V. Yu. Korolev, V. E. Bening, L. M. Zaks, A. I. Zeifman, “Generalized Laplace distribution as a limit law for random sums and statistics constructed from samples with randomsizes”, Inform. Primen., 2012, Volume 6, Issue 4,Pages <nobr>34

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Generalized Laplace distribution as a limit law for random sums and statistics constructed from samples with randomsizes

V. Yu. Korolev^ab, V. E. Bening^ab, L. M. Zaks^c, A. I. Zeifman^bde

^a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Institute for Problems of Informatics of RAS
^c Department of Modeling and Mathematical Statistics, Alpha-Bank
^d Vologda State Pedagogical University
^e VSCC CEMI RAS

Abstract: Limit theorems establishing necessary and sufficient conditions of convergence of random sums and statistics constructed from the samples with random sizes to the generalized Laplace distribution are proved.

Keywords: generalized Laplace distribution; symmetric stable distribution; one-sided stable distribution; scale mixture of normal laws; random sum; sample with random size; mixed Poisson distribution.