Benford定律的简明证明

IF 6.2 3区综合性期刊 Q1 Multidisciplinary

Fundamental Research Pub Date : 2024-07-01 DOI:10.1016/j.fmre.2023.01.002

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引用次数: 0

摘要

本文简明扼要地证明了当分布具有黎曼可积分概率密度函数时的著名本福德定律，并提供了判断分布是否服从该定律的标准。证明直观而优雅，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制的基本属性。该标准可为欺诈检测领域带来极大的便利。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A concise proof of Benford’s law

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A concise proof of Benford’s law

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.

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