Abstract

Benford’s law defines a probability distribution for patterns of significant digits in real numbers. When the law is expected to hold for genuine observations, deviation from it can be taken as evidence of possible data manipulation. We derive results on a transform of the significand function that provide motivation for new tests of conformance to Benford’s law exploiting its sum-invariance characterization. We also study the connection between sum invariance of the first digit and the corresponding marginal probability distribution. We approximate the exact distribution of the new test statistics through a computationally efficient Monte Carlo algorithm. We investigate the power of our tests under different alternatives and we point out relevant situations in which they are clearly preferable to the available procedures. Finally, we show the application potential of our approach in the context of fraud detection in international trade.

摘要

本福德定律定义了实数中有效数字模式的概率分布。当预期法律适用于真实观察时，偏离它可以被视为可能的数据操纵的证据。我们推导出有效数函数变换的结果，该函数为利用其和不变性特征进行新的本福德定律一致性测试提供了动力。我们还研究了第一个数字的和不变性与相应的边际概率分布之间的联系。我们通过计算高效的蒙特卡罗算法来近似新测试统计数据的确切分布。我们调查了我们的测试在不同替代方案下的功效，并指出了它们明显优于可用程序的相关情况。最后，