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Teoriya Veroyatnostei i ee Primeneniya, 1961, Volume 6, Issue 1, Pages 103–105
(Mi tvp4753)
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This article is cited in 42 scientific papers (total in 42 papers)
Short Communications
On Evaluating the Concentration Functions
B. A. Rogozin Moscow
Abstract:
Let $\xi_1,\dots,\xi_n$ be independent random variables, $$Q_k\{l\}=\mathop{\sup}\limits_x\mathbf P\{x\leq\xi _k\leq x+l\},\\Q(L)=\mathop{\sup}\limits_x\mathbf P\{{x\leq\xi_1+\cdots+\xi_n\leq x+L}\},\quad
s=\sum\limits_{k+1}^n(1-Q_k(l)).$$
Theorem 1. If $L\ge l$, then $$Q(L)\leq\frac{CL}{l\sqrt s},$$ where $C$ is an absolute constant.
This is a refinement of the main theorem in [1].
Received: 18.02.1960
Citation:
B. A. Rogozin, “On Evaluating the Concentration Functions”, Teor. Veroyatnost. i Primenen., 6:1 (1961), 103–105; Theory Probab. Appl., 6:1 (1961), 94–97
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https://www.mathnet.ru/eng/tvp4753 https://www.mathnet.ru/eng/tvp/v6/i1/p103
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Abstract page: | 182 | Full-text PDF : | 95 |
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