Cross Reference Up

Flehinger, BJ (1966). On the Probability that a Random Integer has Initial Digit A. American Mathematical Monthly 73(10), pp. 1056-1061.

This work is cited by the following items of the Benford Online Bibliography:

Note that this list may be incomplete, and is currently being updated. Please check again at a later date.

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
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. View Complete Reference Online information Works that this work references Works that reference this work
Allen, DP (1999). A new approach to the first digit phenomenon. The Toth-Maatian Review 14(3), pp. 6839-6847. View Complete Reference Online information Works that this work references No Bibliography works 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
Blondeau Da Silva, S (2020). Limits of Benford’s Law in Experimental Field. International Journal of Applied Mathematics 33(4), pp. 685-695. DOI:10.12732/ijam.v33i4.12. View Complete Reference Online information Works that this work references Works that reference this work
Brady, WG (1978). More on Benford’s law. Fibonacci Quarterly 16(1), pp. 51-52. View Complete Reference Online information Works that this work references Works that reference this work
Burgos, A and Santos, A (2021). The Newcomb–Benford law: Scale invariance and a simple Markov process based on it (Previous title: The Newcomb–Benford law: Do physicists use more frequently the key 1 than the key 9?). Preprint arXiv:2101.12068 [physics.pop-ph]; last accessed August 8, 2022; Published Am. J. Phys. 89, pp. 851-861. View Complete Reference Online information Works that this work references Works that reference this work
Burke, J and Kincanon, E (1991). Benford's Law and Physical Constants - The Distribution of Initial Digits. American Journal of Physics 59 (10), p. 952. ISSN/ISBN:0002-9505. DOI:10.1119/1.16838. View Complete Reference Online information Works that this work references Works that reference this work
Caldwell, CK (2008). Does Benford's law apply to prime numbers?. From: The Prime Pages (prime number research, records and resources) FAQ. View Complete Reference Online information Works that this work references Works that reference this work
Ciofalo, M (2009). Entropy, Benford’s first digit law, and the distribution of everything. Unpublished manuscript. View Complete Reference Online information Works that this work references Works that reference this work
Clenshaw, CV, Olver, FWJ and Turner, PR (1989). Level-Index Arithmetic - An Introductory Survey. Lecture Notes in Mathematics 1397, pp. 95-168. ISSN/ISBN:0075-8434. DOI:10.1007/BFb0085718. View Complete Reference Online information Works that this work references Works that reference this work
Cohen, DIA (1976). An Explanation of the First Digit Phenomenon. Journal of Combinatorial Theory Series A 20(3), pp. 367-370. ISSN/ISBN:0097-3165. View Complete Reference Online information Works that this work references Works that reference this work
Davis, B (1976). Some Remarks on Initial Digits. Fibonacci Quarterly 14(1), pp. 13-14. ISSN/ISBN:0015-0517. View Complete Reference Online information Works that this work references Works that reference this work
Diaconis, P (1977). Examples of the theory of infinite iteration of summability methods. Canadian Journal of Mathematics 29(3), pp. 489-497. DOI:10.4153/CJM-1977-053-1. View Complete Reference Online information Works that this work references Works that reference this work
Diaconis, P (2002). G.H. Hardy and Probability ???. Bulletin of the London Mathematical Society 34(4), pp. 385-402. DOI:10.1112/S002460930200111X. View Complete Reference Online information Works that this work references Works that reference this work
Drmota, M and Tichy, RF (1997). Sequences, Discrepancies and Applications. Lecture Notes in Mathematics 1651. View Complete Reference Online information Works that this work references Works that reference this work
Duncan, RL (1969). Note on the initial digit problem. Fibonacci Quarterly 7(5), pp. 474-475. View Complete Reference Online information Works that this work references Works that reference this work
Filipponi, P and Menicocci, R (1995). Some Probabilistic Aspects of the Terminal Digits of Fibonacci Numbers. Fibonacci Quarterly 33(4), pp. 325-331. ISSN/ISBN:0015-0517. View Complete Reference Online information Works that this work references Works that reference this work
Forster, RP (2006). Auditoria contábil em entidades do terceiro setor : uma aplicação da Lei Newcomb-Benford. Universidade de Brasília, Brasília. POR View Complete Reference Online information Works that this work references Works that reference this work
Fuchs, A and Nanopoulos, P (1985). Mesures invariantes par translation, classes de Dynkin first-digit problem. Advances in Mathematics 55, pp. 24-74. DOI:10.1016/0001-8708(85)90004-0. FRE View Complete Reference Online information Works that this work references Works that reference this work
