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Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law
Mathematics ArXiv
  • Arno Berger, University of Alberta
  • Theodore P Hill, Georgia Institute of Technology - Main Campus
Publication Date
5-14-2010
Abstract

Feller’s classic text An Introduction to Probability Theory and its Applications contains a derivation of the well known significant-digit law called Benford’s law. More specifically, Fellergives a sufficient condition (“large spread”) for a random variable X to be approximately Benford distributed, that is, for log10X to be approximately uniformly distributed moduloone. This note shows that the large-spread derivation, which continues to be widely cited and used, contains serious basic errors. Concrete examples and a new inequality clearly demonstratethat larges pread (or large spread on a logarithmic scale) does not imply that a random variable is approximately Benford distributed, for any reasonable definition of “spread” or measure of dispersion.

Citation Information
Arno Berger and Theodore P Hill. "Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law" Mathematics ArXiv (2010)
Available at: http://works.bepress.com/tphill/75/