On nonuniform estimates of accuracy of normal approximation for distributions of some random sums under relaxed moment conditions
V. Yu. Korolevabc, A. V. Dorofeevab
a 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
b Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
c Hangzhou Dianzi University, Xiasha Higher Education Zone, Hangzhou 310018, China
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.
central limit theorem, normal approximation, random sum, binomial distribution, Poisson distribution, Poisson theorem.
|Russian Foundation for Basic Research
|This work was financially supported by the Russian Foundation for Basic Research (grant No. 18-07-01405).
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V. Yu. Korolev, A. V. Dorofeeva, “On nonuniform estimates of accuracy of normal approximation for distributions of some random sums under relaxed moment conditions”, Inform. Primen., 12:4 (2018), 86–91
Citation in format AMSBIB
\by V.~Yu.~Korolev, A.~V.~Dorofeeva
\paper On nonuniform estimates of accuracy of normal approximation for distributions of some random sums under relaxed moment conditions
\jour Inform. Primen.
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