European Commission, Joint Research Centre (JRC), Ispra, Italy.
PLoS One. 2022 Jul 22;17(7):e0271969. doi: 10.1371/journal.pone.0271969. eCollection 2022.
Benford's Law defines a statistical distribution for the first and higher order digits in many datasets. Under very general condition, numbers are expected to naturally conform to the theorized digits pattern. On the other side, any deviation from the Benford distribution could identify an exogenous modification of the expected pattern, due to data manipulation or even fraud. Many statistical tests are available for assessing the Benford conformity of a sample. However, in some practical applications, the limited number of data to analyze may raise questions concerning their reliability. The first aim of this article is then to analyze and compare the behavior of Benford conformity testing procedures applied to very small samples through an extensive Monte Carlo experiment. Simulations will consider a thorough choice of compliance tests and a very heterogeneous selection of alternative distributions. Secondly, we will use the simulation results for defining a new testing procedure, based on the combination of three tests, that guarantees suitable levels of power in each alternative scenario. Finally, a practical application is provided, demonstrating how a sounding testing Benford compliance test for very small samples is important and profitable in anti-fraud investigations.
本福德定律定义了许多数据集首位和更高阶数字的统计分布。在非常一般的条件下，数字应该自然符合理论上的数字模式。另一方面，任何与本福德分布的偏差都可能表明预期模式发生了外部修改，这可能是由于数据操纵甚至欺诈。有许多统计检验可用于评估样本的本福德一致性。然而，在某些实际应用中，可用于分析的数据数量有限可能会引发对其可靠性的质疑。本文的首要目标是通过广泛的蒙特卡罗实验分析和比较应用于非常小样本的本福德一致性检验程序的行为。模拟将考虑全面的一致性检验选择和非常异构的替代分布选择。其次，我们将使用模拟结果定义一种新的检验程序，该程序基于三个检验的组合，可在每种替代情况下保证适当的功效水平。最后，提供了一个实际应用案例，演示了对非常小的样本进行稳健的本福德一致性检验在反欺诈调查中的重要性和收益。
