Benford's law: A theoretical explanation for base 2

TL;DR

This paper offers a theoretical derivation of Benford's law specifically for base 2, using recursive relations and analytical solutions to explain the distribution of leading digits.

Contribution

It provides the first analytical proof of Benford's law for base 2, complementing previous numerical and heuristic approaches.

Findings

Recursive relation converges to Benford's law

Numerical solutions match theoretical predictions

Analytical derivation confirms law for base 2

Abstract

In this paper, we present a possible theoretical explanation for benford's law. We develop a recursive relation between the probabilities, using simple intuitive ideas. We first use numerical solutions of this recursion and verify that the solutions converge to the benford's law. Finally we solve the recursion analytically to yeild the benford's law for base 2.