Cross Reference Up

Diaconis, P (1977). The Distribution of Leading Digits and Uniform Distribution Mod 1. Annals of Probability 5(1), pp. 72-81.

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.

Anderson, TC, Rolen, L and Stoehr, R (2011). Benford's Law for Coefficients of Modular Forms and Partition Functions. Proceedings of the American Mathematical Society, Vol. 139, No. 5, May 2011, pp. 1533-1541. ISSN/ISBN:0002-9939. View Complete Reference Online information Works that this work references Works that reference this work
Baláž, V, Nagasaka, K and Strauch, O (2010). Benford's law and distribution functions of sequences in (0, 1). Mathematical Notes, 2010, Vol. 88, No. 4, pp 449–463. Published in Russian in Matematicheskie Zametki, 2010, Vol. 88, No. 4, pp. 485–501. ISSN/ISBN:0001-4346. DOI:10.1134/S0001434610090178. View Complete Reference Online information Works that this work references Works that reference this work
Barabesi, L, Cerasa, A, Cerioli, A and Perrotta, D (2018). Goodness-of-fit testing for the Newcomb-Benford law with application to the detection of customs fraud. Journal of Business & Economic Statistics 36(2), pp. 346-358. DOI:10.1080/07350015.2016.1172014. View Complete Reference Online information Works that this work references Works that reference this work
Barabesi, L, Cerasa, A, Cerioli, A and Perrotta, D (2021). On characterizations and tests of Benford’s law. Journal of the American Statistical Association. DOI:10.1080/01621459.2021.1891927. View Complete Reference Online information Works that this work references Works that reference this work
Barabesi, L, Cerioli, A and Perrotta, D (2021). Forum on Benford’s law and statistical methods for the detection of frauds. Statistical Methods & Applications 30, pp. 767–778. DOI:10.1007/s10260-021-00588-0. View Complete Reference Online information Works that this work references Works that reference this work
Barabesi, L and Pratelli, L (2020). On the Generalized Benford law. Statistics & Probability Letters 160, 108702 . DOI:10.1016/j.spl.2020.108702. View Complete Reference Online information Works that this work references Works that reference this work
Baumeister, J and Macedo, TG (2011). Von den Zufallszahlen und ihrem Gebrauch. Stand: 21, November 2011. GER View Complete Reference Online information Works that this work references No Bibliography works 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
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. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Benford’s Law in power-like dynamical systems. Stochastics and Dynamics 5, pp. 587-607. ISSN/ISBN:0219-4937. DOI:10.1142/S0219493705001602. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Multi-dimensional dynamical systems and Benford's law. Discrete and Continuous Dynamical Systems 13(1), pp. 219-237. ISSN/ISBN:1078-0947. DOI:10.3934/dcds.2005.13.219. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2005). Dynamics and digits: on the ubiquity of Benford’s law. In: F. Dumortier, H. Broer, J. Mahwin, A. Vanderbauwhede, S. Verduyn Lunel (eds): Proceedings of Equadiff 2003. World Scientific, pp. 693-695. DOI:10.1142/9789812702067_0115 . View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2010). Large spread does not imply Benford's Law. Technical Report, Dept. of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2011). Some dynamical properties of Benford sequences. Journal of Difference Equations and Applications 17(2), pp. 137-159. DOI:10.1080/10236198.2010.549012. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A (2015). Most linear flows on ℝ^d are Benford . Journal of Differential Equations 259(5), pp. 1933–1957. DOI:10.1016/j.jde.2015.03.016. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Eshun, G (2014). Benford solutions of linear difference equations. Theory and Applications of Difference Equations and Discrete Dynamical Systems, Springer Proceedings in Mathematics & Statistics Volume 102, pp. 23-60. ISSN/ISBN:978-3-662-44139-8. DOI:10.1007/978-3-662-44140-4_2. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Eshun, G (2016). A characterization of Benford's law in discrete-time linear systems. Journal of Dynamics and Differential Equations 28(2), pp. 432-469. ISSN/ISBN:1040-7294. DOI:10.1007/s10884-014-9393-y. View Complete Reference Online information Works that this work references Works that reference this work
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. 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
Berger, A, Hill, TP, Kaynar, B and Ridder, A (2011). Finite-state Markov Chains Obey Benford's Law. SIAM Journal of Matrix Analysis and Applications 32(3), pp. 665-684. DOI:10.1137/100789890. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Siegmund, S (2007). On the distribution of mantissae in nonautonomous difference equations. Journal of Difference Equations and Applications 13(8-9), pp. 829-845. ISSN/ISBN:1023-6198. DOI:10.1080/10236190701388039. View Complete Reference Online information Works that this work references Works that reference this work