Giuliano, R and Janvresse, E (2010). A unifying probabilistic interpretation of Benford's Law. Uniform Distribution Theory 5(2), pp. 169-182. ISSN/ISBN:1336-913X. View Complete Reference Online information Works that this work references Works that reference this work
Hamadeh, N (2004). Wireless Security and Traffic Modeling Using Benford's Law. Master’s Thesis, University of New Mexico, Albuquerque, NM, 2004 (99 pgs). View Complete Reference Online information Works that this work references Works that reference this work
Hill, TP (1988). Random-Number Guessing and the First Digit Phenomenon. Psychological Reports 62(3), pp. 967-971. ISSN/ISBN:0033-2941. DOI:10.2466/pr0.1988.62.3.967. View Complete Reference No online information available 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 (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. View Complete Reference Online information Works that this work references Works that reference this work
Hill, TP (2001). Response to "Benfords Gesetz", Brief an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 3/2001, p 4. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Hobza, T and Vajda, I (2001). On the Newcomb-Benford law in models of statistical data. Revista Matematica Complutense XIV(2), pp. 407-420. ISSN/ISBN:1139-1138. View Complete Reference Online information Works that this work references Works that reference this work
Huber, H (2023). Explanations of Benford’s Law. Undergraduate research paper, William and Mary. View Complete Reference No online information available Works that this work references No Bibliography works reference this work
Humenberger, H (1996). Das Benford-Gesetz über die Verteilung der ersten Ziffer von Zahlen. Stochastik in der Schule 16(3), pp. 2–17. GER View Complete Reference Online information Works that this work references Works that reference this work
Humenberger, H (1997). Eine Ergänzung zum Benford-Gesetz — weitere mögliche schulrelevante Aspekte. Stochastik in der Schule 17(3), pp. 42–48. GER View Complete Reference Online information Works that this work references Works that reference this work
Irmay, S (1997). The relationship between Zipf's law and the distribution of first digits. Journal of Applied Statistics 24(4), pp. 383-393. ISSN/ISBN:0266-4763. DOI:10.1080/02664769723594. View Complete Reference Online information Works that this work references Works that reference this work
Janvresse, E (2009). Quel est le début de ce nombre?. Images des Mathématiques, 26 December. FRE View Complete Reference Online information Works that this work references Works that reference this work
Janvresse, É (2012). Quelques contributions aux probabilités eta la théorie ergodique. Document de synthèse présenté pour l’Habilitation à Diriger des Recherches, l’université de Rouen. FRE View Complete Reference Online information Works that this work references No Bibliography works reference this work
Janvresse, E and De la Rue, T (2003). La loi de Benford. Quadature no. 48, pp. 5-9. FRE View Complete Reference No online information available Works that this work references Works that reference this work
Janvresse, E and de la Rue, T (2004). From Uniform Distributions to Benford’s Law. Journal of Applied Probability 41(4), pp. 1203-1210. ISSN/ISBN:0021-9002. View Complete Reference Online information Works that this work references Works that reference this work
Janvresse, É and de la Rue, T (2009). Benford’s law. (Catalan. Catalan summary). Butl. Soc. Catalana Mat., 24(1):5{12, 2009. Translated by Frederic Utzet. DOI:10.2436/20.2002.01.18. CAT View Complete Reference Online information Works that this work references No Bibliography works reference this work
Janvresse, É and de la Rue, T (2012). Averaging along Uniform Random Integers. Uniform Distribution Theory 7(2), pp. 35–60. View Complete Reference Online information Works that this work references Works that reference this work
Jasak, Z (2010). Benfordov zakon i reinforcement učenje (Benford's Law and reinforcment learning) . MSc Thesis, University of Tuzla, Bosnia. SRP View Complete Reference Online information Works that this work references Works that reference this work
Jasak, Z (2017). Sum invariance testing and some new properties of Benford's law. Doctorial Dissertation, University of Tuzla, Bosnia and Herzegovina. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Kak, SC (1983). Strings of first digits of powers of a number. Indian J. Pure Appl. Math. 14(7), pp. 896-907. View Complete Reference Online information Works that this work references Works that reference this work
Kim, PN, Contreras, J, Ceberio, M and Thach, NN (2023). Economic and Financial Applications of Benford’s Law: from Traditional Use in Audits to Help in Deep Learning. International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems 31(Supp02), pp. 197–207 . DOI:10.1142/S0218488523400111 . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Knuth, DE (1997). The Art of Computer Programming. pp. 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA. View Complete Reference No online information available 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
