Entropy Principle in Direct Derivation of Benford's Law
Discrete Mathematics
2009-07-28 v2 Data Analysis, Statistics and Probability
Abstract
The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although it attracts considerable attention, there is no a priori probabilistic criterion when a data set should or should not obey the law. Here a general criterion is suggested, namely that any file of digits in the Shannon limit (namely, having maximum entropy) has a Benford's law distribution of digits.
Keywords
Cite
@article{arxiv.0901.3047,
title = {Entropy Principle in Direct Derivation of Benford's Law},
author = {Oded Kafri},
journal= {arXiv preprint arXiv:0901.3047},
year = {2009}
}