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Teor. Veroyatnost. i Primenen., 1960, Volume 5, Issue 1, Pages 125–128 (Mi tvp4818)  

This article is cited in 7 scientific papers (total in 7 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
$$\lim_{n\to\infty}\inf_{\substack{-\infty<a<\infty\&lt;0<\sigma<\infty}}\sup_x\sqrt n|F_n(x)-\Phi(\frac{x-a}\sigma)|\leq\frac1{\sqrt{2\pi}}\rho_3,$$
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.

Full text: PDF file (395 kB)

English version:
Theory of Probability and its Applications, 1960, 5:1, 114–117

Received: 10.12.1959

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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    Citing articles on Google Scholar: Russian citations, English citations
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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. I”, Theory Probab. Appl., 50:2 (2006), 298–310  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. I. G. Shevtsova, “Sharpening of the upper-estimate of the absolute constant in the Berry–Esseen inequality”, Theory Probab. Appl., 51:3 (2007), 549–553  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. O. Gaponova, I. G. Shevtsova, “Asimptoticheskie otsenki absolyutnoi postoyannoi v neravenstve Berri–Esseena dlya raspredelenii, ne imeyuschikh tretego momenta”, Inform. i ee primen., 3:4 (2009), 41–56  mathnet
    4. V. Yu. Korolev, I. G. Shevtsova, “An upper estimate for the absolute constant in the Berry–Esseen inequality”, Theory Probab. Appl., 54:4 (2010), 638–658  mathnet  crossref  crossref  mathscinet  isi
    5. I. S. Tyurin, “On the convergence rate in Lyapunov's theorem”, Theory Probab. Appl., 55:2 (2011), 253–270  mathnet  crossref  crossref  mathscinet  isi
    6. I. G. Shevtsova, “On the asymptotically exact constants in the Berry–Esseen–Katz inequality”, Theory Probab. Appl., 55:2 (2011), 225–252  mathnet  crossref  crossref  mathscinet  isi
    7. Theory Probab. Appl., 57:2 (2013), 323–325  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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