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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 2, Pages 396–397
DOI: https://doi.org/10.4213/tvp4513 (Mi tvp4513) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

On one identity for distribution of sums of independent random variables

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
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DOI: https://doi.org/10.4213/tvp4513
Abstract: In a 1957 paper F. Spitzer published, among other things, one estimate of the distribution function of sums of independent symmetric random variables with a common absolutely continuous distribution. This estimation was constructed with the help of one identity for the distribution of a sum of the above-mentioned random variables, the proof of which was not given. In this paper we prove the Spitzer identity for any independent random variables, and by using it we construct an estimate of the distribution of a sum of independent identically distributed random variables. The Spitzer estimate can be derived as a particular case of the proposed estimation.
Keywords: independent random variables; characteristic function; inverse formula.
Received: 05.07.2012
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 2, Pages 329–331
DOI: https://doi.org/10.1137/S0040585X97986576
Bibliographic databases:
Document Type: Article
MSC: 60
Language: Russian
Citation: V. M. Kruglov, “On one identity for distribution of sums of independent random variables”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 396–397; Theory Probab. Appl., 58:2 (2014), 329–331
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v58/i2/p396
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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