Berger, A and Xu, C (2018). Best Finite Approximations of Benford’s Law. Journal of Theoretical Probability. DOI:10.1007/s10959-018-0827-z. View Complete Reference Online information Works that this work references No Bibliography works 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
Bi, Z, Durmić, I and Miller, SJ (2022). Benfordness of the Generalized Gamma Distribution. Preprint arXiv:2201.10514 [math.PR]; last accessed January 31, 2022. Published in The PUMP Journal of Undergraduate Research 5, pp. 89–104. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Bradinoff, N and Duits, M (2023). Benford's law and the CβE. Preprint arXiv:2302.02932 [math.PR]; last accessed March 10, 2023. DOI:10.48550/ARXIV.2302.02932. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Bradley, JR and Farnsworth, DL (2009). What is Benford's Law?. Teaching Statistics 31(1), pp. 2-6. DOI:10.1111/j.1467-9639.2009.00347.x. View Complete Reference Online information Works that this work references Works that reference this work
Bradley, JR and Farnsworth, DL (2009). Beispiele und Schüleraktivitäten zum BENFORD-Gesetz. Stochastik in der Schule (SiS) 29(3), pp. 28-32 . ISSN/ISBN:1614-0443. GER View Complete Reference Online information Works that this work references No Bibliography works 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
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2017). Leading Digits of Mersenne Numbers. Preprint in arXiv:1712.04425 [math.NT]; last accessed October 23, 2018. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2019). The Surprising Accuracy of Benford’s Law in Mathematics. Preprint arXiv:1907.08894 [math.PR]; last accessed July 31, 2019. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2020). The Surprising Accuracy of Benford’s Law in Mathematics. The American Mathematical Monthly 127(3), pp. 217-237. DOI:10.1080/00029890.2020.1690387. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Faust, M, Hildebrand, AJ, Li, J and Zhang, Y (2021). Leading digits of Mersenne numbers. Experimental Mathematics 30(3), pp. 405–421. DOI:10.1080/10586458.2018.1551162. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Hildebrand, AJ and Li, J (2018). A local Benford Law for a class of arithmetic sequences. Preprint arXiv:1808.01496 [math.NT]; last accessed October 22, 2018. View Complete Reference Online information Works that this work references Works that reference this work
Cai, Z, Hildebrand, AJ and Li, J (2019). A local Benford law for a class of arithmetic sequences. International Journal of Number Theory 15(3), pp.613-638. DOI:10.1142/S1793042119500325. View Complete Reference Online information Works that this work references Works that reference this work
Cerasa, A (2022). Testing for Benford’s Law in very small samples: Simulation study and a new test proposal. PLoS ONE 17(7), pp. e0271969. DOI:10.1371/journal.pone.0271969. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Chandee, V, Li, X, Pollack, P and Roy, AS (2022). On Benford's Law for Multiplicative Functions. Preprint arXiv:2203.13117v2 [math.NT]; last accessed May 30, 2022. View Complete Reference Online information Works that this work references Works that reference this work
Chenavier, N, Massé, B and Schneider, D (2018). Products of random variables and the first digit phenomenon. Preprint arXiv:1512.06049 [math.PR]; last accessed January 9, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Chenavier, N and Schneider, D (2018). On the discrepancy of powers of random variables. Statistics & Probability Letters 134, pp. 5-14. DOI:10.1016/j.spl.2017.10.006. View Complete Reference Online information Works that this work references Works that reference this work
Corazza, M, Ellero, A and Zorzi, A (2008). What sequences obey Benford's law?. Working Paper n. 185/2008, November 2008, Department of Applied Mathematics, University of Venice. ISSN/ISBN:1828-6887. 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
Deligny, H and Jolissaint, P (2012). Relations de récurrence linéaires, primitivité et loi de Benford [Linear recurrence relations, primitivity, and Benford's Law]. Elemente der Mathematik, 68(1), pp. 9-21. DOI:10.4171/EM/213. FRE 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
Diaconis, P and Freedman, D (1979). On Rounding Percentages. Journal of the American Statistical Association 74(366), pp. 359-364. ISSN/ISBN:0162-1459. View Complete Reference Online information Works that this work references Works that reference this work
