline.com/loi/ucha20", } @Article{Barabesi:2023:SMB, author = "Lucio Barabesi and Andrea Cerioli and Marco {Di Marzio}", title = "Statistical models and the {Benford} hypothesis: a unified framework", journal = j-TEST, volume = "32", number = "4", pages = "1479--1507", month = dec, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1007/s11749-023-00881-y", ISSN = "1133-0686 (print), 1863-8260 (electronic)", ISSN-L = "1133-0686", MRclass = "99-01", MRnumber = "4683207", bibdate = "Wed Aug 14 12:02:10 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/test.bib", URL = "https://link.springer.com/article/10.1007/s11749-023-00881-y", acknowledgement = ack-nhfb, ajournal = "TEST", fjournal = "TEST: an Official Journal of the Spanish Society of Statistics and Operations Research", journal-URL = "http://link.springer.com/journal/11749", } @Article{Capalbo:2023:LEQ, author = "Francesco Capalbo and Luca Galati and Claudio Lupi and Margherita Smarra", title = "Local elections and the quality of financial statements in municipally owned entities: a {Benford} analysis", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "173", pages = "1--7", year = "2023", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2023.113752", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", MRclass = "91B80 (62P05)", MRnumber = "4612208", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, articleno = "113752", fjournal = "Chaos, Solitons \& Fractals", } @Article{Cerqueti:2023:BLE, author = "Roy Cerqueti and Davide Provenzano", title = "{Benford}'s law for economic data reliability: the case of tourism flows in {Sicily}", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "173", pages = "1--10", year = "2023", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2023.113635", ISSN = "0960-0779,1873-2887", ISSN-L = "0960-0779", MRclass = "62R07 (62P20)", MRnumber = "4598410", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, articleno = "113635", fjournal = "Chaos, Solitons \& Fractals", pagecount = "10", } @Article{Cerqueti:2023:STB, author = "Roy Cerqueti and Claudio Lupi", title = "Severe testing of {Benford}'s law", journal = j-TEST, volume = "32", number = "2", pages = "677--694", month = jun, year = "2023", CODEN = "????", DOI = "https://doi.org/10.1007/s11749-023-00848-z", ISSN = "1133-0686 (print), 1863-8260 (electronic)", ISSN-L = "1133-0686", bibdate = "Wed Oct 11 15:13:55 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/test.bib", URL = "https://link.springer.com/article/10.1007/s11749-023-00848-z", acknowledgement = ack-nhfb, ajournal = "TEST", fjournal = "TEST: an Official Journal of the Spanish Society of Statistics and Operations Research", journal-URL = "http://link.springer.com/journal/11749", MRclass = "99-01", MRnumber = "4621166", } @Article{Chandee:2023:BLM, author = "Vorrapan Chandee and Xiannan Li and Paul Pollack and Akash Singha Roy", title = "On {Benford}'s law for multiplicative functions", journal = j-PROC-AM-MATH-SOC, volume = "151", number = "11", pages = "4607--4619", year = "2023", CODEN = "PAMYAR", DOI = "https://doi.org/10.1090/proc/16480", ISSN = "0002-9939,1088-6826", ISSN-L = "0002-9939", MRclass = "11N60 (11K65)", MRnumber = "4634867", MRreviewer = "Christoph Aistleitner", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Proceedings of the American Mathematical Society", journal-URL = "http://www.ams.org/journals/proc", } @Article{Filho:2023:CDM, author = "T. M. Rocha Filho and J. F. F. Mendes and M. L. Lucio and M. A. Moret", title = "{COVID-19} data, mitigation policies and {Newcomb--Benford} law", journal = j-CHAOS-SOLITONS-FRACTALS, volume = "174", pages = "1--11", year = "2023", CODEN = "CSFOEH", DOI = "https://doi.org/10.1016/j.chaos.2023.113814", ISSN = "0960-0779 (print), 1873-2887 (electronic)", ISSN-L = "0960-0779", MRclass = "92D30 (62P10)", MRnumber = "4618785", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, articleno = "113814", fjournal = "Chaos, Solitons \& Fractals", } @Article{Kazemitabar:2023:GFC, MRclass = "99-01", MRnumber = "4672543", author = "Javad Kazemitabar", title = "A general framework for constructing distributions satisfying {Benford}'s law", journal = j-COMMUN-STAT-SIMUL-COMPUT, volume = "52", number = "12", pages = "6160--6167", year = "2023", CODEN = "CSSCDB", DOI = "https://doi.org/10.1080/03610918.2022.2032153", ISSN = "0361-0918", ISSN-L = "0361-0918", bibdate = "Sat May 18 14:28:31 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput2020.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics: Simulation and Computation", journal-URL = "http://www.tandfonline.com/loi/lssp20", onlinedate = "18 May 2022", } @Article{Kim:2023:EFA, author = "Phuoc Nguyen Kim and Jonatan Contreras and Martine Ceberio and Nguyen Ngoc Thach", title = "Economic and financial applications of {Benford's Law}: from traditional use in audits to help in deep learning", journal = "Internat. J. Uncertain. Fuzziness Knowledge-Based Systems", volume = "31", pages = "197--207", year = "2023", DOI = "https://doi.org/10.1142/S0218488523400111", ISSN = "0218-4885,1793-6411", MRclass = "91B99 (68T07)", MRnumber = "4700940", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems", } @Article{Kondo:2023:HTZ, author = "Illenin O. Kondo and Logan T. Lewis and Andrea Stella", title = "Heavy tailed but not {Zipf}: Firm and establishment size in the {United States}", journal = j-J-APPL-ECONOMETRICS, volume = "38", number = "5", pages = "767--785", month = aug, year = "2023", CODEN = "JAECET", DOI = "https://doi.org/10.1002/jae.2976", ISSN = "0883-7252 (print), 1099-1255 (electronic)", ISSN-L = "0883-7252", bibdate = "Mon Oct 16 14:44:43 MDT 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jappleconometrics.bib", acknowledgement = ack-nhfb, ajournal = "J. Appl. Econometrics", fjournal = "Journal of Applied Econometrics", journal-URL = "https://onlinelibrary.wiley.com/journal/10991255; https://www.jstor.org/journal/japplecon", onlinedate = "23 April 2023", } @Article{Murtagh:2023:WBL, author = "Jack Murtagh", title = "What is {Benford's Law}? {Why} This Unexpected Pattern of Numbers is Everywhere", journal = j-SCI-AMER, volume = "??", number = "??", pages = "??--??", day = "8", month = may, year = "2023", CODEN = "SCAMAC", ISSN = "0036-8733 (print), 1946-7087 (electronic)", ISSN-L = "0036-8733", bibdate = "Mon May 08 09:47:36 2023", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/", acknowledgement = ack-nhfb, fjournal = "Scientific American", journal-URL = "http://www.nature.com/scientificamerican", } @Article{Pollack:2023:BBD, author = "Paul Pollack and Akash Singha Roy", title = "{Benford} behavior and distribution in residue classes of large prime factors", journal = j-CAN-MATH-BULL, volume = "66", number = "2", pages = "626--642", month = jun, year = "2023", CODEN = "CMBUA3", DOI = "https://doi.org/10.4153/S0008439522000601", ISSN = "0008-4395 (print), 1496-4287 (electronic)", ISSN-L = "0008-4395", MRclass = "11A63 (11N37 11N64)", MRnumber = "4584488", MRreviewer = "Steven Joel Miller", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/canmathbull.bib", acknowledgement = ack-nhfb, ajournal = "Can. Math. Bull", fjournal = "Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques", journal-URL = "http://cms.math.ca/cmb/", } @Article{Campanelli:2024:EDS, author = "Leonardo Campanelli", title = "On the {Euclidean} distance statistic of {Benford}'s law", journal = j-COMMUN-STAT-THEORY-METH, volume = "53", number = "2", pages = "451--474", year = "2024", CODEN = "CSTMDC", DOI = "https://doi.org/10.1080/03610926.2022.2082480", ISSN = "0361-0926,1532-415X", ISSN-L = "0361-0926", MRclass = "99-01", MRnumber = "4669200", bibdate = "Tue May 21 16:59:59 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics. Theory and Methods", journal-URL = "http://www.tandfonline.com/loi/lsta20", } @Article{Campanelli:2024:TSB, author = "Leonardo Campanelli", title = "A test of significance for {Benford}'s law based on the {Chebyshev} distance", journal = "Journal of Statistical Research", volume = "58", number = "2", pages = "259--277", year = "2024", ISSN = "0256-422X", ISSN-L = "0256-422X", MRclass = "99-01", MRnumber = "4914668", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "J. Statist. Res.", fjournal = "Journal of Statistical Research", } @Article{Cerqueti:2024:SMD, author = "Roy Cerqueti and Mario Maggi and Jessica Riccioni", title = "Statistical methods for decision support systems in finance: how {Benford}'s law predicts financial risk", journal = j-ANN-OPER-RESEARCH, volume = "342", number = "3", pages = "1445--1469", year = "2024", CODEN = "AOREEV", DOI = "https://doi.org/10.1007/s10479-022-04742-z", ISSN = "0254-5330,1572-9338", ISSN-L = "0254-5330", MRclass = "91G80 (62P05 91B05 91B06)", MRnumber = "4831316", fjournal = "Annals of Operations Research", journal-URL = "http://link.springer.com/journal/10479", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", bibdate = "Sat Dec 13 07:24:49 2025", acknowledgement = ack-nhfb, } @Article{Chang:2024:BLU, author = "Sungkon Chang and Steven J. Miller", title = "{Benford}'s Law under {Zeckendorf} Expansion", journal = j-FIB-QUART, volume = "63", number = "2", pages = "304--335", year = "2024", CODEN = "FIBQAU", DOI = "https://doi.org/10.1080/00150517.2024.2413585", ISSN = "0015-0517", ISSN-L = "0015-0517", bibdate = "Thu Dec 11 11:08:08 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fibquart.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/00150517.2024.2413585", acknowledgement = ack-nhfb, ajournal = "Fib. Quart", fjournal = "The Fibonacci Quarterly. Official Organ of the Fibonacci Association", journal-URL = "http://www.fq.math.ca/", } @Article{Douglass:2024:PPF, author = "Katherine Douglass and Ken Ono", title = "The plane partition function abides by {Benford}'s law", journal = "``Politehnica'' University of Bucharest. Scientific Bulletin. Series A. Applied Mathematics and Physics", volume = "86", number = "2", pages = "123--128", year = "2024", ISSN = "1223-7027 (print), 2286-3672 (electronic)", ISSN-L = "1223-7027", MRclass = "05A17", MRnumber = "4763204", MRreviewer = "Ashok Kumar Agarwal", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys.", fjournal = "``Politehnica'' University of Bucharest. Scientific Bulletin. Series A. Applied Mathematics and Physics", } @Article{Fang:2024:BLR, author = "Xinyu Fang and Steven J. Miller and Maxwell Sun and Amanda Verga", title = "{Benford}'s law and random integer decomposition with congruence stopping condition", journal = j-J-NUMBER-THEORY, volume = "264", number = "??", pages = "307--356", month = nov, year = "2024", CODEN = "JNUTA9", DOI = "https://doi.org/10.1016/j.jnt.2024.05.005", ISSN = "0022-314X (print), 1096-1658 (electronic)", ISSN-L = "0022-314X", bibdate = "Tue Aug 6 14:07:34 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0022314X24001367", acknowledgement = ack-nhfb, ajournal = "J. Number Theory", fjournal = "Journal of Number Theory", journal-URL = "http://www.sciencedirect.com/science/journal/0022314X", MRclass = "11K31", MRnumber = "4772453", MRreviewer = "L\'aszl\'o M\'erai", } @Article{Gupta:2024:ADQ, author = "Solanki Gupta and Vivek Kumar Singh and Sumit Kumar Banshal", title = "Altmetric data quality analysis using {Benford}'s law", journal = j-SCIENTOMETRICS, volume = "129", number = "7", pages = "4597--4621", month = jul, year = "2024", CODEN = "SCNTDX", DOI = "https://doi.org/10.1007/s11192-024-05061-9", ISSN = "0138-9130 (print), 1588-2861 (electronic)", ISSN-L = "0138-9130", bibdate = "Mon Aug 5 13:03:44 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/scientometrics2020.bib", URL = "https://link.springer.com/article/10.1007/s11192-024-05061-9", acknowledgement = ack-nhfb, ajournal = "Scientometrics", fjournal = "Scientometrics", journal-URL = "http://link.springer.com/journal/11192", } @Article{Jianu:2024:TBU, author = "Ionel Jianu and Alexandru Isaic-Maniu and Claudiu Brandas and Marian Pompiliu Cristescu and Corneliu Bente and Claudiu Herteliu", title = "Testing {Benford} and universal laws on gambling and betting data in {Romania}", journal = j-ANN-OPER-RESEARCH, volume = "342", number = "3", pages = "1765--1779", year = "2024", CODEN = "AOREEV", DOI = "https://doi.org/10.1007/s10479-023-05739-y", ISSN = "0254-5330 (print), 1572-9338 (electronic)", ISSN-L = "0254-5330", MRclass = "62P99 (91B99)", MRnumber = "4831330", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Annals of Operations Research", journal-URL = "http://link.springer.com/journal/10479", } @Article{Kossler:2024:SNI, author = "Wolfgang K{\"o}ssler and Hans-J. Lenz and Xing D. Wang", title = "Some new invariant sum tests and {MAD} tests for the assessment of {Benford}'s law", journal = j-COMP-STAT, volume = "39", number = "7", pages = "3779--3800", month = dec, year = "2024", CODEN = "CSTAEB", DOI = "https://doi.org/10.1007/s00180-024-01463-8", ISSN = "0943-4062 (print), 1613-9658 (electronic)", ISSN-L = "0943-4062", bibdate = "Thu Nov 21 06:02:05 MST 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/compstat.bib", URL = "https://link.springer.com/article/10.1007/s00180-024-01463-8", acknowledgement = ack-nhfb, ajournal = "Comp. Stat.", fjournal = "Computational Statistics", journal-URL = "http://link.springer.com/journal/180", } @Article{Stanojevic:2024:SAF, author = "Jelena Stanojevi{\'c} and Dragana Radoji{\v{c}}i{\'c} and Vesna Raji{\'c} and Tatjana Rakonjac-Anti{\'c}", title = "Statistical analysis of fitting {Pareto} and {Weibull} distributions with {Benford}'s law: theoretical approach and empirical evidence", journal = "Hacettepe Journal of Mathematics and Statistics", volume = "53", number = "6", pages = "1724--1741", year = "2024", ISSN = "1303-5010 (print),2651-477X (electronic)", ISSN-L = "1303-5010", MRclass = "60E05 (62P05 62P12 62P30)", MRnumber = "4855691", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Hacet. J. Math. Stat.", fjournal = "Hacettepe Journal of Mathematics and Statistics", journal-URL = "https://dergipark.org.tr/en/pub/hujms", } @Article{Berger:2025:PPB, author = "Arno Berger and Ardalan Rahmatidehkordi", title = "The primes perform a {Benford} dance", journal = j-ANAL-APPL, volume = "23", number = "4", pages = "553--576", year = "2025", DOI = "https://doi.org/10.1142/S0219530524500398", ISSN = "0219-5305 (print), 1793-6861 (electronic)", ISSN-L = "0219-5305", MRclass = "11A63 (11A41 11B39 28A33 60B10)", MRnumber = "4891967", MRreviewer = "Stefan Steinerberger", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Anal. Appl. (Singap.)", fjournal = "Analysis and Applications", journal-URL = "https://www.worldscientific.com/worldscinet/aa", } @Article{Bernik:2025:BLA, author = "V. I. Bernik and N. I. Kalosha and D. V. Vasilyev", title = "{Benford}'s law and approximation of logarithms of natural numbers by rational numbers", journal = "Trudy Instituta Matematiki", volume = "33", number = "1", pages = "7--14", year = "2025", ISSN = "1812-5093", MRclass = "11J71 (11A63)", MRnumber = "4936146", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Tr. Inst. Mat.", fjournal = "Trudy Instituta Matematiki", } @Article{Bradinoff:2025:BL, author = "Nedialko Bradinoff and Maurice Duits", title = "{Benford}'s law and the {$ {\rm C} \beta E $}", journal = "Random Matrices. Theory and Applications", volume = "14", number = "3", pages = "1--34", year = "2025", DOI = "https://doi.org/10.1142/S2010326325500017", ISSN = "2010-3263,2010-3271", MRclass = "60B20 (60F05)", MRnumber = "4942412", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, ajournal = "Random Matrices Theory Appl.", articleno = "2550001", fjournal = "Random Matrices. Theory and Applications", } @Article{Campanelli:2025:TKS, author = "Leonardo Campanelli", title = "Tuning up the {Kolmogorov--Smirnov} test for testing {Benford}'s law", journal = j-COMMUN-STAT-THEORY-METH, volume = "54", number = "3", pages = "739--746", year = "2025", CODEN = "CSTMDC", DOI = "https://doi.org/10.1080/03610926.2024.2318608", ISSN = "0361-0926 (print), 1532-415X (electronic)", ISSN-L = "0361-0926", MRclass = "99-01", MRnumber = "4841139", bibdate = "Wed Nov 19 13:17:59 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Statistics. Theory and Methods", journal-URL = "http://www.tandfonline.com/loi/lsta20", } @Article{Cerqueti:2025:CPM, author = "Roy Cerqueti and Mario Maggi", title = "Classes of probability measures built on the properties of {Benford}'s law", journal = j-ASTA-ADV-STAT-ANAL, volume = "109", number = "1", pages = "197--216", month = mar, year = "2025", CODEN = "????", DOI = "https://doi.org/10.1007/s10182-024-00505-2", ISSN = "1863-8171 (print), 1863-818X (electronic)", ISSN-L = "1863-8171", bibdate = "Tue Mar 4 11:29:15 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/asta.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", MRclass = "99-01", MRnumber = "4873841", URL = "https://link.springer.com/article/10.1007/s10182-024-00505-2", acknowledgement = ack-nhfb, ajournal = "AStA Adv. Stat. Anal.", fjournal = "AStA. Advances in Statistical Analysis", journal-URL = "http://link.springer.com/journal/10182", } @Article{Fernandes:2025:DBF, author = "Pedro Fernandes and S{\'e}amus {\'O} Ciardhu{\'a}in and M{\'a}rio Antunes", title = "Distance-based feature selection using {Benford}'s law for malware detection", journal = j-COMPUT-SECUR, volume = "158", number = "??", pages = "??--??", month = nov, year = "2025", CODEN = "CPSEDU", DOI = "https://doi.org/10.1016/j.cose.2025.104625", ISSN = "0167-4048 (print), 1872-6208 (electronic)", ISSN-L = "0167-4048", bibdate = "Fri Oct 24 11:51:56 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/computsecur2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0167404825003141", acknowledgement = ack-nhfb, ajournal = "Comput. Secur.", articleno = "104625", fjournal = "Computers \& Security", journal-URL = "http://www.sciencedirect.com/science/journal/01674048", } @Article{Kolpakov:2025:BLT, author = "Alexander Kolpakov and Aidan Rocke", title = "{Benford}'s law from {Turing} ensembles and integer partitions", journal = j-PHYS-REV-E, volume = "112", number = "4", articleno = "044149", pages = "??--??", year = "2025", CODEN = "PLEEE8", DOI = "https://doi.org/10.1103/xjlr-sg7r", ISSN = "2470-0045,2470-0053", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", bibdate = "Sat Dec 13 07:24:49 2025", acknowledgement = ack-nhfb, ISSN-L = "1539-3755", MRclass = "94 (62 68)", MRnumber = "4990780", fjournal = "Physical Review E", journal-URL = "http://pre.aps.org/browse", } @InCollection{Kossler:2025:SPT, author = "Wolfgang K{\"o}ssler and Hans-J. Lenz and Xing D. Wang", booktitle = "Stochastic Models, Statistics and Their Applications", title = "On Some Properties and Testing of {Benford's Law}", volume = "499", publisher = pub-SV-CHAM, address = pub-SV-CHAM:adr, pages = "183--198", year = "2025", DOI = "https://doi.org/10.1007/978-3-031-96015-4\_11", ISBN = "3-031-96014-9; 3-031-96015-7", ISBN-13 = "978-3-031-96014-7; 978-3-031-96015-4", MRclass = "99-06", MRnumber = "4995304", bibdate = "Sat Dec 13 07:24:49 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Springer Proc. Math. Stat.", acknowledgement = ack-nhfb, } @Article{Ponnaluri:2025:VMW, author = "Raj V. Ponnaluri", title = "The {Voynich Manuscript} was written in a single, natural language", journal = j-CRYPTOLOGIA, volume = "49", number = "6", pages = "505--524", year = "2025", CODEN = "CRYPE6", DOI = "https://doi.org/10.1080/01611194.2024.2414128", ISSN = "0161-1194 (print), 1558-1586 (electronic)", ISSN-L = "0161-1194", bibdate = "Sat Nov 29 12:38:53 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/cryptologia.bib", URL = "http://www.tandfonline.com/doi/full/10.1080/01611194.2024.2414128", acknowledgement = ack-nhfb, fjournal = "Cryptologia", journal-URL = "https://www.tandfonline.com/loi/ucry20", keywords = "ANOVA (Analysis of Variance); Brevity Law; Heap's Law; Herden's Law; Zipf's Law; Zipf's law of abbreviation", } @Article{Quesada:2025:UNB, author = "Eros Quesada and Massimiliano Cardinale and Nuno Prista and Valerio Bartolino and Patrik B{\"o}rjesson and Mikaela {Bergenius Nord} and Niklas Larson and Annelie Hilvarsson and Katja Ringdahl", title = "Using the {Newcomb--Benford} law to detect species misreporting in mixed pelagic catches", journal = j-ICES-J-MAR-SCI, volume = "82", number = "4", pages = "??--??", month = apr, year = "2025", CODEN = "ICESEC", DOI = "https://doi.org/10.1093/icesjms/fsaf044", ISSN = "1054-3139 (print), 1095-9289 (electronic)", ISSN-L = "1054-3139", bibdate = "Wed Nov 19 09:01:44 MST 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/icesjmarsci2020.bib", URL = "http://academic.oup.com/icesjms/article/82/4/fsaf044/8121722", acknowledgement = ack-nhfb, fjournal = "ICES Journal of Marine Science", journal-URL = "https://academic.oup.com/icesjms", } @Article{Wang:2025:NBL, author = "Zhenhua Wang and Chen Zhang and Ming Ren", title = "A Novel {Benford's Law}-Driven Approach for Detecting Machine-Generated Text", journal = j-TOIS, volume = "43", number = "6", pages = "156:1--156:25", month = nov, year = "2025", CODEN = "ATISET", DOI = "https://doi.org/10.1145/3748305", ISSN = "1046-8188", ISSN-L = "1046-8188", bibdate = "Fri Oct 10 05:49:16 MDT 2025", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/tois.bib", abstract = "Detecting Machine-Generated Text (MGT) is critical for the sustainable development of information systems. Existing studies often overlook the generation inconsistency between AI and human, limiting the effectiveness of detection. This article introduces a novel detection approach, BENADV, and the motivation stems from our recognition that, unlike MGT (probabilistic token prediction), Human-Written Text (HWT) is influenced by individual factors (e.g., personal experience), which constitutes a form of ``manipulation'' at the textual level. Specifically, BENADV is built on our new discovery that MGT adheres more closely to Benford's law compared to HWT. We leverage the adherence patterns as detection mechanisms, and further enhance detection performance through adversarial perturbations controlled by stochastic differential equations. Extensive experiments on general-domain datasets demonstrate that BENADV is SOTA. For instance, on the HC3 dataset, BENADV achieves 99.13\% accuracy and 99.18\% F1, outperforming existing methods by 1.16--7.82\% and 1.37--8.30\%. Moreover, BENADV exhibits remarkable scalability, with its performance consistently exceeding 96\% on vertical domain datasets as AI advances (from GPT-3.5 to GPT-4), far surpassing the 50--60\% performance of existing methods. Notably, BENADV excels in the more challenging short MGT detection. Also, we provide practical insights and discuss implications.", acknowledgement = ack-nhfb, ajournal = "ACM Trans. Inf. Sys.", articleno = "156", fjournal = "ACM Transactions on Information Systems (TOIS)", journal-URL = "https://dl.acm.org/loi/tois", } @Article{Kossler:2026:STB, author = "Wolfgang K{\"o}ssler and Hans-J. Lenz and Xing D. Wang", title = "Scaling tests of {Benford}'s law", journal = j-J-STAT-COMPUT-SIMUL, volume = "96", number = "3", pages = "694--711", year = "2026", CODEN = "JSCSAJ", DOI = "https://doi.org/10.1080/00949655.2025.2571681", ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163", ISSN-L = "0094-9655", bibdate = "Mon Feb 2 06:20:53 MST 2026", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul2020.