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 bette...

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Bibliographic Details
Published inarXiv.org
Main Author Wójcik, Michał Ryszard
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.07.2013
Subjects
Continuity (mathematics)
Convergence
Fourier analysis
Random variables
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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:2331-8422