Dorrestijn, J (2008). Graphing conformity of distributions to Benford’s Law for various bases. MSc thesis, Universiteit Utrecht, The Netherlands. View Complete Reference Online information Works that this work references No Bibliography works 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
Dümbgen, L and Leuenberger, C (2008). Explicit Bounds for the Approximation Error in Benford’s Law. Electronic Communications in Probability 13, pp. 99-112. ISSN/ISBN:1083-589X. DOI:10.1214/ECP.v13-1358. View Complete Reference Online information Works that this work references Works that reference this work
Durmić, I (2022). Benford Behavior of a Higher Dimensional Fragmentation Processes. Undergraduate thesis, Williams College, Williamstown, Massachusetts. View Complete Reference Online information Works that this work references 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
Durst, RF, Huynh, C, Lott, A, Miller, SJ, Palsson, EA, Touw, W and Vreind, G (2016). The Inverse Gamma Distribution and Benford's Law. Preprint in arXiv:1609.04106 [math.PR]; last accessed October 23, 2018. View Complete Reference Online information Works that this work references Works that reference this work
Eliahou, S, Massé, B and Schneider, D (2013). On the mantissa distribution of powers of natural and prime numbers. Acta Mathematica Hungarica, 139(1), pp. 49-63. ISSN/ISBN:0236-5294. DOI:10.1007/s10474-012-0244-1. View Complete Reference Online information Works that this work references Works that reference this work
Engel, HA and Leuenberger, C (2003). Benford's law for exponential random variables. Statistics & Probability Letters 63, pp. 361-365. ISSN/ISBN:0167-7152. View Complete Reference Online information Works that this work references Works that reference this work
Fang, G (2022). Investigating Hill’s question for some probability distributions. AIP Advances 12, 095004. DOI:10.1063/5.0100429. View Complete Reference Online information Works that this work references No Bibliography works reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fang, X, Miller, SJ, Sun, M and Verga, A (2024). Benford’s Law and Random Integer Decomposition with Congruence Stopping Condition. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Farris, M, Luntzlara, N, Miller, SJ, Shao, L and Wang, M (2021). Recurrence Relations and Benford's Law. Statistical Methods & Applications 30, pp. 797–817. DOI:10.1007/s10260-020-00547-1. View Complete Reference Online information Works that this work references Works that reference this work
Farris, M, Luntzlara, N, Miller, SJ, Zhao, L and Wang, M (2019). Recurrence Relations and Benford’s Law. Preprint arXiv:1911.09238 [math.PR]; last accessed December 8, 2019. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fellman, J (2014). The Benford paradox. Journal of statistical and econometric methods 3(4), pp. 1-20. ISSN/ISBN:2241-0384 . View Complete Reference Online information Works that this work references Works that reference this work
Fellman, J (2017). Benfordparadoxen. Arkhimedes 2017(4), pp. 26-33. SWE View Complete Reference Online information Works that this work references No Bibliography works reference this work
Finch, S (2011). Newcomb-Benford Law. Online publication - last accessed July 16, 2018. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Flenghi, R and Jourdain, B (2023). Convergence to the uniform distribution of vectors of partial sums modulo one with a common factor. Preprint arXiv:2308.01874 [math.PR]; last accessed August 24, 2023. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Fonseca, PMT da (2016). Digit analysis using Benford's Law: A Bayesian approach. Masters Thesis, ISEG - Instituto Superior de Economia e Gestão, Lisbon School of Economics & Management, Portugal. 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
Fu, Q, Villas-Boas, SB and Judge, G (2019). Does china income FSDs follow Benford? A comparison between Chinese income first significant digit distribution with Benford distribution. China Economic Journal 12(1), pp. 68-76. DOI:10.1080/17538963.2018.1477418. View Complete Reference Online information Works that this work references Works that reference this work
Gauvrit, N and Delahaye, J-P (2008). Pourquoi la loi de Benford n’est pas mystérieuse - A new general explanation of Benford’s law. Mathematiques et sciences humaines/ Mathematics and social sciences, 182(2), pp. 7-15. ISSN/ISBN:0987-6936. DOI:10.4000/msh.10363. FRE View Complete Reference Online information Works that this work references Works that reference this work
Gauvrit, N and Delahaye, J-P (2009). Scatter and regularity imply Benford's Law ... and more. Preprint arXiv: 0910.1359 [math.PR]; last accessed July 18, 2018 . View Complete Reference Online information Works that this work references Works that reference this work
Gauvrit, N and Delahaye, J-P (2011). Scatter and Regularity Implies Benford's Law... and More. in H. Zenil (Ed.) Randomness Through Complexity, Singapore, World Scientific, 53-69. ISSN/ISBN:13978-981-4327-74-9. View Complete Reference Online information Works that this work references Works that reference this work
