Cross Reference Up

Hamming, R (1970). On the distribution of numbers. Bell Syst. Tech. J. 49(8), pp. 1609-1625.

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.

Allaart, PC (1997). An invariant-sum characterization of Benford's law. Journal of Applied Probability 34(1), pp. 288-291. View Complete Reference Online information Works that this work references Works that reference this work
Barlow, JL and Bareiss, EH (1985). On Roundoff Error Distributions in Floating Point and Logarithmic Arithmetic. Computing 34(4), pp. 325-347. ISSN/ISBN:0010-485X. DOI:10.1007/BF02251833. View Complete Reference Online information Works that this work references Works that reference this work
Becker, PW (1982). Patterns in Listings of Failure-Rate and MTTF Values and Listings of Other Data. IEEE Transactions on Reliability 31(2), 132-134. ISSN/ISBN:0018-9529. 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 (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
Boyle, J (1994). An Application of Fourier Series to the Most Significant Digit Problem. American Mathematical Monthly 101(9), pp. 879-886. ISSN/ISBN:0002-9890. DOI:10.2307/2975136. View Complete Reference Online information Works that this work references Works that reference this work
Brähler, G, Bensmann, M and Jakobi, HR (2011). Das Benfordsche Gesetz und seine Anwendbarkeit bei der digitalen Prüfung von Fahrtenbüchern. Ilmenauer Schriften zur Betriebswirtschaftslehre 3/2011. ISSN/ISBN:978-3-940882-28-8. GER View Complete Reference Online information Works that this work references Works that reference this work
Chaitin-Chatelin, F (1994). Le calcul sur ordinateur a precision finie. Theorie et etat de l’art. CERFACS REPORT TR/PA/94/05. FRE View Complete Reference No online information available Works that this work references Works that reference this work
Chaitin-Chatelin, F (1995). Le calcul qualitatif. Comment donner un sens a des resultats faux?. CERFACS REPORT TR/PA/95/10. FRE View Complete Reference No online information available 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
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
Corazza, M, Ellero, A and Zorzi, A (2018). The importance of being “one” (or Benford’s law). Lettera Matematica 6(1), pp. 33–39. DOI:10.1007/s40329-018-0218-4. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Davic, RD (2022). Correspondence of Newcomb-Benford law with ecological processes . Posted on bioRxiv preprint server of Cold Springs Harbor Laboratory June 27, 2022 . DOI:10.1101/2022.06.27.497806. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Farbaniec, M, Grabiński, T, Zabłocki, B and Zając, W (2011). Application of the first digit law in credibility evaluation of the financial accounting data based on particular cases. Presentation for 10th International Congress on Internal Control, Internal Audit, Fraud and Anti-Corruption Issues, Kraków, September 14-16, 2011. View Complete Reference No online information available Works that this work references Works that 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
Friar, JL, Goldman, T and Pérez-Mercader, J (2016). Ubiquity of Benford’s law and emergence of the reciprocal distribution. Physics Letters A 380(22), pp. 1895–1899. ISSN/ISBN:0375-9601. DOI:10.1016/j.physleta.2016.03.045. View Complete Reference Online information Works that this work references Works that reference this work
Friar, JL, Goldman, T and Pérez–Mercader, J (2012). Genome Sizes and the Benford Distribution. PLoS ONE 7(5): e36624. DOI:10.1371/journal.pone.0036624. 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
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). The Significant-Digit Phenomenon. American Mathematical Monthly 102(4), pp. 322-327. DOI:10.2307/2974952. 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
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
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
Jing, J (2013). Benford’s Law and Stick Decomposition. Undergraduate thesis, Williams College, Williamstown, Massachusetts . View Complete Reference Online information Works that this work references Works that reference this work
Johnstone, P and Petry, FE (1994). Design and Analysis of Nonbinary Radix Floating-Point Representations. Computers & Electrical Engineering 20(1), pp. 39-50. ISSN/ISBN:0045-7906. DOI:10.1016/0045-7906(94)90005-1. View Complete Reference Online information Works that this work references No Bibliography works 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
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 (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
Kossovsky, AE (2014). Arithmetical Tugs of War and Benford's Law. Preprint arXiv:1410.2174 [math.ST]; last accessed October 19, 2020. View Complete Reference Online information Works that this work references Works that reference this work
Kossovsky, AE (2015). Random Consolidations and Fragmentations Cycles Lead to Benford' Law. Preprint arXiv:1505.05235 [math.ST]; last accessed October 19, 2020. View Complete Reference Online information Works that this work references Works that reference this work
Kossovsky, AE (2016). Exponential Growth Series and Benford's Law. Preprint arXiv:1606.04425 [math.ST]; last accessed October 19, 2020. View Complete Reference Online information Works that this work references Works that reference this work
Kreifelts, T (1973). Optimal Choice of Basis for a Floating-Point Arithmetic [Optimale Wahl für eine Gleitkomma-Arithmetik] . Computing 11(4), pp. 353-363. ISSN/ISBN:0010-485X. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Li, Z, Cong, L and Wang, H (2004). Discussion on Benford’s law and its application. posted on arXiv:math/0408057, Aug 4, 2004. 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
