本福特定律的数学基础
The Mathematics of Benford's Law -- A Primer
摘要：
本文提供了一个简明扼要的概述本福德定律的主要数学理论的形式访问的科学家和学生谁有第一次课程微积分和概率。本书的主要目的之一是帮助那些对应用本福德定律感兴趣的研究人员，并需要了解一些基本原理，以澄清什么时候本福德定律会出现在真实数据中，什么时候不会出现。第二个主要目标读者是统计学或数学专业的学生，他们对这一令人惊讶和强大的现象背后的数学感到好奇，并且可能希望更深入地研究该主题。本福德定律背后的基本原理的调查包括许多基本的例子和定理，但不包括定理的证明或最一般的陈述;相反，它提供了精确的参考。
英文摘要：
This article provides a concise overview of the main mathematical theory of Benford's law in a form accessible to scientists and students who have had first courses in calculus and probability. In particular, one of the main objectives here is to aid researchers who are interested in applying Benford's law, and need to understand general principles clarifying when to expect the appearance of Benford's law in real-life data and when not to expect it. A second main target audience is students of statistics or mathematics, at all levels, who are curious about the mathematics underlying this surprising and robust phenomenon, and may wish to delve more deeply into the subject. This survey of the fundamental principles behind Benford's law includes many basic examples and theorems, but does not include the proofs or the most general statements of the theorems; rather it provides precise references where both may be found.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
