This work cites the following items of the Benford Online Bibliography:
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. | ||||
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. | ||||
Barabesi, L and Pratelli, L (2020). On the Generalized Benford law. Statistics & Probability Letters 160, 108702 . DOI:10.1016/j.spl.2020.108702. | ||||
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 and Hill, TP (2011). Benford's Law Strikes Back: No Simple Explanation in Sight for Mathematical Gem. The Mathematical Intelligencer 33(1), pp. 85-91. DOI:10.1007/ s00283-010-9182-3. | ||||
Berger, A and Hill, TP (2011). A basic theory of Benford's Law . Probability Surveys 8, pp. 1-126. DOI:10.1214/11-PS175. | ||||
Berger, A and Hill, TP (2015). An Introduction to Benford's Law. Princeton University Press: Princeton, NJ. ISSN/ISBN:9780691163062. | ||||
Berger, A and Hill, TP (2020). The mathematics of Benford’s law: a primer. Statistical Methods & Applications 30, pp. 779-795. DOI:10.1007/s10260-020-00532-8. | ||||
Bijma, F, Jonker, M and van der Vaart, A (2017). An Introduction to Mathematical Statistics. Amsterdam University Press; 2nd edition (Chapter 2.4 Application), pp. 41-44. ISSN/ISBN:978-9462985100. | ||||
Bolton, RJ and Hand, DJ (2002). Statistical Fraud Detection: a review. Statistical Science 17(3), pp. 235-249. | ||||
Candeloro, D (1998). Some remarks on the first digit problem. Atti Sem. Mat. Fis. Univ. Modena 46 (1998), suppl., 511-532. | ||||
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. | ||||
Chang, M (2012). Paradoxes in scientific inference . CRC Press: Boca Raton (Chapter 1.2.1), pp. 12-13. ISSN/ISBN:978-1466509863. | ||||
Demidenko, E (2020). Advanced Statistics with Applications in R. Wiley: Hoboken, NJ (Chapter 2.16). ISSN/ISBN:1118387988. | ||||
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. | ||||
Dworsky, LN (2019). Probably Not: Future Prediction Using Probability and Statistical Inference. Wiley: Hoboken (Chapter 14). ISSN/ISBN:0470184019. | ||||
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. | ||||
Fuchs, A and Letta, G (1984). Sur le problème du premier chiffre décimal. Bollettino dell'Unione Matematica Italiana, VI. Ser., B 3, pp. 451-461. FRE | ||||
Fuchs, A and Letta, G (1996). Le problème du premier chiffre décimal pour les nombres premiers. The Electronic Journal of Combinatorics 3(2), R25. FRE | ||||
Giuliano-Antonini, R and Grekos, G (2005). Regular sets and conditional density: an extension of Benford's law. Colloquium Mathematicum, 103(2), pp. 173–192. DOI:10.4064/cm103-2-3. | ||||
Gorroochurn, P (2012). Benford and the Peculiar Behavior of the First Significant Digit (1938). Chapter 27 in: Classic problems of probability. John Wiley & Sons: Hoboken, NJ, 2012. ISSN/ISBN:978-1-118-06325-5 . DOI:10.1002/9781118314340. | ||||
Havil, J (2008). Benford's Law. pp. 190-200 in: Impossible? Surprising solutions to counterintuitive conundrums, Princeton University Press, USA. ISSN/ISBN:978-0-691-13131. | ||||
Herzel, A (1956). Sulla distribuzione delle cifre iniziali die numeri statistic [On the frequency of initial digits of statistical numbers]. Atti XV e XVI Riunione sci., Roma, [Proceedings of the XV and XVI Scientific Meeting of the Italian Statistical Society." 1957. Faculty of Demographic and Actural Statistics. Institute of Statistics and Institute of Probability: No. 25] pp. 205-228. ITA | ||||
Hill, TP (1995). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), pp. 322-327. DOI:10.2307/2974952. | ||||
Hill, TP (1995). A Statistical Derivation of the Significant-Digit Law. Statistical Science 10(4), pp. 354-363. ISSN/ISBN:0883-4237. | ||||
Knuth, DE (1997). The Art of Computer Programming. pp. 253-264, vol. 2, 3rd ed, Addison-Wesley, Reading, MA. | ||||
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. | ||||
Miller, SJ (ed.) (2015). Benford's Law: Theory and Applications. Princeton University Press: Princeton and Oxford. ISSN/ISBN:978-0-691-14761-1. | ||||
Mumic, N and Filzmoser, P (2021). A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data. Statistical Methods & Applications 30, 819–840. DOI:10.1007/s10260-021-00582-6. | ||||
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 (1992). The Detection of Income Tax Evasion Through an Analysis of Digital Frequencies. PhD thesis, University of Cincinnati, OH, USA. | ||||
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. | ||||
Olofsson, P (2015). Probabilities: the little numbers that rule our lives. 2nd edition, Wiley: Hoboken (Chapter 9), pp. 294-297. ISSN/ISBN:1118898907. | ||||
Pickover, C (2012). The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics (Sterling Milestones). Sterling Publishing: New York. See: Benford's Law (1881). ISSN/ISBN:978-1-4027-5796-9. | ||||
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 | ||||
Scozzafava, R (1981). Un esempio concreto di probabilita non σ-additiva: la distribuzione della prima cifra significativa dei dati statistici. Boll. Un. Mat. Ital. A(5) 18(3), 403-410. ITA | ||||
Tijms, H (2019). Surprises in probability: Seventeen Short Stories. CRC Press: Boca Raton, (Chapter 5), pp. 31-36. ISSN/ISBN:0367000822. | ||||
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 . | ||||
Weyl, H (1916). Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen 77, 313-352. ISSN/ISBN:0025-5831. DOI:10.1007/BF01475864. GER |