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Berger, A and Hill, TP (2010)

Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law

University of Alberta preprint; posted on math arXiv 14May 2010.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

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, Feller gives a sufficient condition (“large spread”) for a random variable X to be approxi- mately Benford distributed, that is, for log10 X to be approximately uniformly distributed modulo one. 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 demonstrate that large spread (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.

Not available at this time.

Reference Type: Preprint

Subject Area(s): Statistics