论文标题
傅立叶分析和本福德随机变量
Fourier Analysis and Benford Random Variables
论文作者
论文摘要
本文有几个主要目的。中心目的是描述正随机变量的“本福德分析”，并总结了对本福德随机变量基础依赖性的研究结果。用于得出这些结果的主要工具是傅立叶系列和傅立叶变换，本文的第二个主要目的是介绍有关这些工具的介绍性博览会。我写这篇论文的动机是双重的。首先，我认为本福德随机变量的理论和对正随机变量的Benford分析很有趣，值得一提。其次，我认为本福德分析提供了傅立叶系列和变换的实用性的绝妙说明，并揭示了系列和转换之间的某些互连，这些互连从这些主题引入的通常方式中并不明显。
This paper has several major purposes. The central purpose is to describe the "Benford analysis" of a positive random variable and to summarize some results from investigations into base dependence of Benford random variables. The principal tools used to derive these results are Fourier series and Fourier transforms, and a second major purpose of this paper is to present an introductory exposition about these tools. My motivation for writing this paper is twofold. First, I think the theory of Benford random variables and the Benford analysis of a positive random variable are interesting and deserve to be better known. Second, I think that Benford analysis provides a really excellent illustration of the utility of Fourier series and transforms, and reveals certain interconnections between series and transforms that are not obvious from the usual way these subjects are introduced.