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. View Complete Reference Online information Works that this work references Works that reference this work
Kossovsky, AE (2014). Benford's Law: Theory, the General Law of Relative Quantities, and Forensic Fraud Detection Applications. World Scientific Publishing Company: Singapore. ISSN/ISBN:978-981-4583-68-8. View Complete Reference Online information Works that this work references Works that reference this work
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. 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
Lipovetsky, S (2008). Comparison among different patterns of priority vectors estimation methods. International Journal of Mathematical Education in Science 39(3), pp. 301-311. DOI:10.1080/00207390701639532. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Lolbert, T (2006). Digital Analysis: Theory and Applications in Auditing. Hungarian Statistical Review 84, Special number 10, p. 148. ISSN/ISBN:0039 0690. View Complete Reference Online information Works that this work references Works that reference this work
Lolbert, T (2007). Statisztikai eljárások alkalmazása az ellenőrzésben (Applications of statistical methods in monitoring). PhD thesis, Corvinus University, Budapest, Hungary. HUN View Complete Reference Online information Works that this work references No Bibliography works reference this work
Luque, B and Lacasa, L (2009). The first-digit frequencies of prime numbers and Riemann zeta zeros. Proc. Royal Soc. A, published online 22Apr09. DOI:10.1098/rspa.2009.0126. View Complete Reference Online information Works that this work references Works that reference this work
Martín, AB (2003). Sistematización del proceso de depuración de los datos en estudios con seguimientos. PhD Thesis, Universitat Autònoma de Barcelona, Spain. SPA View Complete Reference Online information Works that this work references No Bibliography works reference this work
Massé, B and Schneider, D (2011). A survey on weighted densities and their connection with the first digit phenomenon. Rocky Mountain Journal of Mathematics 41(5), 1395-1415. ISSN/ISBN:0035-7596. DOI:10.1216/RMJ-2011-41-5-1395. View Complete Reference Online information Works that this work references Works that reference this work
Nagasaka, K (1984). On Benford's Law. Annals of the Institute of Statistical Mathematics 36(2), pp. 337-352. ISSN/ISBN:0020-3157. DOI:10.1007/BF02481974. View Complete Reference Online information Works that this work references Works that reference this work
Nagasaka, K (2008). Benford’s Law to Base g of Order r in the Sense of a Certain Density. Short talk at: Colloque international sur la répartition uniforme, Marseille, January 2008. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Nagasaka, K, Kanemitsu, S and Shiue, JS (1990). Benford’s law: The logarithmic law of first digit. In: Győry, K, Halász, G. (eds.) Number theory. Vol. I. Elementary and analytic, Proc. Conf., Budapest/Hung. 1987, Colloq. Math. Soc. János Bolyai 51, pp. 361-391 . View Complete Reference No online information available Works that this work references Works that reference this work
Nguyen, HT, Kreinovich, V and Longpré, L (2003). Dirty pages of logarithm tables, lifetime of the universe, and subjective (fuzzy) probabilities on finite and infinite intervals. The 12th IEEE International Conference on Fuzzy Systems. FUZZ’03. Fuzzy Systems 1, pp. 67-73. DOI:10.1109/FUZZ.2003.1209339. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Nguyen, HT, Kreinovich, V and Longpré, L (2004). Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Innite Intervals. Reliable Computing 10(2), 83-106. DOI:10.1023/B:REOM.0000015848.19449.12. View Complete Reference Online information Works that this work references Works that reference this work
Nigrini, MJ (1992). The Detection of Income Tax Evasion Through an Analysis of Digital Frequencies. PhD thesis, University of Cincinnati, OH, USA. View Complete Reference Online information Works that this work references Works that reference this work
Nigrini, MJ (1996). Digital Analysis and the Reduction of Auditor Litigation Risk. Proceedings of the 1996 Deloitte & Touche / University of Kansas Symposium on Auditing Problems, ed. M. Ettredge, University of Kansas, Lawrence, KS, pp. 69-81. View Complete Reference Online information Works that this work references Works that reference this work
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. 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
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. View Complete Reference Online information Works that this work references Works that reference this work
