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Article

Base Dependence of Benford Random Variables

Benford Applied Math, Salem, OR 97304, USA
Academic Editors: Claudio Lupi, Roy Cerqueti and Marcel Ausloos
Stats 2021, 4(3), 578-594; https://doi.org/10.3390/stats4030034
Received: 4 May 2021 / Revised: 5 June 2021 / Accepted: 7 June 2021 / Published: 2 July 2021
(This article belongs to the Special Issue Benford's Law(s) and Applications)
A random variable X that is base b Benford will not in general be base c Benford when cb. 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. View Full-Text
Keywords: significand function; Benford random variable; base b first digit law; Benford spectrum; Benford analysis; seed functions; base-invariant significant digits significand function; Benford random variable; base b first digit law; Benford spectrum; Benford analysis; seed functions; base-invariant significant digits
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Benford, F. Base Dependence of Benford Random Variables. Stats 2021, 4, 578-594. https://doi.org/10.3390/stats4030034

AMA Style

Benford F. Base Dependence of Benford Random Variables. Stats. 2021; 4(3):578-594. https://doi.org/10.3390/stats4030034

Chicago/Turabian Style

Benford, Frank. 2021. "Base Dependence of Benford Random Variables" Stats 4, no. 3: 578-594. https://doi.org/10.3390/stats4030034

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