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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 2, Pages 392–398
DOI: https://doi.org/10.4213/tvp292 (Mi tvp292) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

Normal and Poisson convergencies

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (924 kB) Citations (4)
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DOI: https://doi.org/10.4213/tvp292
Abstract: The paper provides necessary and sufficient conditions for weak convergence of the distributions of sums of independent random variables to normal and Poisson distributions. The conditions are given in terms of the first through fourth moments of the truncated components and some condition guaranteeing the asymptotic equality between the distribution of the sums mentioned above and the distribution of the sums of the truncated components. The theorems proven in this work are similar to the well-known criteria for normal and Poisson convergencies.
Keywords: normal convergence, Poisson convergence, Lindeberg–Feller central limit theorem, weak convergence, moments of random variables.
Received: 31.10.2002
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 2, Pages 347–355
DOI: https://doi.org/10.1137/S0040585X9780440
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Kruglov, “Normal and Poisson convergencies”, Teor. Veroyatnost. i Primenen., 48:2 (2003), 392–398; Theory Probab. Appl., 48:2 (2004), 347–355
Citation in format AMSBIB
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\jour Theory Probab. Appl.
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\issue 2
\pages 347--355
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  • https://doi.org/10.4213/tvp292
  • https://www.mathnet.ru/eng/tvp/v48/i2/p392
    • This publication is cited in the following 4 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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