How fast increasing powers of a continuous random variable converge to Benford's law

TL;DR

This paper introduces an elementary method to estimate the rate at which powers of a continuous random variable converge to Benford's law, improving upon Fourier analysis especially for uniform distributions.

Contribution

It presents a simpler, more effective approach to estimate convergence rates to Benford's law for powers of continuous random variables, focusing on the uniform case.

Findings

Elementary method provides better convergence estimates

Simplifies analysis compared to Fourier techniques

Effective for uniformly distributed variables

Abstract

It is known that increasing powers of a continuous random variable converge in distribution to Benford's law as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an elementary method, which is easier to apply and provides a better estimation in the widely studied case of a uniformly distributed random variable.