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A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data

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  • Nermina Mumic

    (TU Wien)

  • Peter Filzmoser

    (TU Wien)

Abstract

Benford’s law became a prevalent concept for fraud and anomaly detection. It examines the frequencies of the leading digits of numbers in a collection of data and states that the leading digit is most often 1, with diminishing frequencies up to 9. In this paper we propose a multivariate approach to test whether the observed frequencies follow the theoretical Benford distribution. Our approach is based on the concept of compositional data, which examines the relative information between the frequencies of the leading digits. As a result, we introduce a multivariate test for Benford distribution. In simulation studies and examples we compare the multivariate test performance to the conventional chi-square and Kolmogorov-Smirnov test, where the multivariate test turns out to be more sensitive in many cases. A diagnostics plot based on relative information allows to reveal and interpret the possible deviations from the Benford distribution.

Suggested Citation

  • Nermina Mumic & Peter Filzmoser, 2021. "A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 819-840, September.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:3:d:10.1007_s10260-021-00582-6
    DOI: 10.1007/s10260-021-00582-6
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    References listed on IDEAS

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    1. Deckert, Joseph & Myagkov, Mikhail & Ordeshook, Peter C., 2011. "Benford's Law and the Detection of Election Fraud," Political Analysis, Cambridge University Press, vol. 19(3), pages 245-268, July.
    2. Jane Fry & Tim Fry & Keith McLaren, 2000. "Compositional data analysis and zeros in micro data," Applied Economics, Taylor & Francis Journals, vol. 32(8), pages 953-959.
    3. Juan Manuel Larrosa, 2003. "A Compositional Statistical Analysis of Capital per Worker," Macroeconomics 0301006, University Library of Munich, Germany.
    4. repec:eme:majpps:maj-11-2017-1717 is not listed on IDEAS
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    1. Lucio Barabesi & Andrea Cerioli & Domenico Perrotta, 2021. "Forum on Benford’s law and statistical methods for the detection of frauds," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 767-778, September.

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