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Teoriya Veroyatnostei i ee Primeneniya, 1983, Volume 28, Issue 3, Pages 565–569 (Mi tvp2199)  

This article is cited in 22 scientific papers (total in 22 papers)

Short Communications

A lower bound for the convergence rate in the central limit theorem

V. K. Matskyavichyus

Moscow
Abstract: For every sequence of nonnegative numbers $\varphi(n)\to 0$, $n\to\infty$ there exists a sequence of independent identically distributed random variables $X_1,X_2,\dots$ such that $\mathbf EX_1=0$, $\mathbf DX_1=1$ and for $n\ge n1$
$$ \sup_x|\mathbf P\{n^{-1/2}(X_1+\dots+X_n)<x\}-\Phi(x)|\ge\varphi(n). $$
The distribution of $X_1$ has the form
$$ \mathbf P\{X_1<x\}=\sum_{k=1}^\infty\lambda_k\Phi(x/\sigma_k); $$
$\lambda_k$, $\sigma_k$ and $n_1$ are explicit functions of $\{\varphi(n)\}_{n=1}^\infty$.
Received: 28.12.1982
English version:
Theory of Probability and its Applications, 1984, Volume 28, Issue 3, Pages 596–601
DOI: https://doi.org/10.1137/1128054
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. K. Matskyavichyus, “A lower bound for the convergence rate in the central limit theorem”, Teor. Veroyatnost. i Primenen., 28:3 (1983), 565–569; Theory Probab. Appl., 28:3 (1984), 596–601
Citation in format AMSBIB
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\by V.~K.~Matskyavichyus
\paper A~lower bound for the convergence rate in the central limit theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1983
\vol 28
\issue 3
\pages 565--569
\mathnet{http://mi.mathnet.ru/tvp2199}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=716313}
\zmath{https://zbmath.org/?q=an:0543.60027|0511.60024}
\transl
\jour Theory Probab. Appl.
\yr 1984
\vol 28
\issue 3
\pages 596--601
\crossref{https://doi.org/10.1137/1128054}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1984SY24800011}
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  • https://www.mathnet.ru/eng/tvp2199
  • https://www.mathnet.ru/eng/tvp/v28/i3/p565
    Addendum
    This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
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