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Teoriya Veroyatnostei i ee Primeneniya, 2019, Volume 64, Issue 3, Pages 590–598
DOI: https://doi.org/10.4213/tvp5249 (Mi tvp5249) 		 
Short Communications

On optimal upper bound on the tail probability for sums of random variables

I. Pinelis

Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, USA
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DOI: https://doi.org/10.4213/tvp5249
Abstract: Let $s$ be any given real number. An explicit construction is provided of random variables (r.v.'s) $X$ and $Y$ such that $\sup\mathbf{P}(X+Y\ge s)$ is attained, where the $\sup$ is taken over all r.v.'s $X$ and $Y$ with given distributions.
Keywords: sums of random variables, tails of distributions, probability inequalities, extremal problems.
Received: 12.10.2017
Revised: 23.03.2018
Accepted: 05.04.2018
English version:
Theory of Probability and its Applications, 2019, Volume 64, Issue 3, Pages 474–480
DOI: https://doi.org/10.1137/S0040585X97T989635
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. Pinelis, “On optimal upper bound on the tail probability for sums of random variables”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 590–598; Theory Probab. Appl., 64:3 (2019), 474–480
Citation in format AMSBIB
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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