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Inform. Primen., 2013, Volume 7, Issue 1, Pages 105–115 (Mi ia250)  

This article is cited in 17 scientific papers (total in 17 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

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.

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Citation: L. M. Zaks, V. Yu. Korolev, “Variance-generalized-gamma-distributions as limit laws for random sums”, Inform. Primen., 7:1 (2013), 105–115

Citation in format AMSBIB
\by L.~M.~Zaks, V.~Yu.~Korolev
\paper Variance-generalized-gamma-distributions as~limit laws for~random sums
\jour Inform. Primen.
\yr 2013
\vol 7
\issue 1
\pages 105--115

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