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, Bunimovich, LA and Hill, TP (2005). One-dimensional dynamical systems and Benford's law. Transactions of the American Mathematical Society 357(1), pp. 197-219. ISSN/ISBN:0002-9947. DOI:10.1090/S0002-9947-04-03455-5.
|
|
|
|
|
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.
|
|
|
|
|
Brown, JR and Duncan, RL (1970). Modulo one uniform distribution of the sequence of logarithms of certain recursive sequences. Fibonacci Quarterly 8, pp. 482-486. ISSN/ISBN:0015-0517.
|
|
|
|
|
Costas, E, López-Rodas, V, Toro, FJ and Flores-Moya, A (2008). The number of cells in colonies of the cyanobacterium Microcystis aeruginosa satisfies Benford's law. Aquatic Botany 89(3), pp. 341-343. DOI:10.1016/j.aquabot.2008.03.011.
|
|
|
|
|
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.
|
|
|
|
|
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 (1998). The First-Digit Phenomenon. American Scientist 86 (4), pp. 358-363. ISSN/ISBN:0003-0996. DOI:10.1511/1998.4.358.
|
|
|
|
|
Hürlimann, W (2006). Benford's Law from 1881 to 2006: A Bibliography. posted on math arXiv July 6, 2006; last accessed February 28, 2016.
|
|
|
|
|
Knuth, DE (1997). The Art of Computer Programming. pp. 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA.
|
|
|
|
|
Kontorovich, AV and Miller, SJ (2005). Benford's Law, Values of L-functions and the 3x+ 1 Problem. Acta Arithmetica 120(3), pp. 269-297. ISSN/ISBN:0065-1036. DOI:10.4064/aa120-3-4.
|
|
|
|
|
Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. posted December 21, 2006 on arXiv:math/0612627.
|
|
|
|
|
Lagarias, JC and Soundararajan, K (2006). Benford's law for the 3x+1 function. Journal of the London Mathematical Society 74, pp. 289-303. ISSN/ISBN:0024-6107. DOI:10.1112/S0024610706023131.
|
|
|
|
|
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.
|
|
|
|
|
Mebane, WR Jr (2006). Election Forensics: The Second-digit Benford’s Law Test and Recent American Presidential Elections. pp 161-181 in: Alvarez, RM, Hall, TE and Hyde, SD (eds.), Election Fraud: Detecting and Deterring Electoral Manipulation. Brookings Press, Washington DC. ISSN/ISBN:9780815701606.
|
|
|
|
|
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 and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. ISSN/ISBN:978-0691120607.
|
|
|
|
|
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 and Miller, SJ (2007). Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data. Mathematical Geology 39(5), 469-490. ISSN/ISBN:0882-8121. DOI:10.1007/s11004-007-9109-5.
|
|
|
|
|
Nigrini, MJ and Mittermaier, LJ (1997). The use of Benford's Law as an aid in analytical procedures. Auditing - A Journal of Practice & Theory 16(2), 52-67. ISSN/ISBN:0278-0380.
|
|
|
|
|
Pain, J-C (2008). Benford’s law and complex atomic spectra. Physical Review E 77(1): Art. No. 012102. ISSN/ISBN:1539-3755. DOI:10.1103/PhysRevE.77.012102.
|
|
|
|
|
Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), pp. 521-538. ISSN/ISBN:0002-9890. DOI:10.2307/2319349.
|
|
|
|
|