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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 1, Pages 81–97
DOI: https://doi.org/10.4213/tvp159 (Mi tvp159) 		 
Compactness and the concentration functions of the convolutions of a distribution

B. A. Rogozin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
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DOI: https://doi.org/10.4213/tvp159
Abstract: A relationship is investigated between the compactness conditions of the distributions of sums of independent identically distributed random variables under an appropriate scaling and the behavior of the sequence of concentration functions of these sums.
Keywords: independent identically distributed random variables, sum, convolution, median, quantile, compactness, finite noncompactness, Levy concentration function, censored variance, majorizied varying function, unimodal distribution.
Received: 15.06.2001
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 1, Pages 99–111
DOI: https://doi.org/10.1137/S0040585X97981603
Bibliographic databases:
Language: Russian
Citation: B. A. Rogozin, “Compactness and the concentration functions of the convolutions of a distribution”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 81–97; Theory Probab. Appl., 50:1 (2006), 99–111
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i1/p81
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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