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Teoriya Veroyatnostei i ee Primeneniya, 2021, Volume 66, Issue 4, Pages 676–692
DOI: https://doi.org/10.4213/tvp5504 (Mi tvp5504) 		 
The Chebyshev–Edgeworth correction in the central limit theorem for integer-valued independent summands

S. G. Bobkovab, V. V. Ulyanovcb

a School of Mathematics, University of Minnesota, Minneapolis, USA
b National Research University "Higher School of Economics", Moscow
c Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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DOI: https://doi.org/10.4213/tvp5504
Abstract: We give a short overview of the results related to the refined forms of the central limit theorem, with a focus on independent integer-valued random variables (r.v.'s). In the independent and non-identically distributed (non-i.i.d.) case, an approximation is then developed for the distribution of the sum by means of the Chebyshev–Edgeworth correction containing the moments of the third order.
Keywords: central limit theorem, the Chebyshev–Edgeworth correction, integer-valued random variables.
Funding agency Grant number
National Science Foundation DMS-1855575
Lomonosov Moscow State University
HSE Basic Research Program
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1621
This research was carried out within the framework of the Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, and HSE University Basic Research Programs. The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement 075-15-2019-1621. The research of S. Bobkov was partially supported by NSF grant DMS-1855575.
Received: 31.05.2021
Accepted: 06.07.2021
English version:
Theory of Probability and its Applications, 2022, Volume 66, Issue 4, Pages 537–549
DOI: https://doi.org/10.1137/S0040585X97T990605
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. G. Bobkov, V. V. Ulyanov, “The Chebyshev–Edgeworth correction in the central limit theorem for integer-valued independent summands”, Teor. Veroyatnost. i Primenen., 66:4 (2021), 676–692; Theory Probab. Appl., 66:4 (2022), 537–549
Citation in format AMSBIB
\Bibitem{BobUly21}
\by S.~G.~Bobkov, V.~V.~Ulyanov
\paper The Chebyshev--Edgeworth correction in the central limit theorem for integer-valued independent summands
\jour Teor. Veroyatnost. i Primenen.
\yr 2021
\vol 66
\issue 4
\pages 676--692
\mathnet{http://mi.mathnet.ru/tvp5504}
\crossref{https://doi.org/10.4213/tvp5504}
\zmath{https://zbmath.org/?q=an:7481225}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 66
\issue 4
\pages 537--549
\crossref{https://doi.org/10.1137/S0040585X97T990605}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129608204}
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