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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 353–366 (Mi tvp112)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.4213/tvp112

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English version:
Theory of Probability and its Applications, 2006, 50:2, 298–310

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Received: 22.11.2004

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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\jour Teor. Veroyatnost. i Primenen.
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\pages 353--366
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\transl
\jour Theory Probab. Appl.
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    This publication is cited in the following articles:
    1. V. Yu. Korolev, I. G. Shevtsova, “On the accuracy of the normal approximation. II”, Theory Probab. Appl., 50:3 (2006), 473–482  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Memnonov B.P., “Testirovanie generatorov sluchainykh chisel s pomoschyu chislennogo modelirovaniya tochno reshaemoi zadachi”, Vestn. Sankt-Peterburgskogo un-ta. Ser. 1: Matem., Mekh., Astronom., 2009, no. 1, 23–32  mathscinet  zmath
    3. Dasgupta R., “Quality index and Mahalanobis $D^2$ statistic”, Advances in multivariate statistical methods, Stat. Sci. Interdiscip. Res., 4, World Sci. Publ., Hackensack, NJ, 2009, 367–382  crossref  mathscinet  isi
    4. I. S. Tyurin, “On the convergence rate in Lyapunov's theorem”, Theory Probab. Appl., 55:2 (2011), 253–270  mathnet  crossref  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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