Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Base Dependence of Benford Random Variables

Version 1 : Received: 4 May 2021 / Approved: 6 May 2021 / Online: 6 May 2021 (15:21:24 CEST)

A peer-reviewed article of this Preprint also exists.

Benford, F. Base Dependence of Benford Random Variables. Stats 2021, 4, 578-594. Benford, F. Base Dependence of Benford Random Variables. Stats 2021, 4, 578-594.


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.


significand function; Benford random variables; base b first digit law; Benford spectrum; Benford analysis; see functions; base-invariant significant digits


Computer Science and Mathematics, Probability and Statistics

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 0
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.