Informatics and Applications
2018, Volume 12, Issue 4, pp 86-91
ON NONUNIFORM ESTIMATES OF ACCURACY OF NORMAL APPROXIMATION FOR DISTRIBUTIONS OF SOME RANDOM SUMS UNDER RELAXED MOMENT CONDITIONS
- V. Yu. Korolev
- A.V. Dorofeeva
Abstract
Nonuniform estimates are presented for the rate of convergence in the central limit theorem for sums of a random number of independent identically distributed random variables. Two cases are studied in which the summation index (the number of summands in the sum) has the binomial or Poisson distribution. The index is assumed to be independent of the summands. The situation is considered where the information that only the second moments of the summands exist is available. Particular numerical values of the absolute constants are presented explicitly. Also, the sharpening of the absolute constant in the nonuniform estimate of the rate of convergence in the central limit theorem for sums of a nonrandom number of independent identically distributed random variables is announced for the case where the summands possess only second moments.
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[+] About this article
Title
ON NONUNIFORM ESTIMATES OF ACCURACY OF NORMAL APPROXIMATION FOR DISTRIBUTIONS OF SOME RANDOM SUMS UNDER RELAXED MOMENT CONDITIONS
Journal
Informatics and Applications
2018, Volume 12, Issue 4, pp 86-91
Cover Date
2018-12-30
DOI
10.14357/19922264180412
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
central limit theorem; normal approximation; random sum; binomial distribution; Poisson distribution; Poisson theorem
Authors
V. Yu. Korolev  ,  ,  and A.V. Dorofeeva
Author Affiliations
Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Hangzhou Dianzi University, Xiasha Higher Education Zone, Hangzhou 310018, China
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