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1. Equipartitions and a Distribution for Numbers: A Statistical Model for Benford's Law

Author

Steven J. Miller, Frederick W. Strauch, and Joseph R. Iafrate

Subjects
Principle of maximum entropy, FOS: Physical sciences, Probability and statistics, Statistical model, Upper and lower bounds, Conserved quantity, Power law, Combinatorics, Benford's law, Probability theory, Physics - Data Analysis, Statistics and Probability, Statistical physics, Data Analysis, Statistics and Probability (physics.data-an), Mathematics
Abstract

A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to the distribution of fragments. The resulting power law directly leads to Benford's law for the first digits of the parts.

Published
2015
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