Becker, T, Burt, D, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J, Strauch, FW and Talbut, B (2018). Benford's Law and Continuous Dependent Random Variables. Annals of Physics 388, pp. 350–381. DOI:10.1016/j.aop.2017.11.013.
|
|
|
|
|
Becker, T, Corcoran, TC, Greaves-Tunnell, A, Iafrate, JR, Jing, J, Miller, SJ, Porfilio, JD, Ronan, R, Samranvedhya, J and Strauch, FW (2013). Benford's Law and Continuous Dependent Random Variables. Preprint arXiv:1309.5603 [math.PR]; last accessed October 23, 2018. DOI:10.1016/j.aop.2017.11.013.
|
|
|
|
|
Berger, A and Hill, TP (2015). An Introduction to Benford's Law. Princeton University Press: Princeton, NJ. ISSN/ISBN:9780691163062.
|
|
|
|
|
Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), pp. 879-886. ISSN/ISBN:0002-9890. DOI:10.2307/2975136.
|
|
|
|
|
Cerioli, A, Barabesi, L, Cerasa, A, Menegatti, M and Perrotta, D (2019). Newcomb-Benford law and the detection of frauds in international trade. Proceedings of the National Academy of Sciences 116(1), pp. 106-115. DOI:10.1073/pnas.1806617115.
|
|
|
|
|
De Ceuster, MJK, Dhaene, G and Schatteman, T (1998). On the hypothesis of psychological barriers in stock markets and Benford’s law. Journal of Empirical Finance 5(3), pp. 263-279. DOI:10.1016/S0927-5398(97)00024-8.
|
|
|
|
|
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651.
|
|
|
|
|
Fang, X, Miller, SJ, Sun, M and Verga, A (2023). Generalized Continuous and Discrete Stick Fragmentation and Benford’s Law. Preprint arXiv:2309.00766 [math.PR]; last accessed September 12, 2023.
|
|
|
|
|
Fang, X, Miller, SJ, Sun, M and Verga, A (2024). Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition. Preprint.
|
|
|
|
|
Miller, SJ (2008). Benford’s Law and Fraud Detection, or: Why the IRS Should Care About Number Theory!. Presentation for Bronfman Science Lunch Williams College, October 21.
|
|
|
|
|
Miller, SJ (2016). Can math detect fraud? CSI: Math: The natural behavior of numbers. Presentation at Science Cafe, Northampton, September 26; last accessed July 4, 2019.
|
|
|
|
|
Miller, SJ and Nigrini, MJ (2008). The Modulo 1 Central Limit Theorem and Benford's Law for Products. International Journal of Algebra 2(3), pp. 119 - 130.
|
|
|
|
|
Miller, SJ (ed.) (2015). Benford's Law: Theory and Applications. Princeton University Press: Princeton and Oxford. ISSN/ISBN:978-0-691-14761-1.
|
|
|
|
|
Schatte, P (1986). On the Asymptotic Logarithmic Distribution of the Floating-Point Mantissas of Sums. Math. Nachr. 127, 7-20. ISSN/ISBN:0025-584X. DOI:10.1002/mana.19861250102.
|
|
|
|
|
Schatte, P (1987). On the Asymptotic Behaviour of the Mantissa Distributions of Sums. Journal of Information Processing and Cybernetics EIK 23(7), 353-360.
|
|
|
|
|
Schatte, P (1988). On mantissa distributions in computing and Benford’s law. Journal of Information Processing and Cybernetics EIK 24(9), 443-455. ISSN/ISBN:0863-0593.
|
|
|
|
|
Schatte, P (1988). On a law of the iterated logarithm for sums mod 1 with application to Benford's law. Probability Theory and Related Fields 77(2), 167-178. ISSN/ISBN:0178-8051. DOI:10.1007/BF00334035.
|
|
|
|
|
Schatte, P (1991). On a uniform law of the iterated logarithm for sums mod 1 and Benford’s law. Lithuanian Mathematical Journal 31(1), 133-142. DOI:10.1007/BF00972327.
|
|
|
|
|
Schatte, P (1998). On Benford's law to variable base. Statistics & Probability Letters 37(4): 391-397. ISSN/ISBN:0167-7152. DOI:10.1016/S0167-7152(97)00142-9.
|
|
|
|
|
Szewczak, ZS (2010). A limit theorem for random sums modulo 1. Statistics & Probability Letters 80(9) pp. 747-751. DOI:10.1016/j.spl.2010.01.005.
|
|
|
|
|