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Fang, X, Miller, SJ, Sun, M and Verga, A (2024). Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition. Preprint.

This work cites the following items of the Benford Online Bibliography:


Adhikari, AK (1969). Some Results on Distribution of Most Significant Digit. Sankhya-The Indian Journal of Statistics Series B, 31 (Dec), pp. 413-420. ISSN/ISBN:0581-5738. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Benford, F (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, Vol. 78, No. 4 (Mar. 31, 1938), pp. 551-572. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, pp. 1-126. DOI:10.1214/11-PS175. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Hill, TP (2015). An Introduction to Benford's Law. Princeton University Press: Princeton, NJ. ISSN/ISBN:9780691163062. View Complete Reference Online information Works that this work references Works that reference this work
Betti, L, Durmić, I, McDonald, Z, Miller, JB and Miller, SJ (2023). Benfordness of Measurements Resulting from Box Fragmentation. Preprint arXiv:2304.08335 [math.PR]; last accessed April 29, 2023. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Cuff, V , Lewis, A and Miller, SJ (2015). The Weibull distribution and Benford’s law. Involve Vol. 8 No. 5, pp. 859–874. DOI:10.2140/involve.2015.8.859. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Duncan, RL (1967). An application of uniform distributions to the Fibonacci numbers. Fibonacci Quarterly 5, pp. 137-140. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Durmić, I and Miller SJ (2023). Benford Behavior of a Higher-Dimensional Fragmentation Process. Preprint arXiv:2308.07404 [math.PR]; last accessed August 24, 2023. View Complete Reference Online information Works that this work references Works that reference this work
Eliazar, II (2017). Harmonic statistics. Annals of Physics, Volume 380, pp. 168-187. DOI:10.1016/j.aop.2017.03.016. View Complete Reference Online information Works that this work references Works that reference this work
Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363. ISSN/ISBN:0883-4237. View Complete Reference Online information Works that this work references Works that reference this work
Hill, TP (1998). The First-Digit Phenomenon. American Scientist 86 (4), pp. 358-363. ISSN/ISBN:0003-0996. DOI:10.1511/1998.4.358. View Complete Reference Online information Works that this work references Works that reference this work
Iafrate, JR, Miller, SJ and Strauch, FW (2015). Equipartitions and a distribution for numbers: A statistical model for Benford's law. Phys. Rev. E 91, 062138. DOI:10.1103/PhysRevE.91.062138. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. posted December 21, 2006 on arXiv:math/0612627. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Lemons, DS (1986). On the Numbers of Things and the Distribution of first Digits. American Journal of Physics 54(9), pp. 816-817. ISSN/ISBN:0002-9505. DOI:10.1119/1.14453. View Complete Reference Online information Works that this work references Works that reference this work
Lévy, P (1939). L'addition des variables aléatoires définies sur une circonférence. Bull. Soc. Math. France 67, pp. 1-41. FRE View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Miller, SJ and Takloo-Bighash, R (2006). An invitation to modern number theory. Princeton University Press. ISSN/ISBN:978-0691120607. View Complete Reference Online information Works that this work references Works that reference this work
Miller, SJ (ed.) (2015). Benford's Law: Theory and Applications. Princeton University Press: Princeton and Oxford. ISSN/ISBN:978-0-691-14761-1. View Complete Reference Online information Works that this work references Works that reference this work
Moret, MA, de Senna, V, Pereira, MG and Zebende, GF (2006). Newcomb-Benford law in astrophysical sources. International Journal of Modern Physics C 17(11), pp. 1597-1604. ISSN/ISBN:0129-1831. DOI:10.1142/S0129183106010054. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Ni, D, Wei, L and Ren, Z (2009). Benford's Law and β-Decay Half-Lives. Commun. Theor. Phys. 51, 713-716. DOI:10.1088/0253-6102/51/4/25. View Complete Reference Online information Works that this work references Works that reference this work
Nigrini, MJ (2012). Benford's Law: Applications for Forensic Accounting, Auditing, and Fraud Detection . John Wiley & Sons: Hoboken, New Jersey. ISSN/ISBN:978-1-118-15285-0. DOI:10.1002/9781119203094. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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 . View Complete Reference Online information Works that this work references Works that reference this work
Perez-Gonzalez, F, Heileman, GL and Abdallah, CT (2007). Benford's Law in Image Processing. Image Processing, pp I-405 - I-408. ICIP 2007. IEEE International Conference. ISSN/ISBN:1522-4880. DOI:10.1109/ICIP.2007.4378977. View Complete Reference Online information Works that this work references Works that reference this work
Pietronero, L, Tosatti, E, Tosatti, V and Vespignani, A (2001). Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf. Physica A - Statistical Mechanics and its Applications 293(1-2), 297-304. ISSN/ISBN:0378-4371. DOI:10.1016/S0378-4371(00)00633-6. View Complete Reference Online information Works that this work references Works that reference this work
Raimi, RA (1976). The First Digit Problem. American Mathematical Monthly 83(7), pp. 521-538. ISSN/ISBN:0002-9890. DOI:10.2307/2319349. View Complete Reference Online information Works that this work references Works that reference this work
Sarkar, BP (1973). An Observation on the Significant Digits of Binomial Coefficients and Factorials. Sankhya - The Indian Journal of Statistics Series B 35(3), 363-364. ISSN/ISBN:0581-5738. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1983). On sums modulo 2π of independent random variables. Math. Nachr. 110, 243-262. DOI:10.1002/mana.19831100118. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1984). On the asymptotic uniform distribution of sums reduced mod 1. Math. Nachr. 115, 275-281. DOI:10.1002/mana.19841150121. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Shao, L and Ma, BQ (2010). Empirical mantissa distributions of pulsars. Astroparticle Physics 33, 255-262. DOI:10.1016/j.astropartphys.2010.02.003. View Complete Reference Online information Works that this work references Works that reference this work
Tödter, K-H (2009). Benford's Law as an Indicator of Fraud in Economics. German Economic Review 10(3), 339-351. DOI:10.1111/j.1468-0475.2009.00475.x. View Complete Reference Online information Works that this work references Works that reference this work
Villas-Boas, SB, Fu, Q and Judge, G (2017). Benford’s law and the FSD distribution of economic behavioral micro data . Physica A: Statistical Mechanics and its Applications Volume 486, pp. 711-719. DOI:10.1016/j.physa.2017.05.093. View Complete Reference Online information Works that this work references Works that reference this work
Washington, LC (1981). Benford’s law for Fibonacci and Lucas numbers. Fibonacci Quarterly 19, 175-177. View Complete Reference No online information available Works that this work references Works that reference this work