Massé, B and Schneider, D (2012). Random number sequences and the first digit phenomenon. Electronic Journal of Probability, Vol 17, Article 86, pp. 1-17 . DOI:10.1214/EJP.v17-1900. View Complete Reference Online information Works that this work references Works that reference this work
Matula, VV and Kornerup, P (1980). Foundations of Finite Precision Rational Arithmetic. pp 85-111 in: Alefeld, G, Grigorieff, RD (eds.) Fundamentals of Numerical Computation (Computer-Oriented Numerical Analysis), Computing Supplementum 2, Springer, Wien-New York. View Complete Reference No online information available Works that this work references Works that reference this work
McLaughlin, WI and Lundy, SA (1984). Digit functions of integer sequences. Fibonacci Quarterly 22(2), pp. 105-115. ISSN/ISBN:0015-0517. 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 (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 (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
Mochty, L (2002). Die Aufdeckung von Manipulationen im Rechnungswesen - Was leistet das Benford's Law?. Die Wirtschaftsprüfung 14, pp. 725-736. GER View Complete Reference Online information 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
Ozawa, K (2019). Continuous Distributions on (0, ∞) Giving Benford’s Law Exactly. Preprint arXiv:1905.02031 [math.PR]; last accessed June 6, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Palacios, NT (2020). Benford's Law. History, mathematical justification and applications. Degree in Statistics Final Degree Project, Universidad de Valladolid. Facultad de Ciencias. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Pimbley, JM (2014). Benford’s Law as a Logarithmic Transformation. Maxwell Consulting Archives. Last retrieved 20 April 2018. View Complete Reference Online information Works that this work references Works that reference this work
Pippenger, N (2002). Expected acceptance counts for finite automata with almost uniform input. Algorithms and Computation, Proceedings. Lecture Notes in Computer Science 2518, pp. 636-646. ISSN/ISBN:0302-9743. DOI:10.1007/3-540-36136-7_56. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Pippenger, N (2004). Entropy and expected acceptance counts for finite automata. IEEE Transactions on Information Theory 50(1), pp. 78-88. ISSN/ISBN:0018-9448. DOI:10.1109/TIT.2003.821997. 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 (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
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
Rajagopal, AK, Uppuluri, VRR, Scott, DS, Iyengar, SS and Yellayi, M (1984). New structural properties of strings generated by leading digits of 2N. Applied Mathematics and Computation 14(3), pp. 221-244. DOI:10.1016/0096-3003(84)90023-7. View Complete Reference Online information Works that this work references Works that reference this work
Rauch, B, Göttsche, M, El Mouaaouy, F and Geidl, F (2013). Empirical methods in competition analysis – Applying Benford’s law to the Western Australian petroleum market. Available at SSRN: https://ssrn.com/abstract=2364384; last accessed Dec 7, 2019. DOI:10.2139/ssrn.2364384. View Complete Reference Online information Works that this work references Works that reference this work
Rodriguez, RJ (2004). Reducing False Alarms in the Detection of Human Influence on Data. Journal of Accounting, Auditing & Finance 19(2), pp. 141-158. DOI:10.1177/0148558X0401900202. View Complete Reference Online information Works that this work references Works that reference this work
Schäfer, C, Schräpler, J-P and Müller, KR (2004). Identification, Characteristics and Impact of Faked and Fraudulent Interviews in Surveys. Proceedings of European Conference on Quality and Methodology in Official Statistics. View Complete Reference Online information Works that this work references Works that reference this work
Schäfer, C, Schräpler, J-P, Müller, KR and Wagner GG (2004). Automatic Identification of Faked and Fraudulent Interviews in Surveys by Two Different Methods. Discussion paper 441, DIW Berlin (German Institute for Economic Research). ISSN/ISBN:1619-4535. 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 (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
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
Schräpler, J-P (2010). Benford's Law as an instrument for fraud detection in surveys using the data of the Socio-Economic Panel (SOEP). Socio-Economic Panel (SOEP) paper No. 273, March 2, 2010. DOI:10.2139/ssrn.1562574. View Complete Reference Online information Works that this work references Works that reference this work
Schräpler, J-P (2011). Benford's Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP). Jahrbücher für Nationalökonomie und Statistik 231(5-6). DOI:10.1515/jbnst-2011-5-609. 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
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
Valadier, M (2012). The Benford phenomenon for random variables. Discussion of Feller's way. Math arXiv:1203.2518; posted 19 Apr 2012. View Complete Reference Online information Works that this work references Works that reference this work
Watrin, C, Struffert, R and Ullmann, R (2008). Benford’s Law: an instrument for selecting tax audit targets?. Review of Managerial Science 2(3), 219-237. DOI:10.1007/s11846-008-0019-9. View Complete Reference Online information Works that this work references Works that reference this work
Wojcik, MR (2013). Notes on scale-invariance and base-invariance for Benford's Law. arXiv:1307.3620 [math.PR]. View Complete Reference Online information Works that this work references Works that reference this work
Wolowik, P (2005). Prawo Benforda – testowanie i wery kacja poprawności danych pomiarowych [Benford's Law - testing and verification of the correctness of measurement data] . Pr- zegląd Telekomunikacyjny – Wiadomości Telekomunikacyjne” 11, pp. 414-418. POL View Complete Reference Online information Works that this work references Works that reference this work