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Kıvraklar, K and Demirci, M (2019). Benford Yasası’nın Mali Denetim Alanında Kullanımı Üzerine Bir Uygulama [An Application On The Use Of Benford Law In The Field Of Financial Inspection]. Muhasebe ve Vergi Uygulamaları Dergisi 12(2), pp. 289-316. DOI:10.29067/muvu.340793. TUR View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kaczmarek, K (2008). Fun (and Fraud Detection) with Benford's Law. Posted on Kirix.com July 22; last accessed April 26, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Kafri, O (2007). The Second Law as a Cause of the Evolution. Preprint arXiv: 0711.4507, 2007 - arxiv.org. View Complete Reference Online information Works that this work references Works that reference this work
Kafri, O (2008). Sociological Inequality and the Second Law. http://arxiv.org/abs/0805.3206. View Complete Reference Online information Works that this work references Works that reference this work
Kafri, O (2009). Entropy Principle in Direct Derivation of Benford's Law. posted on arXiv 8 March 2009 - arXiv:0901.3047v2. View Complete Reference Online information Works that this work references Works that reference this work
Kafri, O (2009). The Distributions in Nature and Entropy Principle. CoRR, vol. abs/0907.4852. View Complete Reference Online information Works that this work references Works that reference this work
Kafri, O (2020). Microcanonical Partition Function. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kaiser, M (2019). Benford’s Law As An Indicator Of Survey Reliability—Can We Trust Our Data?. Journal of Economic Surveys Vol. 00, No. 0, pp. 1–17. DOI:10.1111/joes.12338. 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
Kalaichelvan, M and Jie, SLK (2012). A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford's Law. International Research Journal of Finance and Economics 95, pp. 196-210. ISSN/ISBN:1450-2887. 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
Kapoor, M, Malani, A, Ravi, S and Agarwal, A (2020). Authoritarian Governments Appear to Manipulate COVID Data. Preprint arXiv:2007.09566 [econ.GN]; last accessed August 29, 2020. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kappal, S (2017). HealthCare Industry’s Savior: Using the Benford's Law (The Law of First Digit) to Debunk the Fraudsters. Blog on Data Science Central, posted on January 16, 2017; last accessed October 15, 2018. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kappal, S (2019). Deplyoing [sic] Advance Data Analytics Techniques with Conversational Analytics Outputs for Fraud Detection . International Journal of Mathematical Sciences and Computing (IJMSC) 5(1), pp. 42-52 . DOI:10.5815/ijmsc.2019.01.04. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Karavardar, A (2014). Benford’s Law and an Analysis in Istanbul Stock Exchange (BIST). International Journal of Business and Management, 9(4), pp. 160-172. DOI:10.5539/ijbm.v9n4p160. View Complete Reference Online information Works that this work references Works that reference this work
Karthik, D, Stelzer, G, Gershanov, S, Baranes, D and Salmon-Divon, M (2016). Elucidating tissue specific genes using the Benford distribution. BMC Genomics 17(1), pp. 595-610. DOI:10.1186/s12864-016-2921-x. View Complete Reference Online information No Bibliography works referenced by this work. 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
Kazemitabar, Jal and Kazemitabar, Jav (2019). Measuring the conformity of distributions to Benford's law. Communications in Statistics - Theory and Methods, pp. 1-7. DOI:10.1080/03610926.2019.1590599. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kellerman, L (2014). Evaluating the effectiveness of Benford’s law as an investigative tool for forensic accountants. Masters thesis (Magister Commercii) in Forensic Accountancy at the Potchefstroom Campus of the North-West University. View Complete Reference Online information Works that this work references Works that reference this work
Kelly, C (2011). Benford's Law to the Rescue. Internal Auditor, Vol. 68, No. 1, pp. 25-27 . View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Kempf, D and Fischer, A (2008). Digitale Datenanalyse – ein adäquates Mittel zur Aufdeckung von Unregelmäßigkeiten in der Rechnungslegung. online document Universität Münster, Germany. GER View Complete Reference Online information Works that this work references Works that reference this work
Kendal, WS (2004). Taylor’s ecological power law as a consequence of scale invariant exponential dispersion models. Ecological Complexity 1(3), pp. 193-209. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kennard, R and Reith, J (1981). On the distribution of first digits. Communications in Statistics. Simulation and computation 10(1), pp. 97-98. DOI:10.1080/03610918108812195. View Complete Reference Online information Works that this work references Works that reference this work
