This article is cited in 5 papers

On the real accuracy of approximation in the central limit theorem

V. V. Senatov

Moscow State University, Moscow, Russia

Abstract: We consider various approximations in the central limit theorem for distributions of sums of independent random variables. We study how many summands in the normalized sums guarantee the precision $10^{-3}$ for these approximations. It turns out that for the same distribution but different approximations this number varies from hundreds of thousands to a few tens.

Keywords: central limit theorem, accuracy of approximation, asymptotic expansions.

UDC: 519.21

Received: 06.01.2011

 English version: Siberian Mathematical Journal, 2011, 52:4, 727–746

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