Adhikari, AK and Sarkar, BP (1968). Distribution of most significant digit in certain functions whose arguments are random variables. Sankhya-The Indian Journal of Statistics Series B, no. 30, pp. 47-58. ISSN/ISBN:0581-5738.
|
|
|
|
|
Allaart, PC (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability 34(1), pp. 288-291.
|
|
|
|
|
Beber, B and Scacco, A (2012). What the Numbers Say: A Digit-Based Test for Election Fraud. Political Analysis 20 (2), pp. 211-234. DOI:10.1093/pan/mps003.
|
|
|
|
|
Benford, F (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, Vol. 78, No. 4 (Mar. 31, 1938), pp. 551-572.
|
|
|
|
|
Berger, A and Hill, TP (2007). Newton’s method obeys Benford’s law. American Mathematical Monthly 114 (7), pp. 588-601. ISSN/ISBN:0002-9890.
|
|
|
|
|
Breunig, C and Goerres, A (2011). Searching for Electoral Irregularities in an Established Democracy: Applying Benford’s Law Tests to Bundestag Elections in Unified Germany. Electoral Studies 30(3) September 2011, pp. 534-545.
|
|
|
|
|
Buck, B, Merchant, AC and Perez, SM (1993). An illustration of Benford’s first digit law using alpha decay half lives. European Journal of Physics 14, pp. 59-63.
|
|
|
|
|
Carslaw, CAPN (1988). Anomalies in Income Numbers: Evidence of Goal Oriented Behavior. The Accounting Review 63(2), pp. 321-327.
|
|
|
|
|
Cho, WKT and Gaines, BJ (2007). Breaking the (Benford) law: Statistical fraud detection in campaign finance. American Statistician 61(3), pp. 218-223. ISSN/ISBN:0003-1305. DOI:10.1198/000313007X223496.
|
|
|
|
|
Christian, CW and Gupta, S (1993). New evidence on "Secondary Evasion". The Journal of the American Taxation Association 15(1), pp. 72-93.
|
|
|
|
|
Cleary, R and Thibodeau, JC (2005). Applying Digital Analysis Using Benford‘s Law to Detect Fraud: The Dangers of Type I Errors. Auditing - A Journal of Practice & Theory 24(1), pp. 77-81. ISSN/ISBN:0278-0380. DOI:10.2308/aud.2005.24.1.77.
|
|
|
|
|
Deckert, J, Myagkov, M and Ordeshook, PC (2011). Benford's Law and the Detection of Election Fraud. Political Analysis 19(3), pp. 245-268. DOI:10.1093/pan/mpr014.
|
|
|
|
|
Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), pp. 72-81. ISSN/ISBN:0091-1798.
|
|
|
|
|
Dorrell, DD and Gadawski, GA (2012). Financial Forensics Body of Knowledge. Wiley Finance: Hoboken, NJ. ISSN/ISBN:978-0-470-88085-2.
|
|
|
|
|
Durtschi, C, Hillison, W and Pacini, C (2004). The effective use of Benford’s law to assist in detecting fraud in accounting data. Journal of Forensic Accounting 1524-5586/Vol. V, pp. 17-34.
|
|
|
|
|
Engel, HA and Leuenberger, C (2003). Benford's law for exponential random variables. Statistics & Probability Letters 63, pp. 361-365. ISSN/ISBN:0167-7152.
|
|
|
|
|
Fewster, RM (2009). A Simple Explanation of Benford's Law. American Statistician 63(1), pp. 26-32. DOI:10.1198/tast.2009.0005.
|
|
|
|
|
Flehinger, BJ (1966). On the Probability that a Random Integer has Initial Digit A. American Mathematical Monthly 73(10), pp. 1056-1061. ISSN/ISBN:0002-9890. DOI:10.2307/2314636.
|
|
|
|
|
Gava, AM and Vitiello, LRdS (2007). Inflation, Quarterly Financial Statements and Fraud: Benford’s Law and the Brazilian Case. XXXI Encontro da ANPAD, Rio de Janeiro, Sep 22-26, 2007.
|
|
|
|
|
Hamming, R (1970). On the distribution of numbers. Bell Syst. Tech. J. 49(8), pp. 1609-1625. ISSN/ISBN:0005-8580. DOI:10.1002/j.1538-7305.1970.tb04281.x.
|
|
|
|
|
Henselmann, K, Scherr, E and Ditter, D (2013). Applying Benford's Law to individual financial reports: An empirical investigation on the basis of SEC XBRL filings. Working Papers in Accounting Valuation Auditing, No. 2012-1 [rev.].
|
|
|
|
|
Hill, TP (1995). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), pp. 322-327. DOI:10.2307/2974952.
|
|
|
|
|
Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363. ISSN/ISBN:0883-4237.
|
|
|
|
|
Hill, TP (1995). Base-Invariance Implies Benford's Law. Proceedings of the American Mathematical Society 123(3), pp. 887-895. ISSN/ISBN:0002-9939. DOI:10.2307/2160815.
|
|
|
|
|
Hill, TP (1998). The First-Digit Phenomenon. American Scientist 86 (4), pp. 358-363. ISSN/ISBN:0003-0996. DOI:10.1511/1998.4.358.
|
|
|
|
|
Jang, D, Kang, JU, Kruckman, A, Kudo, J and Miller, SJ (2009). Chains of distributions, hierarchical Bayesian models and Benford's Law. Journal of Algebra, Number Theory: Advances and Applications 1(1), pp. 37-60.