Kennedy, S and Matthews, S (2013). China Data Suspected Says 75-Year-Old Theory: Cutting Research. Bloomberg News, January 10, 2013. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kentucky, FC (2010). Benford's Law And A Theory of Everything. A View from Emerging Technology from the arXiv, MIT Technology Review, May 7, 2010. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kha, V and Lam, B (2011). Das Benford’sche Gesetz. Facharbeit Mathematik, Max-von-Laue-Gymnasium Koblenz. GER View Complete Reference No online information available Works that this work references No Bibliography works reference this work
Khan, S and Hart, V (2012). Vi and Sal talk about the mysteries of Benford's law. Khan Academy online tutorial. Last accessed Mar 6, 2015. View Complete Reference Online information No Bibliography works referenced by this work. No Bibliography works reference this work
Khan, S and Hart, V (2012). Benford's law explanation (sequel to mysteries of Benford's law). Khan Academy online tutorial. Last accessed Mar 6, 2015. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Khoshnevisan, M and Bhattacharya, S (2002). A short note on financial data set detection using neutrosophic probability. pp 74-79 in: Smarandache, F (ed), Proceedings of the first international conference on neutrosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, University of New Mexico - Gallup, Dec 2001. View Complete Reference Online information Works that this work references Works that reference this work
Khosravani, A and Rasinariu, C (2012). Transformation invariance of Benford variables and their numerical modeling. Recent Researches in Automatic Control and Electronics - Proceedings of the 14th International Conference on Automatic Control, Modelling & Simulation (ACMOS '12) and Proceedings of the 11th International Conference on Microelectronics, Nanoelectronics. ISSN/ISBN:978-1-61804-080-0. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Khosravani, A and Rasinariu, C (2013). n-Digit Benford Distributed Random Variables. Advances and Applications in Statistics, 36, pp. 119-130. View Complete Reference Online information 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. Unpublished manuscript. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kienle, S (2015). What Benford Can Tell Us About Cover Pools – An Empirical Analysis. International Business & Economic Research Journal 14(6), pp. 829-834. DOI:10.19030/iber.v14i6.9489. View Complete Reference Online information Works that this work references Works that reference this work
Kim, H (2019). Financial Statements Errors in Japanese Firms : Using a Benfordʼs Law. The Journal of Tokyo Keizai University: Business 302, pp. 19-42. JPN View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kim, H-J, Mannino, M and Nieschwietz, R (2011). Instructional Materials for Benford’s Law: Conceptual Background and Guided Software Instruction with Supporting Teaching Notes. A Compendium of Classroom Cases and Tools (C3) 5. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kim, S (2012). Benford’s law in non-equilibrium processes: Droplet collisions case. Physica A: Statistical Mechanics and its Applications, Vol. 391, No. 20, pp. 4970–4975. DOI:10.1016/j.physa.2012.05.043. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kinnunen, J and Koskela, M (2003). Who Is Miss World in Cosmetic Earnings Management? A Cross-National Comparison of Small Upward Rounding of Net Income Numbers among Eighteen Countries. Journal of International Accounting Research 2, pp. 39-68. DOI:10.2308/jiar.2003.2.1.39. View Complete Reference Online information Works that this work references Works that reference this work
Kisets, D (2002). Informational optimality of decimal numeration system. Academic Open Internet Journal 6. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Klimek, P, Yegorov, Y, Hanel, R and Thurner, S (2012). Statistical detection of systematic election irregularities. Proceedings of the National Academy of Science October 109(41), pp. 16469-16473. DOI:10.1073/pnas.1210722109. View Complete Reference Online information Works that this work references Works that reference this work
Klimov, Y and Klimov, O (2018). Benford's Law in Information Science. Intellectual Archive 7. DOI:10.32370/2018_09_3. RUS View Complete Reference Online information Works that this work references No Bibliography works reference this work
Klink, S and Henke, M (2004). Das Gesetz der ersten Ziffer. Projektarbeit im Rahmen des Fachwissenschaftlichen Seminars (Leitung: Prof. Dr. Maria Specovius-Neugebauer), Universität Kassel, Germany. GER View Complete Reference No online information available Works that this work references No Bibliography works reference this work
Knopfmacher, J (1981). Initial digits in number theory. Fibonacci Quarterly 19(2), pp. 121-126. View Complete Reference No online information available Works that this work references Works that reference this work
Knot, R (2016). The Mathematical Magic of the Fibonacci Numbers. Posted on R. Knot's Fibonacci blog - see Chapter 7; last accessed August 1, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Knudsen, T (2001). Zipf’s Law for Cities and Beyond - The Case of Denmark. American Journal of Economics and Sociology 60(1), pp. 123-146. ISSN/ISBN:0002-9246. DOI:10.1111/1536-7150.00057. 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
