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Teoriya Veroyatnostei i ee Primeneniya, 2004, Volume 49, Issue 1, Pages 178–184
DOI: https://doi.org/10.4213/tvp244 (Mi tvp244) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

Completely asymmetric stable laws and Benford's law

A. A. Kulikovaa, Yu. V. Prokhorovb

a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (670 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp244
Abstract: Let $Y$ be a random variable with a completely asymmetric stable law and parameter $\alpha$. This paper proves that a probability 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 $\alpha\to 0$. This implies that the distribution of the first significant digit of $Y$ for small $\alpha$ can be approximately described by the Benford law.
Keywords: completely asymmetric stable law, Benford law, Poisson summation formula.
Received: 20.01.2004
English version:
Theory of Probability and its Applications, 2005, Volume 49, Issue 1, Pages 163–169
DOI: https://doi.org/10.1137/S0040585X97980944
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Kulikova, Yu. V. Prokhorov, “Completely asymmetric stable laws and Benford's law”, Teor. Veroyatnost. i Primenen., 49:1 (2004), 178–184; Theory Probab. Appl., 49:1 (2005), 163–169
Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 2005
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\issue 1
\pages 163--169
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  • https://www.mathnet.ru/eng/tvp/v49/i1/p178
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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