Fundamental Flaws in Feller’s Classical Derivation of Benford’s Law
 Citation data:

Mathematics ArXiv
 Publication Year:
 2010

 Bepress 163

 Bepress 62
 Repository URL:
 http://digitalcommons.calpoly.edu/rgp_rsr/77
 Author(s):
article description
Feller’s classic text An Introduction to Probability Theory and its Applications contains a derivation of the well known significantdigit 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 largespread 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.