Kocameşe, M (2006). Benford Kanunu ve Vergi Denetiminde Kullanılabilirliğinin Đncelenmesi [Benford's Law and Review of the Usability of Tax Audit]. Masters Thesis, Marmara University, Institute of Social Sciences, Business Administration, Department Of Accounting. TUR View Complete Reference Online information Works that this work references Works that reference this work
Koch, C and Okamura, K (2020). Benford's Law and COVID-19 Reporting. Posted on SSRN April 28, 2020; last accessed November 17, 2020. View Complete Reference Online information Works that this work references Works that reference this work
Koesters, N, McMenemy, A and Bélanger, Y (2020). Simulating Epidemics with a SIRD Model and Testing with Benford’s Law. Preprint. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Komulainen, T (2004). Self-similarity and power laws. Heikki Hyötyniemi (ed.): Complex Systems - Science on the Edge of Chaos. Helsinki University of Technology, Control Engineering Laboratory, Report 145, 2004. View Complete Reference Online information Works that this work references Works that reference this work
Konheim, AG (1965). Mantissa distribution. Mathematics of Computation 19, pp. 143-144. DOI:10.1090/S0025-5718-1965-0175159-1. View Complete Reference Online information No Bibliography works referenced by this work. 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
Kopczewski, T and Okhrimenko, I (2019). Playing with Benford’s Law. E-print posted on http://www.nbp.pl/badania/seminaria/8ii2019.pdf; last accessed June 6, 2019. View Complete Reference Online information Works that this work references Works that reference this work
Koppisch, D, Van Gelder, R and Gabriel, S (2013). Benford's law and the quality of data . Inhaled Particles XI (IPXI). 23.-25. September 2013, Nottingham/Great Britain – Poster . View Complete Reference Online information Works that this work references No Bibliography works reference this work
Koppisch, D, Van Gelder, R, Gabriel, S and Stamm, R (2014). Benford's law and the quality of occupational hygiene data. Ann Occup Hyg. 58(3), pp. 397-400. DOI:10.1093/annhyg/meu003. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Korauš, A, Gombár, M, Kelemen, P and Backa, S (2019). Using Quantitative Methods to Identify Security and Unusual Business Operations. Entrepreneurship And Sustainability Issues 6(3), pp.1101-1112. DOI:10.9770/jesi.2019.6.3(3). View Complete Reference Online information Works that this work references No Bibliography works reference this work
Koskivaara, E (2004). Artificial neural networks in analytical review procedures. Managerial Auditing Journal 19(2), pp. 191-223. View Complete Reference Online information Works that this work references Works that reference this work
Kossovsky, AE (2006). Towards a Better Understanding of the Leading Digits Phenomena. posted December 21, 2006 on arXiv:math/0612627. View Complete Reference Online information Works that this work references Works that reference this work
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
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
Kossovsky, AE (2017). Small is Beautiful. https://www.amazon.com/Small-Beautiful-Numerous-Rare-World/dp/069291241X. ISSN/ISBN:069291241X. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Kottke, J (2006). Catching cheaters with Benford's Law . http://www.kottke.org/06/02/catching-cheaters-with-benfords-law. View Complete Reference Online information Works that this work references Works that reference this work
Kowalski, JM (2016). Few more Comments on Benford’s Law. arXiv:1612.04200 [math.HO], last accessed February 16, 2017. View Complete Reference Online information Works that this work references No Bibliography works 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
Krakar, Z and Žgela, M (2009). Evaluation of Benford's Low Application in Stock Prices and Stock Turnover. Informatologia 42(3), pp. 158-165. View Complete Reference Online information Works that this work references Works that reference this work
Krakar, Z and Žgela, M (2009). Application of Benford's Law in information systems auditing. Journal of Information and Organizational Sciences, 33(1), pp. 39-51. View Complete Reference No online information available Works that this work references Works that reference this work
Krawiec, J (2012). Prawo Benforda jako narzędzie wykrywania manipulacji finansowych [Benford's law as a tool for detecting financial manipulation]. KWARTALNIK NAUK O PRZEDSIĘBIORSTWIE, 2012, 4, pp. 86-91. POL View Complete Reference Online information Works that this work references No Bibliography works 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
Kreiner, WA (2002). First digit law. Preprint, Universität Ulm. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kreiner, WA (2003). On the Newcomb-Benford Law. Zeitschrift für Naturforschung Section A - A Journal of Physical Sciences 58(11), pp. 618-622. ISSN/ISBN:0932-0784. DOI:10.1515/zna-2003-1105. View Complete Reference Online information Works that this work references Works that reference this work
