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Teoriya Veroyatnostei i ee Primeneniya, 1996, Volume 41, Issue 3, Pages 561–577
DOI: https://doi.org/10.4213/tvp3137 (Mi tvp3137) 		 
This article is cited in 7 scientific papers (total in 7 papers)

An estimate of the concentration function by the Esseen method

N. P. Salikhov

Essential Administration of Information Systems
Full-text PDF (779 kB) Citations (7)
DOI: https://doi.org/10.4213/tvp3137
Abstract: The paper deals with the Esseen method of obtaining upper estimates for the concentration function of a random variable $X$ in terms of the characteristic function of $X$. Some problems of the parametric optimization of such estimates are solved. Applications are described to the estimation of the probabilities of large deviations of the sums of identically distributed random variables.
Keywords: concentration function, characteristic function, probabilities of large deviations, Poisson summation formula, Esseen inequality, Euler numbers.
Received: 02.08.1993
English version:
Theory of Probability and its Applications, 1997, Volume 41, Issue 3, Pages 504–518
DOI: https://doi.org/10.1137/S0040585X9797523X
Bibliographic databases:
Language: Russian
Citation: N. P. Salikhov, “An estimate of the concentration function by the Esseen method”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 561–577; Theory Probab. Appl., 41:3 (1997), 504–518
Citation in format AMSBIB
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\by N.~P.~Salikhov
\paper An estimate of the concentration function by the Esseen method
\jour Teor. Veroyatnost. i Primenen.
\yr 1996
\vol 41
\issue 3
\pages 561--577
\mathnet{http://mi.mathnet.ru/tvp3137}
\crossref{https://doi.org/10.4213/tvp3137}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1450074}
\zmath{https://zbmath.org/?q=an:0883.60020}
\transl
\jour Theory Probab. Appl.
\yr 1997
\vol 41
\issue 3
\pages 504--518
\crossref{https://doi.org/10.1137/S0040585X9797523X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1997XZ71800007}
Linking options:
  • https://www.mathnet.ru/eng/tvp3137
  • https://doi.org/10.4213/tvp3137
  • https://www.mathnet.ru/eng/tvp/v41/i3/p561
    • This publication is cited in the following 7 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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