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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 1, Pages 193–198
DOI: https://doi.org/10.4213/tvp5483 (Mi tvp5483) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

On Senatov moments in asymptotic expansions in the central limit theorem

V. N. Soboleva, A. E. Kondratenkob

a Russian State University of Trade and Economics, Moscow
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (306 kB) Citations (3)
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DOI: https://doi.org/10.4213/tvp5483
Abstract: Representations are put forward for the moments and the truncated Senatov quasi-moments of normalized sums of random variables (r.v.'s) in terms of the Senatov moments of the original distribution. These representations make possible the direct transition from new asymptotic expansions in the central limit theorem to Gram–Charlier type expansions and are applied in the new proof of formulas for the convergence rate of these moments.
Keywords: central limit theorem, asymptotic expansions, Edgeworth–Cramér expansions, Gram–Charlier expansions, Senatov moments, Senatov quasi-moments.
Received: 20.02.2021
Accepted: 08.07.2021
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 1, Pages 154–157
DOI: https://doi.org/10.1137/S0040585X97T990824
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. N. Sobolev, A. E. Kondratenko, “On Senatov moments in asymptotic expansions in the central limit theorem”, Teor. Veroyatnost. i Primenen., 67:1 (2022), 193–198; Theory Probab. Appl., 67:1 (2022), 154–157
Citation in format AMSBIB
\Bibitem{SobCon22}
\by V.~N.~Sobolev, A.~E.~Kondratenko
\paper On Senatov moments in asymptotic expansions in the central limit theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 1
\pages 193--198
\mathnet{http://mi.mathnet.ru/tvp5483}
\crossref{https://doi.org/10.4213/tvp5483}
\zmath{https://zbmath.org/?q=an:7523566}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 1
\pages 154--157
\crossref{https://doi.org/10.1137/S0040585X97T990824}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85130996561}
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  • https://www.mathnet.ru/eng/tvp/v67/i1/p193
    • This publication is cited in the following 3 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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