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

S. G. Bobkov; V. V. Ulyanov

doi:10.1137/S0040585X97T990605

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

S. G. Bobkov, V. V. Ulyanov

Mathematics

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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 language	English (US)
Pages (from-to)	537-549
Number of pages	13
Journal	Theory of Probability and its Applications
Volume	66
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97T990605
State	Published - 2022

Bibliographical note

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

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Keywords

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