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This article is cited in 3 scientific papers (total in 3 papers)
Estimates for the concentration functions under the weakened moments
V. Yu. Korolevabc, A. V. Dorofeyevab a Hangzhou Dianzi University, Zhejiang
b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
c Federal Research Center "Computer Science and Control" of Russian Academy of Sciences
Abstract:
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the moments of summands of higher orders. The results obtained are extended to Poisson-binomial, binomial, and Poisson random sums. Under the same assumptions, bounds are obtained for the approximation of the concentration functions of mixed Poisson random sums by the corresponding limit distributions. In particular, bounds are put forward for the accuracy of approximation of the concentration functions of geometric, negative binomial, and Sichel random sums by exponential, folded variance gamma, and folded Student distributions. Numerical estimates of all the constants involved are written down explicitly.
Keywords:
distribution function, central limit theorem, normal distribution, folded normal distribution, uniform metric, Poisson-binomial distribution, Poisson-binomial random sum, binomial random sum, Poisson random sum, mixed Poisson random sum, geometric random sum, gamma distribution, negative binomial random sum, inverse gamma distribution, Sichel distribution, Laplace distribution, exponential distribution, folded variance gamma distribution, folded Student distribution, absolute constant.
Received: 15.09.2016 Accepted: 20.10.2016
Citation:
V. Yu. Korolev, A. V. Dorofeyeva, “Estimates for the concentration functions under the weakened moments”, Teor. Veroyatnost. i Primenen., 62:1 (2017), 104–121; Theory Probab. Appl., 62:1 (2018), 84–97
Linking options:
https://www.mathnet.ru/eng/tvp5099https://doi.org/10.4213/tvp5099 https://www.mathnet.ru/eng/tvp/v62/i1/p104
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Abstract page: | 514 | Full-text PDF : | 69 | References: | 60 | First page: | 28 |
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