Pavlović, V, Knežević, G, Joksimović, M and Joksimović, D (2019). Fraud Detection in Financial Statements Applying Benford's Law with Monte Carlo Simulation. Acta oeconomica 69(2), pp.217-239. DOI:10.1556/032.2019.69.2.4. View Complete Reference Online information Works that this work references Works that reference this work
Peter, M (2003). The asymptotic distribution of elements in automatic sequences. Theoretical Computer Science 301(1-3), pp. 285-312. DOI:10.1016/S0304-3975(02)00587-X. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Raimi, RA (1969). On Distribution of First Significant Figures. American Mathematical Monthly 76(4), pp. 342-348. ISSN/ISBN:0002-9890. DOI:10.2307/2316424. 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
Richter, R (2015). Em busca de transparência: a Lei de Benford aplicada às despesas eleitorais. Monografia (Bacharelado em Ciências Econômicas)- Universidade de Brasília, Brasília. POR View Complete Reference Online information Works that this work references No Bibliography works 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 (1973). Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgröße (Distribution of Mantissa in Floating Point Diagram of Random Variable). Zeitschrift fur Angewandte Mathematik und Mechanik 53(8), 553-565. ISSN/ISBN:0044-2267. DOI:10.1002/zamm.19730530807. GER View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1983). On H∞ -summability and the uniform distribution of sequences. Math. Nachr. 113, 237-243. DOI:10.1002/mana.19831130122. 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
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. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (1988). On the Almost Sure Convergence of Floating-Point Mantissas and Benford Law. Math. Nachr. 135, 79-83. ISSN/ISBN:0025-584X. DOI:10.1002/mana.19881350108. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Schatte, P (2001). Briefe an die Herausgeber. Mitteilungen der Deutschen Mathematiker Vereinigung, 2/2001, pp 6-7. View Complete Reference No online information available Works that this work references No Bibliography works reference this work
Scheidt, JK and Schelin, CW (1987). Distributions of floating point numbers. Computing 38(4), 315-324. ISSN/ISBN:0010-485X. DOI:10.1007/BF02278709. View Complete Reference Online information Works that this work references Works that reference this work
Scott, PD and Fasli, M (2001). Benford’s law: an empirical investigation and a novel explanation. CSM Technical Report 349, Department of Computer Science, University of Essex, UK. View Complete Reference Online information Works that this work references Works that reference this work
Sharpe, MJ (2006). Limit Laws and Mantissa Distributions. Probability and Mathematical Statistics 26(1), 175-185. View Complete Reference Online information Works that this work references Works that reference this work
Sugiarto, T, Noorzaman, S, Madu, L, Subagyo, A and Amiri, AM (2017). First Digit Lucas, Fibonacci and Benford Number in Financial Statement. Proceedings of the 2017 International Conference on Economic Development and Education Management (ICEDEM 2017). DOI:10.2991/icedem-17.2017.6. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Tsao, NK (1974). On the Distributions of Significant Digits and Roundoff Errors. Communications of the ACM 17(5), 269-271. ISSN/ISBN:0001-0782. DOI:10.1145/360980.360998. View Complete Reference Online information Works that this work references Works that reference this work
Turner, PR (1982). The Distribution of Leading Significant Digits. IMA Journal orf Numerical Analysis 2(4), 407-412. ISSN/ISBN:0272-4979. DOI:10.1093/imanum/2.4.407. View Complete Reference Online information Works that this work references Works that reference this work
Turner, PR (1984). Further Revelations on L.S.D.. IMA Journal of Numerical Analysis 4(2), 225-231. ISSN/ISBN:0272-4979. DOI:10.1093/imanum/4.2.225. View Complete Reference Online information Works that this work references Works that reference this work
Volcic, A (1996). The First Digit Problem and Scale-Invariance. In: P. Marcellini, G. Talenti and E. Vesentini (eds), Partial differential equations and applications: collected papers in honor of Carlo Pucci. Marcel Dekker, pp. 329-340 . View Complete Reference Online information Works that this work references Works that reference this work
Wang, L and Ma, B-Q (2023). A concise proof of Benford’s law. Fundamental Research . DOI:10.1016/j.fmre.2023.01.002. View Complete Reference Online information Works that this work references Works that reference this work
Weisstein, EW (2003). Benford's Law. pp 181-182 in: CRC concise encyclopedia of mathematics, Chapman & Hall. View Complete Reference Online information Works that this work references Works that reference this work
Weisstein, EW (2009). Benford's Law. MathWorld (A Wolfram Web Resource). View Complete Reference Online information Works that this work references Works that reference this work