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Statistical Computation and Simulation", journal-URL = "http://www.tandfonline.com/loi/gscs20", onlinedate = "11 Oct 2025", } @Book{Mebane:20xx:EF, author = "Walter R. {Mebane, Jr.}", title = "Election Forensics", publisher = "????", address = "????", pages = "????", year = "20xx", bibdate = "Sat Sep 10 14:28:31 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", note = "Book in preparation.", acknowledgement = ack-nhfb, keywords = "Benford's Law", remark = "Still not found in library catalogs on 19 November 2025.", } %%% ==================================================================== %%% Cross-referenced entries must come last: @Proceedings{Apers:1989:VLD, editor = "P. M. G. (Petrus Maria Gerardus) Apers and Gio Wiederhold", booktitle = "Very large data bases: proceedings: proceedings of the Fifteenth International Conference on Very Large Data Bases, August 22--25, 1989, Amsterdam, The Netherlands", title = "Very large data bases: proceedings: proceedings of the Fifteenth International Conference on Very Large Data Bases, August 22--25, 1989, Amsterdam, The Netherlands", publisher = pub-MORGAN-KAUFMANN, address = pub-MORGAN-KAUFMANN:adr, pages = "xii + 467", year = "1989", ISBN = "1-55860-101-5", ISBN-13 = "978-1-55860-101-7", LCCN = "QA 76.9 D3 I61 1989", bibdate = "Sat Dec 7 13:05:35 MST 1996", bibsource = "DBLP; http://dblp.uni-trier.de; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, keywords = "database management -- congresses", } @Book{Gell-Mann:1997:QJA, author = "Murray Gell-Mann", booktitle = "The quark and the jaguar: adventures in the simple and the complex", title = "The quark and the jaguar: adventures in the simple and the complex", publisher = pub-W-H-FREEMAN, address = pub-W-H-FREEMAN:adr, pages = "xviii + 392", year = "1997", ISBN = "0-7167-2725-0 (paperback)", ISBN-13 = "978-0-7167-2725-5 (paperback)", LCCN = "QC774.G45 A3 1994", bibdate = "Fri Aug 8 06:26:36 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/prng.bib", URL = "http://www.gbv.de/dms/bowker/toc/9780716725817.pdf; http://www.zentralblattmath.org/zmath/en/search/?an=0833.00011", abstract = "From one of the architects of the new science of simplicity and complexity comes a highly personal, unifying vision of the natural world. As a theoretical physicist, Murray Gell-Mann has explored nature at its most fundamental level. His achievements include the 1969 Nobel Prize for work leading up to his discovery of the quark --- the basic building block of all atomic nuclei throughout the universe. But Gell-Mann is a man of many intellectual passions, with lifelong interests in fields that seek to understand existence at its most complex: natural history, biological evolution, the history of language, and the study of creative thinking. These seemingly disparate pursuits come together in Gell-Mann's current work at the Santa Fe Institute, where scientists are investigating the similarities and differences among complex adaptive systems --- systems that learn or evolve by utilizing acquired information. They include a child learning his or her native language, a strain of bacteria becoming resistant to an antibiotic, the scientific community testing new theories, or an artist implementing a creative idea. The Quark and the Jaguar is Gell-Mann's own story of finding the connections between the basic laws of physics and the complexity and diversity of the natural world. The simple: a quark inside an atom. The complex: a jaguar prowling its jungle territory in the night. Exploring the relationship between them becomes a series of exciting intellectual adventures.", acknowledgement = ack-nhfb, subject = "Gell-Mann, Murray; Travel; Ecuador; Particles (Nuclear physics); Nuclear physicists; United States; Biography; Description and travel", tableofcontents = "Part 1. The Simple and the Complex \\ 1. Prologue: An Encounter in the Jungle \\ 2. Early Light \\ 3. Information and Crude Complexity \\ 4. RANDomness \\ 5. A Child Learning a Language \\ 6. Bacteria Developing Drug Resistance \\ 7. The Scientific Enterprise \\ 8. The Power of Theory \\ 9. What Is Fundamental? \\ Part 2. The Quantum Universe \\ 10. Simplicity and Randomness in the Quantum Mechanics Universe \\ 11. A Contemporary View of Quantum Mechanics \\ 12. Quantum Mechanics and Flapdoodle \\ 13. Quarks and All That: The Standard Model \\ 14. Superstring Theory: Unification at Last? \\ 15. Time's Arrow's: Forward and Backward Time \\ Part 3. Selection and Fitness \\ 16. Selection at Work in Biological Evolution and Elsewhere \\ 17. From Learning to Creative Thinking \\ 18. Superstition and Skepticism \\ 19. Adaptive and Maladaptive Schema \\ 20. Machines That Learn or Simulate Learning \\ Part 4. Diversity and Sustainability \\ 21. Diversities Under Threat \\ 22. Transitions to a More Sustainable World \\ 23. Afterword \\ Index", } @Proceedings{ACM:2000:PIC, editor = "{ACM}", booktitle = "{Proceedings of the 2000 International Conference on Software Engineering: ICSE 2000, the new millennium: June 4--11, 2000, Limerick, Ireland}", title = "{Proceedings of the 2000 International Conference on Software Engineering: ICSE 2000, the new millennium: June 4--11, 2000, Limerick, Ireland}", publisher = pub-ACM, address = pub-ACM:adr, pages = "xviii + 843", year = "2000", ISBN = "1-58113-206-9, 0-7803-6325-6 (casebound), 0-7803-6326-4 (microfiche)", ISBN-13 = "978-1-58113-206-9, 978-0-7803-6325-0 (casebound), 978-0-7803-6326-7 (microfiche)", LCCN = "QA76 N271 2000", bibdate = "Sun Feb 17 08:56:25 MST 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.bibsys.no:2100/BIBSYS", acknowledgement = ack-nhfb, } @Proceedings{Raidl:2003:AEC, editor = "Gunther Raidl", booktitle = "{Applications of evolutionary computing: EvoWorkshops 2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}", title = "{Applications of evolutionary computing: EvoWorkshops 2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}", volume = "2611", publisher = pub-SV, address = pub-SV:adr, pages = "xxi + 708", year = "2003", CODEN = "LNCSD9", DOI = "????", ISBN = "3-540-00976-0 (softcover)", ISBN-13 = "978-3-540-00976-4 (softcover)", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", LCCN = "QA76.618 .E899 2003", bibdate = "Thu Aug 21 09:09:03 MDT 2003", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/lncs.bib", series = ser-LNCS, URL = "http://link.springer-ny.com/link/service/series/0558/tocs/t2611.htm; http://www.springerlink.com/content/978-3-540-00976-4; http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2611", acknowledgement = ack-nhfb, keywords = "evolutionary computation --- congresses; evolutionary programming (computer science) --- congresses", } @Article{Rybski:2023:ALZ, author = "Diego Rybski and Antonio Ciccone", title = "{Auerbach}, {Lotka}, and {Zipf}: pioneers of power-law city-size distributions", journal = j-ARCH-HIST-EXACT-SCI, volume = "77", number = "6", pages = "601--613", month = nov, year = "2023", CODEN = "AHESAN", DOI = "https://doi.org/10.1007/s00407-023-00314-0", ISSN = "0003-9519 (print), 1432-0657 (electronic)", ISSN-L = "0003-9519", bibdate = "Wed Mar 27 09:47:28 MDT 2024", bibsource = "https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", URL = "https://link.springer.com/article/10.1007/s00407-023-00314-0", acknowledgement = ack-nhfb, ajournal = "Arch. Hist. Exact Sci.", fjournal = "Archive for History of Exact Sciences", journal-URL = "http://link.springer.com/journal/407", } @Book{Warren:2003:HD, author = "Henry S. Warren", booktitle = "Hacker's delight", title = "Hacker's delight", publisher = pub-AW, address = pub-AW:adr, pages = "xiv + 306", year = "2003", ISBN = "0-201-91465-4", ISBN-13 = "978-0-201-91465-8", LCCN = "QA76.6 .W375 2003", bibdate = "Tue Jan 03 18:20:34 2006", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", note = "While this book does not specifically address computational aspects of floating-point arithmetic (apart from the nine-page Chapter 15), it has extensive coverage of, and clever algorithms for, integer arithmetic operations that are fundamental for implementing hardware floating-arithmetic and software multiple-precision arithmetic.", URL = "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654; http://www.hackersdelight.org/; http://www.hackersdelight.org/hackerTOC.pdf; http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf", acknowledgement = ack-nhfb, keywords = "DEC PDP-10; division by constants; Gray code; Hilbert curves; IEEE 754 floating-point arithmetic; integer cube root; integer division; integer exponentiation; integer logarithm; integer square root; prime numbers; unusual number bases", remark = "Foreword by Guy L. Steele, Jr., who begins ``When I first got a summer job at MIT's Project MAC almost 30 years ago, I was delighted to be able to work with the DEC PDP-10 computer, which was more fun to program in assembly language than any other computer, bar none, because of its rich yet tractable set of instructions for performing bit tests, bit masking, field manipulation, and operations on integers. Though the PDP-10 has not been manufactured for quite some years, there remains a thriving cult of enthusiasts who keep old PDP-10 hardware running and who run old PDP-10 software---entire operating systems and their applications---by using personal computers to simulate the PDP-10 instruction set.''", subject = "Computer programming; Computer hackers", tableofcontents = "Preface\par 1. Introduction\par Notation\par Instruction Set and Execution Time Model\par 2. Basis\par Manipulating Rightmost Bits \\ Addition Combined with Logical Operations \\ Inequalities among Logical and Arithmetic Expressions \\ Absolute Value Function \\ Sign Extension \\ Shift Right Signed from Unsigned \\ Sign Function \\ Three-Valued Compare \\ Transfer of Sign \\ Decoding a `Zero Means 2**n' Field \\ Comparison Predicates \\ Overflow Detection \\ Condition Code Result of Add, Subtract, and Multiply \\ Rotate Shifts \\ Double-Length Add/Subtract \\ Double-Length Shifts \\ Multibyte Add, Subtract, Absolute Value \\ Doz, Max, Min \\ Exchanging Registers \\ Alternating among Two or More Values\par 3. Power-of-2 Boundaries\par Rounding Up/Down to a Multiple of a Known Power of 2 \\ Rounding Up/Down to the Next Power of 2 \\ Detecting a Power-of-2 Boundary Crossing\par 4. Arithmetic Bounds\par Checking Bounds of Integers \\ Propagating Bounds through Adds and Subtracts \\ Propagating Bounds through Logical Operations \\ Signed Bounds\par 5. Counting Bits\par Counting 1-bits \\ Parity \\ Counting Leading 0's \\ Counting Trailing 0's\par 6. Searching Words\par Find First 0-Byte \\ Find First String of 1-Bits of a Given Length\par 7. Rearranging Bits and Bytes\par Reversing Bits and Bytes \\ Shuffling Bits \\ Transposing a Bit Matrix \\ Compress, or Generalized Extract \\ General Permutations, Sheep and Goats Operation \\ Rearrangements and Index Transformations\par 8. Multiplication\par Multiword Multiplication \\ High-Order Half of 64-Bit Product \\ High-Order Product Signed from/to Unsigned \\ Multiplication by Constants\par 9. Integer Division\par Preliminaries \\ Multiword Division \\ Unsigned Short Division from Signed Division \\ Unsigned Long Division\par 10. Integer Division by Constants\par Signed Division by a Known Power of 2 \\ Signed Remainder from Division by a Known Power of 2 \\ Signed Division and Remainder by Non-powers of 2 \\ Signed Division by Divisors >= 2 \\ Signed Division by Divisors <= -2 \\ Incorporation into a Compiler \\ Miscellaneous Topics \\ Unsigned Division \\ Unsigned Division by Divisors >= 1 \\ Incorporation into a Compiler (Unsigned) \\ Miscellaneous Topics (Unsigned) \\ Applicability to Modulus and Floor Division \\ Similar Methods \\ Sample Magic Numbers \\ Exact Division by Constants \\ Test for Zero Remainder after Division by a Constant\par 11. Some Elementary Functions\par Integer Square Root \\ Integer Cube Root \\ Integer Exponentiation \\ Integer Logarithm\par 12. Unusual Bases for Number Systems\par Base -2 \\ Base -1 + i \\ Other Bases \\ What is the Most Efficient Base?\par 13. Gray Code \\ Gray Code \\ Incrementing a Gray Coded Integer \\ Negabinary Gray Code \\ Brief History and Applications\par 14. Hilbert's Curve\par A Recursive Algorithm for Generating the Hilbert Curve \\ Coordinates from Distance along the Hilbert Curve \\ Distance from Coordinates on the Hilbert Curve \\ Incrementing the Coordinates on the Hilbert Curve \\ Non-recursive Generating Algorithms \\ Other Space-Filling Curves \\ Applications\par 15. Floating-Point\par IEEE Format \\ Comparing Floating-Point Numbers Using Integer Operations \\ The Distribution of Leading Digits \\ Table of Miscellaneous Values\par 16. Formulas for Primes\par Introduction \\ Willans's Formulas \\ Wormell's Formula \\ Formulas for Other Difficult Functions\par Appendix A. Arithmetic Tables for a 4-Bit Machine\par Appendix B. Newton's Method\par Bibliography.", } @Proceedings{Gama:2005:MLE, editor = "Jo{\~a}ao Gama and Rui Camacho and Pavel Brazdil and Al{\'\i}pio M{\'a}rio Jorge and Lu{\'\i}s Torgo", booktitle = "{Machine learning --- ECML 2005: 16th European Conference on Machine Learning, Porto, Portugal, October 3--7, 2005: proceedings}", title = "{Machine learning --- ECML 2005: 16th European Conference on Machine Learning, Porto, Portugal, October 3--7, 2005: proceedings}", volume = "3720", publisher = pub-SV, address = pub-SV:adr, pages = "xxiii + 769", year = "2005", ISBN = "3-540-29243-8", ISBN-13 = "978-3-540-29243-2", ISSN = "0302-9743 (print), 1611-3349 (electronic)", LCCN = "Q325.5 .E26 2005", bibdate = "Tue Nov 15 08:57:03 MST 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", series = ser-LNCS # " and " # ser-LNAI, URL = "http://www.loc.gov/catdir/enhancements/fy0663/2005933045-d.html; http://www.springerlink.com/openurl.asp?genre=issue\%26issn=0302-9743\%26volume=3720", acknowledgement = ack-nhfb, meetingname = "ECML 2005 (2005: Porto, Portugal)", subject = "Machine learning; Congresses", } @Proceedings{Neumann:2005:CAE, editor = "L{\'a}szl{\'o} Neumann and Mateu Sbert and Bruce Gooch and Werner Purgathofer", booktitle = "{Computational aesthetics 2005: Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, Girona, Spain, 18--20 May 2005}", title = "{Computational aesthetics 2005: Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, Girona, Spain, 18--20 May 2005}", publisher = "Eurographics Association", address = "Aire-la-Ville, Switzerland", pages = "245", year = "2005", ISBN = "3-905673-27-4", ISBN-13 = "978-3-905673-27-2", ISSN = "1816-0859", bibdate = "Tue Nov 15 06:34:24 2011", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Computational aesthetics", acknowledgement = ack-nhfb, } @Book{Alvarez:2008:EFD, editor = "R. Michael Alvarez and Thad E. (Thad Edward) Hall and Susan D. Hyde", booktitle = "Election Fraud: Detecting and Deterring Electoral Manipulation", title = "Election Fraud: Detecting and Deterring Electoral Manipulation", publisher = "Brookings Institution Press", address = "Washington, DC, USA", pages = "xiii + 255", year = "2008", ISBN = "0-8157-0138-1 (hardcover), 0-8157-0139-X (paperback)", ISBN-13 = "978-0-8157-0138-5 (hardcover), 978-0-8157-0139-2 (paperback)", LCCN = "JK1994 .E43 2008", bibdate = "Sat Sep 10 14:23:39 MDT 2016", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/toc/ecip0810/2008005719.html", abstract = "Brings together experts on election law, election administration, and U.S. and comparative politics to examine the U.S. understanding of election fraud. With survey data, incident reports, and state-collected fraud allegations, measures the extent and nature of election fraud in U.S. Analyzes techniques for detecting and potentially deterring fraud..", acknowledgement = ack-nhfb, keywords = "Benford's Law", subject = "Elections; Corrupt practices; United States; Prevention; Ballot; Security measures; Case studies", tableofcontents = "Corruption of the election process under U.S. federal law / Craig C. Donsanto \\ International principles for election integrity / Thad E. Hall and Tova Andrea Wang \\ Beyond election fraud: manipulation, violence, and foreign power intervention / Gamze {\eth}Cavdar \\ Measuring perceptions of election threats: survey data from voters and elites / R. Michael Alvarez and Thad E. Hall \\ Caught in the act: recent federal election fraud cases / Delia Bailey \\ Correlates of fraud: studying state election fraud allegations / R. Michael Alvarez and Frederick J. Boehmke \\ Fraud or failure? what incident reports reveal about election anomalies and irregularities / D. Roderick Kiewiet \ldots{} [et al.] \\ Identifying and preventing signature fraud on ballot measure petitions / Todd Donovan and Daniel A. Smith \\ The case of the 2002 general election / R. Michael Alvarez and Jonathan N. Katz \\ Election forensics: the second-digit Benford's law test and recent American presidential elections / Walter R. Mebane, Jr. \\ On the trail of fraud: estimating the flow of votes between Russia's elections / Mikhail Myagkov, Peter C. Ordeshook, and Dimitry Shaikin \\ How international election observers detect and deter fraud / Susan D. Hyde \\ Unintended consequences of election monitoring / Alberto Simpser", } @Book{Horgan:2009:PRI, author = "Jane M. Horgan", booktitle = "Probability with {R}: an introduction with computer science applications", title = "Probability with {R}: an introduction with computer science applications", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xviii + 393", year = "2009", ISBN = "0-470-28073-5 (cloth)", ISBN-13 = "978-0-470-28073-7 (cloth)", LCCN = "QA76.9.M35 H863 2009", bibdate = "Wed Sep 15 09:37:35 MDT 2010", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/s-plus.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/toc/ecip0819/2008022817.html; http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470280735.html", acknowledgement = ack-nhfb, subject = "computer science; mathematics; probabilities; R (computer programming language)", } @Proceedings{Paredaens:2009:PTE, editor = "Jan Paredaens and Jianwen Su", booktitle = "{Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems: PODS'09, Providence, Rhode Island, June 29--July 1, 2009}", title = "{Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems, PODS'09, Providence, Rhode Island, June 29--July 1, 2009}", publisher = pub-ACM, address = pub-ACM:adr, pages = "x + 288", year = "2009", ISBN = "1-60558-553-X", ISBN-13 = "978-1-60558-553-6", LCCN = "????", bibdate = "Thu Jul 02 12:41:14 2009", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Nigrini:2011:FAM, author = "Mark J. (Mark John) Nigrini", booktitle = "Forensic analytics: methods and techniques for forensic accounting investigations", title = "Forensic analytics: methods and techniques for forensic accounting investigations", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xvi + 463", year = "2011", DOI = "https://doi.org/10.1002/9781118386798", ISBN = "0-470-89046-0, 1-118-08763-1 (e-book), 1-118-08766-6 (e-book), 1-118-08768-2 (e-book), 1-118-38679-5 (e-book)", ISBN-13 = "978-0-470-89046-2, 978-1-118-08763-3 (e-book), 978-1-118-08766-4 (e-book), 978-1-118-08768-8 (e-book), 978-1-118-38679-8 (e-book)", LCCN = "HV6768 .N54 2011", bibdate = "Sat Feb 23 17:38:11 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "Wiley corporate F and A", URL = "http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-d.html; http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-t.html; http://catdir.loc.gov/catdir/enhancements/fy1109/2011007210-b.html", abstract = "The book will review and discuss (with Access and Excel examples) the methods and techniques that investigators can use to uncover anomalies in corporate and public sector data. These anomalies would include errors, biases, duplicates, number rounding, and omissions. The focus will be the detection of fraud, intentional errors, and unintentional errors using data analytics. Despite the quantitative and computing bias, the book will still be interesting to read with interesting vignettes and illustrations. Most chapters will be understandable by accountants and auditors that usually are lacking in the rigors of mathematics and statistics. The data interrogation methods are based on (a) known statistical techniques, and (b) the author's own published research in the field.", acknowledgement = ack-nhfb, subject = "Forensic accounting; Fraud; Misleading financial statements; LAW / Forensic Science", tableofcontents = "Front Matter \\ Using Access in Forensic Investigations \\ Using Excel in Forensic Investigations \\ Using PowerPoint in Forensic Presentations \\ High-Level Data Overview Tests \\ Benford's Law: The Basics \\ Benford's Law: Assessing Conformity \\ Benford's Law: The Second-Order and Summation Tests \\ Benford's Law: The Number Duplication and Last-Two Digits Tests \\ Testing the Internal Diagnostics of Current Period and Prior Period Data \\ Identifying Fraud Using the Largest Subsets and Largest Growth Tests \\ Identifying Anomalies Using the Relative Size Factor Test \\ Identifying Fraud Using Abnormal Duplications within Subsets \\ Identifying Fraud Using Correlation \\ Identifying Fraud Using Time-Series Analysis \\ Fraud Risk Assessments of Forensic Units \\ Examples of Risk Scoring with Access Queries \\ The Detection of Financial Statement Fraud \\ Using Analytics on Purchasing Card Transactions \\ References \\ Index", } @Book{Zenil:2011:RTC, editor = "Hector Zenil", booktitle = "Randomness through computation: some answers, more questions", title = "Randomness through computation: some answers, more questions", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "xviii + 419", year = "2011", ISBN = "981-4327-74-3", ISBN-13 = "978-981-4327-74-9", LCCN = "QA274 .R363 2011", bibdate = "Mon Feb 18 18:30:30 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, subject = "Stochastic processes; Computational complexity; Random polynomials", tableofcontents = "Is randomness necessary? / R. Graham \\ Probability is a lot of logic at once: if you don't know which one to pick, take 'em all / T. Toffoli \\ Statistical testing of randomness: new and old procedures / A. L. Rukhin \\ Scatter and regularity imply Benford's law\ldots{} and more / N. Gauvrit, J.