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Teoriya Veroyatnostei i ee Primeneniya, 1960, Volume 5, Issue 1, Pages 125–128 (Mi tvp4818)  

This article is cited in 17 scientific papers (total in 17 papers)

Short Communications

A Remark on Esseen's Paper “A Moment Inequality with an Application to the Central Limit Theorem”

B. A. Rogozin

Moscow
Abstract: It is proved that
$$\lim_{n\to\infty}\inf_{\substack{-\infty<a<\infty\\<0<\sigma<\infty}}\sup_x\sqrt n\left|F_n(x)-\Phi\left(\frac{x-a}\sigma\right)\right|\leq\frac1{\sqrt{2\pi}}\rho_3,$$
where $\Phi (x)$ is a normal distribution function and $F_n (x)$ is a distribution function of a normed sum of independent identically distributed random variables. The constant $(2\pi)^{-1/2}$ cannot be improved.
Received: 10.12.1959
English version:
Theory of Probability and its Applications, 1960, Volume 5, Issue 1, Pages 114–117
DOI: https://doi.org/10.1137/1105010
Document Type: Article
Language: Russian
Citation: B. A. Rogozin, “A Remark on Esseen's Paper “A Moment Inequality with an Application to the Central Limit Theorem””, Teor. Veroyatnost. i Primenen., 5:1 (1960), 125–128; Theory Probab. Appl., 5:1 (1960), 114–117
Citation in format AMSBIB
\Bibitem{Rog60}
\by B.~A.~Rogozin
\paper A Remark on Esseen's Paper ``A Moment Inequality with an Application to the Central Limit Theorem''
\jour Teor. Veroyatnost. i Primenen.
\yr 1960
\vol 5
\issue 1
\pages 125--128
\mathnet{http://mi.mathnet.ru/tvp4818}
\transl
\jour Theory Probab. Appl.
\yr 1960
\vol 5
\issue 1
\pages 114--117
\crossref{https://doi.org/10.1137/1105010}
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  • This publication is cited in the following 17 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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