This work cites the following items of the Benford Online Bibliography:
Allaart, PC (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability 34(1), pp. 288-291. | ||||
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 (2011). A basic theory of Benford's Law . Probability Surveys 8, pp. 1-126. DOI:10.1214/11-PS175. | ||||
Bumby, R and Ellentuck, E (1969). Finitely additive measures and the first digit problem. Fundamenta Mathematicae 65, pp. 33-42. ISSN/ISBN:0016-2736. | ||||
Cigler, J (1964). Methods of summability and uniform distribution mod 1. Compositio Mathematica 16, pp. 44-51. | ||||
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. | ||||
Dlugosz, S and Müller-Funk, U (2009). The value of the last digit: statistical fraud detection with digit analysis. Advances in Data Analysis and Classification 3, pp. 281-290. DOI:10.1007/s11634-009-0048-5. | ||||
Dumas, CF and Devine, JH (2000). Detecting Evidence of Non-Compliance in Self- Reported Pollution Emissions Data: An Application of Benford’s Law. Selected Paper, American Agricultural Economics Association, Annual meeting. | ||||
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. | ||||
Goudsmit, SA and Furry, WH (1944). Significant figures of numbers in statistical tables. Nature 154(3921), pp. 800-801. ISSN/ISBN:0028-0836. DOI:10.1038/154800a0. | ||||
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. | ||||
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. | ||||
Hürlimann, W (2009). Generalizing Benford’s law using power laws: application to integer sequences. International Journal of Mathematics and Mathematical Sciences, Article ID 970284. DOI:10.1155/2009/970284. | ||||
Iudica, F (2012). Benford’s Law: Mathematical Properties and Forensic Accounting Applications. Master’s Thesis, Luiss Guido Carli University, Rome, Italy, 2012. | ||||
Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG. | ||||
Jasak, Z (2010). Benfordov zakon i reinforcement učenje (Benford's Law and reinforcment learning) . MSc Thesis, University of Tuzla, Bosnia. SRP | ||||
Jasak, Z (2011). Benford’s Law and Invariances. Journal of Mathematics and System Science, Volume 1, No.1 (Serial No.1). ISSN/ISBN:2159-5291. | ||||
Jasak, Z (2015). Benford's Law and Arithmetic Sequences. Journal of Mathematical Sciences: Advances and Applications, 32, pp. 1-16. ISSN/ISBN:0974-5750. | ||||
Jasak, Z and Banjanovic-Mehmedovic, L (2008). Detecting Anomalies by Benford's Law. In Proceedings of IEEE International Symposium on Signal Processing and Information Technology, 2008. ISSPIT 2008, pp. 453-458 . ISSN/ISBN:978-1-4244-3554-8. DOI:10.1109/ISSPIT.2008.4775660. | ||||
Jech, T (1992). The Logarithmic Distribution of Leading Digits and Finitely Additive Measures. Discrete Mathematics 108(1-3), pp. 53-57. ISSN/ISBN:0012-365X. DOI:10.1016/0012-365X(92)90659-4. | ||||
Konheim, AG (1965). Mantissa distribution. Mathematics of Computation 19, pp. 143-144. DOI:10.1090/S0025-5718-1965-0175159-1. | ||||
Kozlov, VV (2005). Weighted averages, uniform distribution, and strict ergodicity. Russian Mathematical Surveys 60(6), pp. 1121-1146. ISSN/ISBN:0036-0279. DOI:10.1070/RM2005v060n06ABEH004284. | ||||
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. | ||||
Li, Z, Cong, L and Wang, H (2004). Discussion on Benford’s law and its application. posted on arXiv:math/0408057, Aug 4, 2004. | ||||
Lolbert, T (2006). Digital Analysis: Theory and Applications in Auditing. Hungarian Statistical Review 84, Special number 10, p. 148. ISSN/ISBN:0039 0690. | ||||
Mebane, WR Jr (2007). Statistics for digits. 2007 Summer Meeting of the Political Methodology Society, Penn State University, University Park, PA. | ||||
Miller, SJ and Nigrini, MJ (2008). Order Statistics and Benford's Law. International Journal of Mathematics and Mathematical Sciences, Art. ID 382948. ISSN/ISBN:0161-1712. DOI:10.1155/2008/382948. | ||||
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 (2011). Forensic Analytics: Methods and Techniques for Forensic Accounting Investigations. John Wiley & Sons: Hoboken, New Jersey; (2nd edition published in 2020, isbn 978-1-119-58576-3). ISSN/ISBN:978-0-470-89046-2. | ||||
Nigrini, MJ and Miller, SJ (2009). Data Diagnostics Using Second-Order Tests of Benford's Law. Auditing: A Journal of Practice & Theory 28(2), pp. 305-324. DOI:10.2308/aud.2009.28.2.305 . | ||||
Pavlov, AI (1982). On the distribution of fractional parts and Benford’s law. Math. USSR Izvestija 19(1), 65-77. English translation of: Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45(4), 760–774. DOI:10.1070/IM1982v019n01ABEH001411. | ||||
Posch, PN (2008). A Survey on Sequences and Distribution Functions satisfying the First-Digit-Law. Journal of Statistics & Management Systems 11(1), pp. 1-19. DOI:10.1080/09720510.2008.10701294. | ||||
Posch, PN and Kreiner, WA (2005). A general approach to digital analysis exemplified by stock market indices. Online unpublished manuscript; link broken; copy available upon request. | ||||
Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), pp. 521-538. ISSN/ISBN:0002-9890. DOI:10.2307/2319349. | ||||
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. | ||||
Shao, L and Ma, BQ (2010). First-digit law in nonextensive statistics. Physical Review E 82, 041110. DOI:10.1103/PhysRevE.82.041110. | ||||
Sharpe, MJ (2006). Limit Laws and Mantissa Distributions. Probability and Mathematical Statistics 26(1), 175-185. | ||||
Tsuji, M (1952). On the uniform distribution of numbers mod 1. Journal of the Mathematical Society of Japan 4(3/4), pp. 313-322. DOI:10.2969/jmsj/00430313. | ||||
Weyl, H (1916). Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen 77, 313-352. ISSN/ISBN:0025-5831. DOI:10.1007/BF01475864. GER | ||||
Wong, SCY (2010). Testing Benford’s Law with the first two significant digits. Master's Thesis, University of Victoria, Canada. |