arXiv subjects

Frank Benford

Publications and source records attributed to Frank Benford.

2 recordsLinked to original sources

arXiv2021

Base Dependence of Benford Random Variables

A random variable X that is base b Benford will not in general be base c Benford when c is not equal to b. This paper builds on two of my earlier papers and is an attempt to cast some light on the issue of base dependence. Following some introductory material, the "Benford spectrum" of a positive random variable is introduced and known analytic results about Benford spectra are summarized. Some standard machinery for a "Benford analysis" is introduced and combined with my method of "seed functions" to yield tools to analyze the base c Benford properties of a base b Benford random variable. Examples are generated by applying these general methods to several families of Benford random variables. Berger and Hill's concept of "base-invariant significant digits" is discussed. Some potential extensions are sketched.

math.GM↗

arXiv2020

Fourier Analysis and Benford Random Variables

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.

stat.OT↗