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Informatika i Ee Primeneniya [Informatics and its Applications], 2013, Volume 7, Issue 1, Pages 105–115
(Mi ia250)
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This article is cited in 19 scientific papers (total in 19 papers)
Variance-generalized-gamma-distributions as limit laws for random sums
L. M. Zaksa, V. Yu. Korolevbc a Department of Modeling and Mathematical Statistics, Alpha-Bank
b Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University
c IPI RAN
Abstract:
A general theorem is proved establishing necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to variance-mean mixtures of normal laws. As a corollary, necessary and sufficient conditions for the convergence of the distributions of sums of a random number of independent identically distributed random variables to variance-generalized-gamma-distributions are obtained. For a special case of continuous-time random walks generated by compound doubly stochastic Poisson processes, convergence rate estimates are presented.
Keywords:
random sum; generalized hyperbolic distribution; generalized inverse Gaussian distribution; generalized gamma-distribution; variance-generalized-gamma-distribution; mixture of probability distributions; identifiable mixtures; additively closed family; convergence rate estimate.
Citation:
L. M. Zaks, V. Yu. Korolev, “Variance-generalized-gamma-distributions as limit laws for random sums”, Inform. Primen., 7:1 (2013), 105–115
Linking options:
https://www.mathnet.ru/eng/ia250 https://www.mathnet.ru/eng/ia/v7/i1/p105
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Abstract page: | 861 | Full-text PDF : | 367 | References: | 75 | First page: | 8 |
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