|
|
|
|
|
Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. posted on arXiv 8 March 2009 - arXiv:0901.3047v2.
|
|
|
|
|
Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. posted December 21, 2006 on arXiv:math/0612627.
|
|
|
|
|
Kossovsky, AE (2012). Statistician's New Role as a Detective - Testing Data for Fraud. Ciencias Económicas 30(2), pp. 179-200 . ISSN/ISBN:0252-9521.
|
|
|
|
|
Lee, J, Cho, WKT and Judge, G (2010). Stigler’s approach to recovering the distribution of first significant digits in natural data sets. Statistics and Probability Letters 80(2), pp. 82-88. DOI:10.1016/j.spl.2009.09.015.
|
|
|
|
|
Leemis, LM, Schmeiser, BW and Evans, DL (2000). Survival Distributions Satisfying Benford's Law. American Statistician 54(4), pp. 236-241. ISSN/ISBN:0003-1305. DOI:10.2307/2685773.
|
|
|
|
|
Ley, E (1996). On the Peculiar Distribution of the US Stock Indexes' Digits. American Statistician 50(4), pp. 311-313. ISSN/ISBN:0003-1305. DOI:10.1080/00031305.1996.10473558.
|
|
|
|
|
Linville, M (2008). The Problem Of False Negative Results In The Use Of Digit Analysis. Journal of Applied Business Research, Vol. 24 Issue 1, pp. 17-25.
|
|
|
|
|
Logan, JL and Goudsmit, SA (1978). The First Digit Phenomenon. Proceedings of the American Philosophical Society 122(4), pp. 193-197. ISSN/ISBN:0003-049X.
|
|
|
|
|
Mebane, WR Jr (2006). Detecting Attempted Election Theft: Vote Counts, Voting Machines and Benford’s Law. Paper prepared for the 2006 Annual Meeting of the Midwest Political Science Association, Chicago, IL.
|
|
|
|
|
Mebane, WR Jr (2006). Election Forensics: The Second-digit Benford’s Law Test and
Recent American Presidential Elections. Proceedings of the Election Fraud Conference, Salt Lake City, Utah, September 29-30, 2006.
|
|
|
|
|
Newcomb, S (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics 4(1), pp. 39-40. ISSN/ISBN:0002-9327. DOI:10.2307/2369148.
|
|
|
|
|
Nigrini, MJ (1992). The Detection of Income Tax Evasion Through an Analysis of Digital Frequencies. PhD thesis, University of Cincinnati, OH, USA.
|
|
|
|
|
Nigrini, MJ (1994). Using digital frequencies to detect fraud. Fraud Magazine, The White Paper Index 8(2), pp. 3-6.
|
|
|
|
|
Pinkham, RS (1961). On the Distribution of First Significant Digits. Annals of Mathematical Statistics 32(4), pp. 1223-1230. ISSN/ISBN:0003-4851.
|
|
|
|
|
Raimi, RA (1969). The Peculiar Distribution of First Digits. Scientific American 221(6), pp. 109-120. ISSN/ISBN:0036-8733. DOI: 10.1038/scientificamerican1269-109.
|
|
|
|
|
Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), pp. 521-538. ISSN/ISBN:0002-9890. DOI:10.2307/2319349.
|
|
|
|
|
Raimi, RA (1985). The First Digit Phenomenon Again. Proceedings of the American Philosophical Society 129(2), pp. 211-219. ISSN/ISBN:0003-049X.
|
|
|
|
|
Ross, KA (2011). Benford's Law, a growth industry. American Mathematical Monthly 118 (7), pp. 571-583. ISSN/ISBN:0002-9890. DOI:10.4169/amer.math.monthly.118.07.571.
|
|
|
|
|
Sambridge, M, Tkalčić, H and Arroucau, P (2011). Benford's Law of First Digits: From Mathematical Curiosity to Change Detector. Asia Pacific Mathematics Newsletter 1(4), October 2011, 1-6. ISSN/ISBN:2010-3484.
|
|
|
|
|
Sambridge, M, Tkalčić, H and Jackson, A (2010). Benford's law in the Natural Sciences. Geophysical Research Letters 37: L22301. DOI:10.1029/2010GL044830.
|
|
|
|
|
Saville, A (2006). Using Benford's law to detect data error and fraud: an examination of companies listed on the Johannesburg Stock Exchange. South African Journal of Economic and Management Sciences 9(3), 341-354. ISSN/ISBN:1015-8812.
|
|
|
|
|
Shao, L and Ma, BQ (2010). Empirical mantissa distributions of pulsars. Astroparticle Physics 33, 255-262. DOI:10.1016/j.astropartphys.2010.02.003.
|
|
|
|
|
Shao, L and Ma, BQ (2010). The significant digit law in statistical physics. Physica A 389, 3109-3116. DOI:10.1016/j.physa.2010.04.021.
|
|
|
|
|
Stigler, GJ (1945). The distribution of leading digits in statistical tables. University of Chicago, Regenstein Library, Special Collections, George J. Stigler Archives.
|
|
|
|
|
Varian, HR (1972). Benford’s law. The American Statistician 26(3), 65-66. DOI:10.1080/00031305.1972.10478934.
|
|
|
|
|
Weaver, W (1963). The distribution of first significant digits. pp 270-277 in: Lady Luck: The Theory of Probability, Doubleday Anchor Series, New York. Republished by Dover, 1982. ISSN/ISBN:978-0486243429.
|
|
|
|
|