THE CHEBYSHEV–EDGEWORTH CORRECTION IN THE CENTRAL LIMIT THEOREM FOR INTEGER-VALUED INDEPENDENT SUMMANDS

S. G. Bobkov, V. V. Ulyanov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)537-549
Number of pages13
JournalTheory of Probability and its Applications
Volume66
Issue number4
DOIs
StatePublished - 2022

Bibliographical note

Funding Information:
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. Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 66 (2021), pp. 676–692.

Funding Information:
∗Received by the editors May 31, 2021. 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. Originally published in the Russian journal Teoriya Veroyatnostei i ee Primeneniya, 66 (2021), pp. 676–692. https://doi.org/10.1137/S0040585X97T990605 †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 USA (bobkov@math. umn.edu).

Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics Translated from Russian Journal.

Keywords

  • central limit theorem
  • integer-valued random variables
  • the Chebyshev–Edgeworth correction

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