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Teoriya Veroyatnostei i ee Primeneniya, 1960, Volume 5, Issue 1, Pages 125–128
(Mi tvp4818)
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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
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
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https://www.mathnet.ru/eng/tvp4818 https://www.mathnet.ru/eng/tvp/v5/i1/p125
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Abstract page: | 198 | Full-text PDF : | 87 |
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