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

Michał Ryszard Wójcik

Statistics & Probability Letters, 2013, vol. 83, issue 12, 2688-2692

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.

Keywords: Benford’s law; Uniform distribution modulo 1; Mantissa distribution; Significand distribution; Fourier coefficients (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2013.09.003

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