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

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 est...

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Bibliographic Details
Published inStatistics & probability letters Vol. 83; no. 12; pp. 2688 - 2692
Main Author Wójcik, Michał Ryszard
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2013
Subjects
Benford’s law
Fourier coefficients
Mantissa distribution
Significand distribution
Uniform distribution modulo 1
Uniform distribution modulo 1
Mantissa distribution
Significand distribution
60-02
Benford’s law
Fourier coefficients
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2013.09.003