Golafshan, M and Mitrofanov, I (2024). Complexity function of the most significant digits of 2ND. arXiv:2402.16210. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Goto, K (1992). Some examples of Benford sequences. Mathematical Journal of the Okayama University 34, pp. 225-232. View Complete Reference Online information Works that this work references Works that reference this work
Grendar, M, Judge, G and Schechter, L (2007). An empirical non-parametric likelihood family of data-based Benford-like distributions. Physica A: Statistical Mechanics and its Applications 380, pp. 429-438. ISSN/ISBN:0378-4371. DOI:10.1016/j.physa.2007.02.062. View Complete Reference Online information Works that this work references Works that reference this work
He, X, Hildebrand, AJ, Li, Y and Zhang, Y (2018). Complexity of Leading Digit Sequences. Preprint in arXiv:1804.00221 [math.NT]; last accessed October 23, 2018. 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 (1997). Benford law. Encyclopedia of Mathematics Supplement, vol. 1, pp. 102-103. View Complete Reference Online information Works that this work references Works that reference this work
Hüngerbühler, N (2007). Benfords Gesetz über führende Ziffern: Wie die Mathematik Steuersündern das Fürchten lehrt. EDUCETH - Das Bildungsportal der ETH Zürich. GER View Complete Reference Online information Works that this work references Works that reference this work
Hürlimann, W (2003). A generalized Benford law and its application. Advances and Applications in Statistics 3(3), pp. 217-228. View Complete Reference Online information Works that this work references Works that reference this work
Hürlimann, W (2004). Integer powers and Benford’s law. International Journal of Pure and Applied Mathematics 11(1), pp. 39-46. View Complete Reference No online information available Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Hürlimann, W (2015). Prime powers and generalized Benford law. Pioneer Journal of Algebra, Number Theory and its Applications 12/2015; 10(1-2):51-70. View Complete Reference Online information Works that this work references Works that reference this work
Iyengar, SS, Rajagopal, AK and Uppuluri, VRR (1983). String Patterns of Leading Digits. Applied Mathematics and Computation 12(4), pp. 321-337. ISSN/ISBN:0096-3003. DOI:10.1016/0096-3003(83)90045-0. View Complete Reference Online information Works that this work references Works that reference this work
Jamain, A (2001). Benford’s Law. Master Thesis. Imperial College of London and ENSIMAG. View Complete Reference Online information Works that this work references Works that reference this work
Jameson, M, Thorner, J and Ye, L (2014). Benford's Law for Coefficients of Newforms. arXiv:1407.1577 [math.NT]; posted July 7, 2014; last accessed November 10, 2014. 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
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 (2009). Benford's Law and First Letters. Unpublished manuscript. View Complete Reference No online information available Works that this work references No Bibliography works 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
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. 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
Jolissaint, P (2009). Loi de Benford, relations de récurrence et suites équidistribuées II. Elem. Math. 64 (1), pp. 21-36. FRE View Complete Reference Online information Works that this work references Works that reference this work
Jolissaint, P (2017). L’étonnante loi de Benford. VSMP Bulletin No. 135, pp. 13-17. FRE View Complete Reference Online information Works that this work references No Bibliography works reference this work
Judge, G and Schechter, L (2009). Detecting problems in survey data using Benford’s law. J. Human Resources 44, pp. 1-24. DOI:10.3368/jhr.44.1.1. View Complete Reference Online information Works that this work references Works that reference this work
Kanemitsu, S, Nagasaka, K, Rauzy, G and Shiue, JS (1988). On Benford’s law: the first digit problem. Lecture Notes in Mathematics 1299, pp. 158-169 (eds. Watanabe, S, and Prokhorov, YV). ISSN/ISBN:978-3-540-18814-8. DOI:10.1007/BFb0078471. View Complete Reference Online information Works that this work references Works that reference this work
Katz, TM and Cohen, DIA (1986). The first digit property for exponential sequences is independent of the underlying distribution. Fibonacci Quarterly 24(1), pp. 2-7. View Complete Reference No online information available Works that this work references Works that reference this work
