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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 366–371 (Mi tvp113)  

This article is cited in 2 scientific papers (total in 2 papers)

Short Communications

H.F.D. ($H$-function distribution) and the Benford law. I

A. A. Kulikovaa, Yu. V. Prokhorovb, V. I. Khokhlovb

a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper notes a connection among a wide class of the so-called $HF$-random variables, approximately uniform distributions, and Benford's law. This connection is considered in detail with the help of examples of random variables having gamma-distribution. Let $Y$ be a random variable having gamma-distribution with parameter $\alpha$. It is proved that the distribution of a fractional part of the logarithm of $Y$ with respect to any base larger than 1 converges to the uniform distribution on the interval $[0,1]$ for $\alpha\to0$. This implies that the probability distribution of the first significant digit of $Y$ for small $\alpha$ can be approximately described by Benford's law. The order of the approximation is illustrated by tables.

Keywords: $H$-function distribution, gamma-distributions, Benford law, Poisson summation formula.

DOI: https://doi.org/10.4213/tvp113

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English version:
Theory of Probability and its Applications, 2006, 50:2, 311–315

Bibliographic databases:

Received: 13.05.2004

Citation: A. A. Kulikova, Yu. V. Prokhorov, V. I. Khokhlov, “H.F.D. ($H$-function distribution) and the Benford law. I”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 366–371; Theory Probab. Appl., 50:2 (2006), 311–315

Citation in format AMSBIB
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\by A.~A.~Kulikova, Yu.~V.~Prokhorov, V.~I.~Khokhlov
\paper H.F.D.\ ($H$-function distribution) and the Benford law.~I
\jour Teor. Veroyatnost. i Primenen.
\yr 2005
\vol 50
\issue 2
\pages 366--371
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\crossref{https://doi.org/10.4213/tvp113}
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\zmath{https://zbmath.org/?q=an:1098.60021}
\elib{http://elibrary.ru/item.asp?id=9153128}
\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 2
\pages 311--315
\crossref{https://doi.org/10.1137/S0040585X97981706}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000238760000011}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Ya. Kuznetsova, “On mixing of unimodal distributions”, Theory Probab. Appl., 51:3 (2007), 535–536  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. O. V. Viskov, V. I. Khokhlov, “Four areas of Yu. V. Prokhorov's studies and their perspectives”, Theory Probab. Appl., 60:2 (2016), 336–342  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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