Krengel, U (2005). Die Anfangszifferverteilung. pp. 136-137 in: Einführung in die Wahrscheinlichkeitstheorie und Statistik, 8th ed, Vieweg und Sohn, Wiesbaden. ISSN/ISBN:3-8348-0063-5. GER View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kreuzer, M, Jordan, D, Antkowiak, B, Drexler, B, Kochs, EF and Schneider, G (2014). Brain electrical activity obeys Benford's law. Anesth. Analg. 118(1), pp. 183-91. DOI:10.1213/ANE.0000000000000015. View Complete Reference Online information Works that this work references Works that reference this work
Kriel, E (2008). Technology Solutions to Detect Fraud. Paper 158-2008, SAS Global Forum 2008. View Complete Reference Online information Works that this work references Works that reference this work
Kriel, E (2010). Discussion of 'Data mining journal entries for fraud detection: An exploratory study'. International Journal of Accounting Information Systems 11 (3), pp. 186–188 . DOI:10.1016/j.accinf.2010.07.009. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work
Kruger, PS and Yadavalli, VSS (2017). The Power of One: Benford's Law. South African Journal of Industrial Engineering Vol 28(2), pp. 1-13. DOI:10.7166/28-2-1753. View Complete Reference Online information Works that this work references Works that reference this work
Kruszelnicki, K (2000). Benford's Law. Dr. Karl Great Moments in Science website; last accessed December 6, 2019. View Complete Reference Online information No Bibliography works referenced by this work. No Bibliography works reference this work
Krygier, J (2009). Psychological relevance of Benford’s Law: Sensitivity to statistical regularities and implications for theories of number representation. Honours thesis, University of Sydney, Sydney, NSW, Australia. View Complete Reference No online information available No Bibliography works referenced by this work. Works that reference this work
Kubaščíková, Z and Pakšiová, R (2014). Applying Benford’s Law. European Financial Systems 2014 - Proceedings of the 11th International Scientific Conference, V.Kajurová, O. Deev, and J. Krajíček (Editors), pp. 359-363. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kuipers, L (1969). Remark on a paper by R.L. Duncan concerning the uniform distribution mod 1 of the sequence of the logarithms of the Fibonacci numbers. Fibonacci Quarterly 7, pp. 465-466, 473. View Complete Reference No online information available Works that this work references Works that reference this work
Kuipers, L and Niederreiter, H (1974). Uniform Distribution of Sequences. J. Wiley; newer edition - 2006 from Dover. ISSN/ISBN:0486450198. View Complete Reference Online information Works that this work references Works that reference this work
Kuipers, L and Shiue, JS (1973). Remark on a paper by Duncan and Brown on the sequence of logarithms of certain recursive sequences. Fibonacci Quarterly 11(3), pp. 292-294. View Complete Reference No online information available Works that this work references Works that reference this work
Kulikova, AA and Prokhorov, YV (2005). Completely asymmetric stable laws and Benford’s law. Theory of Probability and its Application 49(1), pp. 163-169. DOI:10.1137/S0040585X97980944. View Complete Reference Online information Works that this work references Works that reference this work
Kulikova, AA, Prokhorov, YV and Khokhlov, VI (2006). H.F.D. (H-function Distribution) and Benford's Law. I. Theory of Probability & Its Applications 50(2), pp. 311-315 . DOI:10.1137/S0040585X97981706. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kumar, K and Bhattacharya, S (2003). Benford’s law and its application in financial fraud detection. Advances in Financial Planning and Forecasting 11, pp. 57-70. View Complete Reference No online information available No Bibliography works referenced by this work. Works that reference this work
Kumar, K and Bhattacharya, S (2007). Detecting the dubious digits: Benford’s law in forensic accounting. Significance 4(2), pp. 81-83. DOI:10.1111/j.1740-9713.2007.00234.x. View Complete Reference Online information Works that this work references Works that reference this work
Kundt, TC (2014). Applying "Benford's law" to the Crosswise Model: Findings from an online survey on tax evasion . Helmut-Schnidt-University, Department of Economics, Working Paper, 148/2014. View Complete Reference Online information Works that this work references Works that reference this work
Kunoff, S (1987). N! has the first digit property. Fibonacci Quarterly 25, pp. 365-367. View Complete Reference No online information available Works that this work references Works that reference this work
Kuruppu, N (2019). The Application of Benford’s Law in Fraud Detection: A Systematic Methodology. International Business Research, Canadian Center of Science and Education 12(10), pp. 1-10. DOI:10.5539/ibr.v12n10p1. View Complete Reference Online information Works that this work references No Bibliography works reference this work
Kyd, C (2017). Use Benford's Law & Charts in Excel to Improve Business Planning. Posted on exceluser.com; last accessed October 11, 2019. View Complete Reference Online information No Bibliography works referenced by this work. Works that reference this work

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