Khosravani, A and Rasinariu, C (2015). n-digit Benford converges to Benford. Int. J. Math. Math. Sci. 2015, Art. ID 123816, 4 pp. 60F25 (11K45). DOI:10.1155/2015/123816. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Khosravani, A and Rasinariu, C (2018). Emergence of Benford's Law in Classical Music. Journal of Mathematical Sciences: Advances and Applications 54, pp. 11-24. DOI:10.18642/jmsaa_7100122017. View Complete Reference Online information Works that this work references Works that reference this work
Kirchner, M and Chakraborty, S (2015). A second look at first significant digit histogram restoration. Proceedings of 2015 IEEE International Workshop on Information Forensics and Security (WIFS), Rome, pp. 1-6. DOI:10.1109/WIFS.2015.7368578. 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 (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
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. 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
Lusk, EJ and Halperin, M (2014). Test of Proportions Screening for the Newcomb-Benford Screen in the Audit Context: A Likelihood Triaging Protocol. Journal of Accounting and Finance Research 3(4), pp. 166-180. DOI:10.5430/afr.v3n4p166. View Complete Reference Online information Works that this work references Works that reference this work
Mainusch, NM (2020). On Benford's law - Computing a Bayes factor with the Savage-Dickey method to quantify conformance of numerical data to Benford's law. Bachelor's Thesis, University of Osnabrueck, Institute of Cognitive Science, Germany. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Manack, C and Miller, SJ (2015). Leading digit laws on linear Lie groups. Research in Number Theory 1:22. DOI:10.1007/s40993-015-0024-4. View Complete Reference Online information Works that this work references Works that 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
Michalski, T and Stoltz, G (2013). Do Countries Falsify Economic Data Strategically? Some Evidence That They Might. The Review of Economics and Statistics, Vol. 95, No. 2, pp. 591-616. DOI:10.1162/REST_a_00274. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Miller, SJ and Nigrini, MJ (2006). Order Statistics and Shifted Almost Benford Behavior. Posted on Math Arxiv, January 13, 2006. View Complete Reference Online information Works that this work references 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 (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
Montaño, VS, Utida, S and Remolar, A (2017). Forensic Analytics of Financial Report in Philippines Property Sector. The Benford's Law Application. Munich Germany: Grin Verlag. ISSN/ISBN:9783668543904. View Complete Reference Online information Works that this work references Works that reference this work
Mori, Y and Takashima, K (2016). On the distribution of the leading digit of an: a study via 𝜒2 statistics. Period. Math. Hungar. 73(2), 224-239. ISSN/ISBN:0031-5303. DOI:10.1007/s10998-016-0138-z. View Complete Reference Online information Works that this work references Works that reference this work
Mörters, P (2001). Benford’s Gesetz über die Verteilung der Ziffern. Habilitationsvorlesung. Kaiserslauten und Bath. GER View Complete Reference Online information Works that this work references Works that reference this work
Mosimann, JE, Wiseman CV and Edelman RE (1995). Data fabrication: Can people generate random digits?. Accountability in Research: Policies and Quality Assurance 4(1), pp. 31-55. DOI:10.1080/08989629508573866. 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
Nagasaka, K and Shiue, JS (1987). Benford's law for linear recurrence sequences. Tsukuba Journal of Mathematics 11(2), pp. 341-351. View Complete Reference No online information available 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
Ohkubo, Y and Strauch, O (2016). Distribution of leading digits of numbers. Uniform Distribution Theory 11(1), pp. 23-45 . DOI:10.1515/udt-2016-0003. View Complete Reference Online information Works that this work references Works that reference this work
Ohkubo, Y and Strauch, O (2019). Distribution of leading digits of numbers II. Uniform Distribution Theory 14(1), pp. 19-42. DOI:10.2478/udt-2019–0003. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Oleksy, M (2010). Data Mining und Benford's Law als Controllinginstrumente. Band 45, Wismarer Schriften zu Management und Recht, Europäischer Hochschulverlag, Bremen. ISSN/ISBN:978-3867414-40. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Park, JA, Kim, M and Yoon, S (2016). Evaluation of Large-scale Data to Detect Irregularity in Payment for Medical Services. Methods of Information in Medicine 55(03), pp. 284-291. DOI:10.3414/ME15-01-0076. View Complete Reference Online information Works that this work references Works that reference this work
Patil, SA and Uppuluri, VRR (1986). The distribution of first j digits. College Mathematical Journal 17(3), pp. 240-243. View Complete Reference Online information Works that this work references Works that reference this work
