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

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  • Wójcik, Michał Ryszard

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.

Suggested Citation

  • Wójcik, Michał Ryszard, 2013. "How fast increasing powers of a continuous random variable converge to Benford’s law," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2688-2692.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2688-2692
    DOI: 10.1016/j.spl.2013.09.003
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    References listed on IDEAS

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    1. Lolbert, Tamás, 2008. "On the non-existence of a general Benford's law," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 103-106, March.
    2. repec:cai:poeine:pope_204_0753 is not listed on IDEAS
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