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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 2, Pages 353–366
DOI: https://doi.org/10.4213/tvp112 (Mi tvp112) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Short Communications

On the accuracy of the normal approximation. I

V. Yu. Korolev, I. G. Shevtsova

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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DOI: https://doi.org/10.4213/tvp112
Abstract: Presented are practically applicable estimates of the accuracy of the normal approximation for the distributions of sums of independent identically distributed absolutely continuous random variables with finite moments of order $2+\delta$, $0<\delta\le 1$. The right-hand side of the estimate is the sum of two summands, the first being the Lyapunov fraction with the absolute constant arbitrarily close to the asymptotically exact one, whereas the second summand decreases exponentially fast.
Keywords: central limit theorem, normal approximation, Berry–Esseen inequality, convergence rate estimate, asymptotically exact constant.
Received: 22.11.2004
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 2, Pages 298–310
DOI: https://doi.org/10.1137/S0040585X9798168X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. I”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 353–366; Theory Probab. Appl., 50:2 (2006), 298–310
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i2/p353
    Cycle of papers
    This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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