V. Yu. Korolev, I. A. Sokolov, “Skew Student distributions, variance-gamma distributions and their generalizations as asymptotic approximations”, Inform. Primen., 2012, Volume 6, Issue 1,Pages <nobr>3

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Skew Student distributions, variance-gamma distributions and their generalizations as asymptotic approximations

V. Yu. Korolev^a, I. A. Sokolov^b

^a M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^b Institute of Informatics Problems RAS

Abstract: The paper demonstrates that skew Student distributions and (skew) variance-gamma distributions can appear as limit laws in rather simple limit theorems for regular statistics, in particular, in the scheme of random summation of random variables and, hence, can be regarded as asymptotic approximations to the distributions of many processes related to the evolution of complex systems.

Keywords: skew Student distribution; variance-gamma distribution; limit theorem; random sum; transfer theorem.