Patterson, C and Scheepers, M (2024). Benford's Law in the ring ℤ(√ D). arXiv:2402.10864 . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Pocheau, A (2006). The significant digit law: a paradigm of statistical scale symmetries . European Physical Journal B 49(4), pp. 491-511. ISSN/ISBN:1434-6028. DOI:10.1140/epjb/e2006-00084-2. View Complete Reference Online information Works that this work references Works that reference this work
Pollack, P (2023). Two Problems on the Distribution of Carmichael’s Lambda Function. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Pollack, P and Roy, AS (2022). Dirichlet, Sierpiński, and Benford. Journal of Number Theory (pre-proof). DOI:10.1016/j.jnt.2021.12.010. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Pollack, P and Roy, AS (2022). Benford Behavior and Distribution in Residue Classes of Large Prime Factors. Preprint; last accessed May 30, 2022. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Posch, PN (2005). Ziffernanalyse in Theorie und Praxis. Testverfahren zur Fälschungsaufspürung mit Benfords Gesetz. Diploma thesis, Universität Bonn, Germany, 2003. Published by Shaker Verlag, Aachen. GER View Complete Reference No online information available Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Posch, PN (2010). Ziffernanalyse mit dem Newcomb-Benford Gesetz in Theorie und Praxis. VEW Verlag Europäische Wirtschaft: Munich 2nd edition. GER View Complete Reference Online information Works that this work references Works that reference this work
Posch, PN (2013). Benford Or Not-Benford? How To Test For The First-Digit-Law. JP Journal of Fundamental and Applied Statistics 4(1/2), pp. 1-22. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Ravikumar, B (2008). The Benford-Newcomb Distribution and Unambiguous Context-Free Languages. International Journal of Foundations of Computer Science 19(3), pp. 717-727. ISSN/ISBN:0129-0541. DOI:10.1142/S0129054108005905. View Complete Reference Online information Works that this work references Works that reference this work
Ravikumar, B (2009). A simple multiplication game and its analysis. Accepted for publication in the International Journal of Combinatorial Number Theory. View Complete Reference Online information Works that this work references Works that reference this work
Regazzini, E (1982). La legge di Benford-Furlan come legge statistica (The Benford-Furlan law as a statistical law). Statistica 42(3), pp. 351-370. ITA View Complete Reference No online information available Works that this work references Works that reference this work
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. View Complete Reference Online information Works that this work references Works that reference this work
Ross, KA (2012). First Digits of Squares and Cubes. Mathematics Magazine 85(1), pp. 36-42. DOI:10.4169/math.mag.85.1.36. 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 (1989). On measures of uniformly distributed sequences and Benford's law. Monatshefte für Mathematik 107(3), 245-256. ISSN/ISBN:0026-9255. DOI:10.1007/BF01300347. 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
Schürger, K (2008). Extensions of Black-Scholes processes and Benford's law. Stochastic Processes and their Applications 118(7), 1219-1243. ISSN/ISBN:0304-4149. DOI:10.1016/j.spa.2007.07.017. View Complete Reference Online information Works that this work references Works that reference this work
Snyder, MA, Curry, JH and Dougherty, AM (2001). Stochastic aspects of one-dimensional discrete dynamical systems: Benford's law. Physical Review E 64(2), Art. No. 026222. ISSN/ISBN:1063-651X. DOI:10.1103/PhysRevE.64.026222. View Complete Reference Online information Works that this work references Works that reference this work
Uhlig, N (2016). Rundum das Benfordsche Gesetz. Diploma thesis, University of Leipzig, Fakultät für Mathematik und Informatik. GER View Complete Reference Online information Works that this work references No Bibliography works 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
Wang, J, Cha, B-H, Cho, S-H and Kuo, C-CJ (2009). Understanding Benford’s Law and its Vulnerability in Image Forensics. IEEE International Conference on Multimedia and Expo, ICME 2009, pp. 1568 - 1571. ISSN/ISBN:1945-7871. DOI:10.1109/ICME.2009.5202811. 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
Ylvisaker, D (1977). Test Resistance. Journal of the American Statistical Association 72(359), 551-556. ISSN/ISBN:0162-1459. DOI:10.1080/01621459.1977.10480612. View Complete Reference Online information Works that this work references Works that reference this work
Zheng, S (2013). Necessary and Sufficient Conditions for Benford Sequences. Pi Mu Epsilon Journal 13(9), pp. 553 – 561. View Complete Reference Online information Works that this work references Works that reference this work