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A multivariate test for detecting fraud based on Benford’s law, with application to music streaming data
Statistical Methods & Applications ( IF 1 ) Pub Date : 2021-07-27 , DOI: 10.1007/s10260-021-00582-6
Nermina Mumic 1 , Peter Filzmoser 1
Affiliation  

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.



中文翻译:

基于本福德定律的用于检测欺诈的多变量测试,适用于音乐流数据

本福德定律成为欺诈和异常检测的流行概念。它检查一组数据中数字前导数字的频率,并指出前导数字最常见的是 1,频率递减的频率高达 9。在本文中,我们提出了一种多变量方法来测试观察到的频率是否遵循理论本福德分布。我们的方法基于组合数据的概念,它检查前导数字频率之间的相关信息。因此,我们引入了 Benford 分布的多变量检验。在模拟研究和示例中,我们将多元检验性能与传统的卡方检验和 Kolmogorov-Smirnov 检验进行了比较,结果证明多元检验在许多情况下更为敏感。

更新日期:2021-07-27
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