-P. Delahaye \\ Some bridging results and challenges in classical, quantum and computational randomness / G. Longo, C. Palamidessi, T. Paul \\ Metaphysics, metamathematics and metabiology / G. Chaitin \\ Uncertainty in physics and computation / M. A. Stay \\ Indeterminism and randomness through physics / K. Svozil \\ The Martin-L{\"o}f--Chaitin thesis: the identification by recursion theory of the mathematical notion of random sequence / J.-P. Delahaye \\ The road to intrinsic randomness / S. Wolfram \\ Algorithmic probability its discovery, it's properties and application to strong AI / R. J. Solomonoff \\ Algorithmic randomness as foundation of inductive reasoning and artificial intelligence / M. Hutter \\ Randomness, Occam's razor, AI, creativity and digital physics / J. Schmidhuber \\ Randomness everywhere: my path to algorithmic information theory / C. S. Calude \\ The impact of algorithmic information theory on our current views on complexity, randomness, information and prediction / P. G\'acs \\ Randomness, computability and information / J. S. Miller \\ Studying randomness through computation / A. Nies \\ Computability, algorithmic randomness and complexity / R. G. Downey \\ Is randomness native to computer science? Ten years after / M. Ferbus-Zanda, S. Grigorieff \\ Randomness as circuit complexity (and the connection to pseudorandomness) / E. Allender \\ Randomness: a tool for constructing and analyzing computer programs / A. Ku{\v{c}}era \\ Connecting randomness to computation / M. Li \\ From error-correcting codes to algorithmic informational theory / L. Staiger \\ Randomness in algorithms / O. Watanabe \\ Is the universe random? / C. S. Calude, J. L. Casti, G. J. Chaitin, P. C. W. Davies, K. Svozil, S. Wolfram \\ What is computation? (How) Does nature computer? / C. S. Calude, G. J. Chaitin, E. Fredkin, A. J. Leggett, R. de Ruyter, T. Toffoli, S. Wolfram", } @Book{Gorroochurn:2012:CPP, author = "Prakash Gorroochurn", booktitle = "Classic Problems of Probability", title = "Classic Problems of Probability", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xi + 314", year = "2012", DOI = "https://doi.org/10.1002/9781118314340", ISBN = "1-118-06325-2 (paperback), 1-118-31432-8, 1-118-31433-6 (e-book), 1-118-31434-4 (e-book), 1-118-31431-X (e-book)", ISBN-13 = "978-1-118-06325-5 (paperback), 978-1-118-31432-6, 978-1-118-31433-3 (e-book), 978-1-118-31434-0 (e-book), 978-1-118-31431-9 (e-book)", LCCN = "QA273.A4", bibdate = "Mon Feb 25 05:50:42 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, tableofcontents = "Front Matter / i?-xi \\ Chapter 1: Cardano and Games of Chance (1564) / 1--8 \\ Chapter 2: Galileo and a Discovery Concerning Dice (1620) / 9--12 \\ Chapter 3: The Chevalier de M{\'e}r{\'e} Problem I: The Problem of Dice (1654) / 13--19 \\ Chapter 4: The Chevalier de M{\'e}r{\'e} Problem II: The Problem of Points (1654) / 20--38 \\ Chapter 5: Huygens and the Gambler's Ruin (1657) / 39--48 \\ Chapter 6: The Pepys--Newton Connection (1693) / 49--53 \\ Chapter 7: Rencontres with Montmort (1708) / 54--61 \\ Chapter 8: Jacob Bernoulli and his Golden Theorem (1713) / 62--80 \\ Chapter 9: De Moivre's Problem (1730) / 81--88 \\ Chapter 10: De Moivre, Gauss, and the Normal Curve (1730, 1809) / 89--107 \\ Chapter 11: Daniel Bernoulli and the St. Petersburg Problem (1738) / 108--118 \\ Chapter 12: d'Alembert and the ``Croix ou Pile'' Article (1754) / 119--123 \\ Chapter 13: d'Alembert and the Gambler's Fallacy (1761) / 124--128 \\ Chapter 14: Bayes, Laplace, and Philosophies of Probability (1764, 1774) / 129--155 \\ Chapter 15: Leibniz's Error (1768) / 156--158 \\ Chapter 16: The Buffon Needle Problem (1777) / 159--168 \\ Chapter 17: Bertrand's Ballot Problem (1887) / 169--174 \\ Chapter 18: Bertrand's Strange Three Boxes (1889) / 175--178 \\ Chapter 19: Bertrand's Chords (1889) / 179--185 \\ Chapter 20: Three Coins and a Puzzle from Galton (1894) / 186--188 \\ Chapter 21: Lewis Carroll's Pillow Problem No. 72 (1894) / 189--193 \\ Chapter 22: Borel and a Different Kind of Normality (1909) / 194--198 \\ Chapter 23: Borel's Paradox and Kolmogorov's Axioms (1909, 1933) / 199--207 \\ Chapter 24: Of Borel, Monkeys, and the New Creationism (1913) / 208--214 \\ Chapter 25: Kraitchik's Neckties and Newcomb's Problem (1930, 1960) / 215--223 \\ Chapter 26: Fisher and the Lady Tasting Tea (1935) / 224--232 \\ Chapter 27: Benford and the Peculiar Behavior of the First Significant Digit (1938) / 233--239 \\ Chapter 28: Coinciding Birthdays (1939) / 240--246 \\ Chapter 29: L{\'e}vy and the Arc Sine Law (1939) / 247--252 \\ Chapter 30: Simpson's Paradox (1951) / 253--259 \\ Chapter 31: Gamow, Stern, and Elevators (1958) / 260--263 \\ Chapter 32: Monty Hall, Cars, and Goats (1975) / 264--270 \\ Chapter 33: Parrondo's Perplexing Paradox (1996) / 271--276 \\ Bibliography / 277--295 \\ Photo Credits / 296--298 \\ Index / 299--314", } @Proceedings{Niola:2012:RRA, editor = "Vincenzo Niola and Michel Kadoch and Alexander Zemliak", booktitle = "{Recent researches in automatic control and electronics: proceedings of the 14th International conference on automatic control, modelling and simulation (ACMOS '12): proceedings of the 11th International conference on microelectronics, nanoelectronics, optoelectronics (MINO '12): Saint Malo and Mont Saint-Michel, France, April 2--4, 2012}", title = "{Recent researches in automatic control and electronics: proceedings of the 14th International conference on automatic control, modelling and simulation (ACMOS '12): proceedings of the 11th International conference on microelectronics, nanoelectronics, optoelectronics (MINO '12): Saint Malo and Mont Saint-Michel, France, April 2--4, 2012}", publisher = "WSEAS", address = "???, Greece", pages = "209", year = "2012", ISBN = "1-61804-080-4 (paperback)", ISBN-13 = "978-1-61804-080-0 (paperback)", LCCN = "????", bibdate = "Tue Feb 19 06:02:11 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, } @Book{Tijms:2012:UPC, author = "Henk C. Tijms", booktitle = "Understanding probability: chance rules in everyday life", title = "Understanding probability: chance rules in everyday life", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, edition = "Third", pages = "x + 562", year = "2012", ISBN = "1-107-65856-X", ISBN-13 = "978-1-107-65856-1", LCCN = "QA273", bibdate = "Mon Feb 18 06:48:08 MST 2013", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", acknowledgement = ack-nhfb, tableofcontents = "Preface \\ Introduction \\ Part I. Probability in Action \\ 1. Probability questions \\ 2. The law of large numbers and simulation \\ 3. Probabilities in everyday life \\ 4. Rare events and lotteries \\ 5. Probability and statistics \\ 6. Chance trees and Bayes' rule \\ Part II. Essentials of Probability \\ 7. Foundations of probability theory \\ 8. Conditional probability and Bayes \\ 9. Basic rules for discrete random variables \\ 10. Continuous random variables \\ 11. Jointly distributed random variables \\ 12. Multivariate normal distribution \\ 13. Conditioning by random variables \\ 14. Generating functions \\ 15. Discrete-time Markov chains \\ 16. Continuous-time Markov chains \\ Appendix \\ Counting methods and ex \\ Recommended reading \\ Answers to odd-numbered problems \\ Bibliography \\ Index", } @Book{Abergel:2013:ESR, editor = "Fr{\'e}d{\'e}ric Abergel and Bikas K. Chakrabarti and Anirban Chakraborti and Asim Ghosh", booktitle = "Econophysics of systemic risk and network dynamics", title = "Econophysics of systemic risk and network dynamics", publisher = "Springer Italia", address = "Milan, Italy", bookpages = "????", pages = "119--129", year = "2013", DOI = "https://doi.org/10.1007/978-88-470-2553-0", ISBN = "88-470-2553-2, 88-470-2552-4", ISBN-13 = "978-88-470-2553-0, 978-88-470-2552-3", bibdate = "Mon Feb 18 16:48:12 2013", bibsource = "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib", series = "New Econ. Windows", acknowledgement = ack-nhfb, tableofcontents = "Part 1. Systemic risk, network dynamics and other empirical studies \\ Diffusion of Defaults Among Financial Institutions / Gabrielle Demange \\ Systemic Risk and Complex Systems: A Graph-Theory Analysis / Delphine Lautier and Franck Raynaud \\ Omori Law After Exogenous Shocks on Supplier-Customer Network / Yoshi Fujiwara \\ Aftershock Prediction for High-Frequency Financial Markets' Dynamics / Fulvio Baldovin, Francesco Camana, Michele Caraglio, Attilio L. Stella and Marco Zamparo \\ How Unstable Are Complex Financial Systems? Analyzing an Inter-bank Network of Credit Relations / Sitabhra Sinha, Maximilian Thess and Sheri Markose \\ Study of Statistical Correlations in Intraday and Daily Financial Return Time Series / Gayatri Tilak, Tam{\'a}s Sz{\'e}ll, R{\'e}my Chicheportiche and Anirban Chakraborti \\ A Robust Measure of Investor Contrarian Behaviour / Damien Challet and David Morton de Lachapelle \\ Evolution of Zipf's Law for Indian Urban Agglomerations Vis-{\`a}-Vis Chinese Urban Agglomerations / Kausik Gangopadhyay and Banasri Basu \\ Part 2. Model-based studies \\ Reaction to Extreme Events in a Minimal Agent Based Model / Andrea Zaccaria, Matthieu Cristelli and Luciano Pietronero \\ Predatory Trading and Risk Minimisation: How to (B)Eat the Competition / Anita Mehta \\ Statistical Mechanics of Labor Markets / He Chen and Jun-ichi Inoue \\ Kolkata Paise Restaurant Problem: An Introduction / Asim Ghosh, Soumyajyoti Biswas, Arnab Chatterjee, Anindya Sundar Chakrabarti and Tapan Naskar, et al. \\ Kolkata Paise Restaurant Problem and the Cyclically Fair Norm / Priyodorshi Banerjee, Manipushpak Mitra and Conan Mukherjee \\ An Introduction to Multi-player, Multi-choice Quantum Games: Quantum Minority Games and Kolkata Restaurant Problems / Puya Sharif and Hoshang Heydari \\ Part 3. Miscellaneous reports \\ Cluster Analysis and Gaussian Mixture Estimation of Correlated Time-Series by Means of Multi-dimensional Scaling / Takero Ibuki, Sei Suzuki and Jun-ichi Inoue \\ Analyzing Crisis in Global Financial Indices / Sunil Kumar and Nivedita Deo \\ Study of Systemic Risk Involved in Mutual Funds / Kishore C. Dash and Monika Dash \\ Characterizing Price Index Behavior Through Fluctuation Dynamics / Prasanta K. Panigrahi, Sayantan Ghosh, Arjun Banerjee, Jainendra Bahadur and P. Manimaran", } @Book{Miller:2015:BLT, editor = "Steven J. Miller", booktitle = "{Benford's Law}: theory and applications", title = "{Benford's Law}: theory and applications", publisher = pub-PRINCETON, address = pub-PRINCETON:adr, pages = "xxvi + 438", year = "2015", DOI = "https://doi.org/10.1515/9781400866595", ISBN = "0-691-14761-2 (hardcover), 1-4008-6659-6 (e-book)", ISBN-13 = "978-0-691-14761-1 (hardcover), 978-1-4008-6659-5 (e-book)", LCCN = "QA273.6 .B46 2015", MRclass = "60-06 (62-06)", MRnumber = "3408774", bibdate = "Tue Nov 17 09:41:52 MST 2015", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/statpapers.bib", URL = "http://press.princeton.edu/titles/10527.html", acknowledgement = ack-nhfb, subject = "Distribution (Probability theory); Probability measures; MATHEMATICS / Applied; MATHEMATICS / Probability and Statistics / General; Distribution (Probability theory); Probability measures.", tableofcontents = "Foreword / xiii \\ Preface / xvii \\ Notation / xxiii \\ Part I. General Theory I: Basis of Benford's Law / 1 \\ Chapter 1. A Quick Introduction to Benford's Law / 3 \\ Chapter 2. A Short Introduction to the Mathematical Theory of Benford's Law / 23 \\ Chapter 3. Fourier Analysis and Benford's Law / 68 \\ Part II. General Theory II: Distributions and Rates of Convergence / 107 \\ Chapter 4. Benford's Law Geometry / 109 \\ Chapter 5. Explicit Error Bounds via Total Variation / 119 \\ Chapter 6. L{\'e}vy Processes and Benford's Law / 135 \\ Part III. Applications I: Accounting and Vote Fraud / 175 \\ Chapter 7. Benford's Law as a Bridge between Statistics and Accounting / 177 \\ Chapter 8. Detecting Fraud and Errors Using Benford's Law / 191 \\ Chapter 9. Can Vote Counts Digits and Benford's Law Diagnose Elections? Chapter 10. Complementing Benford's Law for Small N: A Local Bootstrap Bootstrap Model / 227 \\ Part IV. Applications II: Economics / 233 \\ Chapter 11. Measuring the Quality of European Statistics / 235 \\ Chapter 12. Benford's Law and Fraud in Economic Research / 244 \\ Chapter 13. Testing for Strategic Manipulation of Economic and Financial Data / 257 \\ Part V. Applications III: Sciences / 265 \\ Chapter 14. Psychology and Benford's Law / 267 \\ Chapter 15. Managing Risk in Numbers Games: Benford's Law and the Small-Number Phenomenon / 276 \\ Chapter 16. Benford's Law in the Natural Sciences / 290 \\ Chapter 17. Generalizing Benford's Law: A Reexamination of Falsified Clinical Data / 304 \\ Part VI. Applications IV: Images / 317 \\ Chapter 18. Partial Volume Modeling of Medical Imaging Systems Using the Benford Distribution / 319 \\ Chapter 19. Application of Benford's Law to Images / 338 \\ Part VII. Exercises / 371 \\ Chapter 20. Exercises / 373 \\ Phenomenon / 399 \\ Distribution / 401 \\ Bibliography / 402 \\ Index / 433", } @Proceedings{Cornea:2020:ISC, editor = "Marius Cornea and Weiqiang Liu and Arnaud Tisserand", booktitle = "{2020 27th IEEE Symposium on Computer Arithmetic: ARITH 2020: proceedings: Portland, Oregon, USA, 7--10 June 2020}", title = "{2020 27th IEEE Symposium on Computer Arithmetic: ARITH 2020: proceedings: Portland, Oregon, USA, 7--10 June 2020}", publisher = pub-IEEE, address = pub-IEEE:adr, year = "2020", DOI = "https://doi.org/10.1109/ARITH48897.2020", ISBN = "1-72817-120-2, 1-72817-121-0", ISBN-13 = "978-1-72817-120-3, 978-1-72817-121-0", LCCN = "????", bibdate = "Wed Jul 7 06:23:45 MDT 2021", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/benfords-law.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib", URL = "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973", acknowledgement = ack-nhfb, } %%% Last MathSciNet search (2019--2030): Wed Nov 19 13:19:03 2025