Wang Luohan, Ma Bo-Qiang
School of Physics, Peking University, Beijing 100871, China.
Center for High Energy Physics, Peking University, Beijing 100871, China.
Fundam Res. 2023 Jan 13;4(4):841-844. doi: 10.1016/j.fmre.2023.01.002. eCollection 2024 Jul.
This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and elegant, accessible to anyone with basic knowledge of calculus, revealing that the law originates from the basic property of human number system. The criterion can bring great convenience to the field of fraud detection.
本文给出了著名的本福特定律在分布具有黎曼可积概率密度函数时的一个简洁证明，并提供了一个判断分布是否服从该定律的准则。该证明直观且优美，任何具有微积分基础知识的人都能理解，揭示了该定律源于人类数字系统的基本性质。该准则可为欺诈检测领域带来极大便利。
