This article is cited in 5 papers

On the real accuracy of approximation in the central limit theorem. II

V. V. Senatov

Lomonosov Moscow State University, Moscow, Russia

Abstract: In the present article, we obtain new explicit estimates for accuracy of approximation in the central limit theorem (CLT). We construct these approximations with the use of asymptotic expansions. We compare the estimates with the real accuracy of approximation for a specific distribution. We also discuss the following question: Why the estimate from the Berry–Esseen theorem cannot catch even the order of proximity of distributions in the CLT?

Key words: central limit theorem, accuracy of approximation, asymptotic expansions, Berry–Esseen theorem.

UDC: 519.21

Received: 28.02.2016

DOI: 10.17377/mattrudy.2016.19.207

 English version: Siberian Advances in Mathematics, 2017, 27:2, 133–152

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