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

TL;DR

This paper develops a statistical model based on maximum entropy and partition theory to explain Benford's law, showing how fragment distributions follow a power law that predicts the distribution of leading digits.

Contribution

It introduces a novel model linking fragmentation processes with Benford's law through entropy maximization and partition bounds.

Findings

Derives bounds for restricted partitioning problems.

Shows power law distribution leads to Benford's law.

Provides a theoretical foundation for Benford's law in fragmentation processes.

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.