RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Teor. Veroyatnost. i Primenen.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 1, Pages 178–184 (Mi tvp244)  

This article is cited in 3 scientific papers (total in 3 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

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.

DOI: https://doi.org/10.4213/tvp244

Full text: PDF file (670 kB)
References: PDF file   HTML file

English version:
Theory of Probability and its Applications, 2005, 49:1, 163–169

Bibliographic databases:

Received: 20.01.2004

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
\Bibitem{KulPro04}
\by A.~A.~Kulikova, Yu.~V.~Prokhorov
\paper Completely asymmetric stable laws and
Benford's law
\jour Teor. Veroyatnost. i Primenen.
\yr 2004
\vol 49
\issue 1
\pages 178--184
\mathnet{http://mi.mathnet.ru/tvp244}
\crossref{https://doi.org/10.4213/tvp244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2141338}
\zmath{https://zbmath.org/?q=an:1098.60024}
\transl
\jour Theory Probab. Appl.
\yr 2005
\vol 49
\issue 1
\pages 163--169
\crossref{https://doi.org/10.1137/S0040585X97980944}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000228185300013}


Linking options:
  • http://mi.mathnet.ru/eng/tvp244
  • https://doi.org/10.4213/tvp244
  • http://mi.mathnet.ru/eng/tvp/v49/i1/p178

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Kulikova, Yu. V. Prokhorov, V. I. Khokhlov, “H.F.D. ($H$-function distribution) and the Benford law. I”, Theory Probab. Appl., 50:2 (2006), 311–315  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. Ya. Kuznetsova, “On mixing of unimodal distributions”, Theory Probab. Appl., 51:3 (2007), 535–536  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. 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
    Number of views:
    This page:685
    Full text:76
    References:84

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019