Asymptotic results for families of power series distributions

2021/01/15 by Claudio Macci, Macci, Claudio, Barbara Pacchiarotti +3
Mathematics · #60E05 #60F10 #60G22 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E05 #msc:60F10 #msc:60G22

paper · pdf · doi:10.48550/arxiv.2101.06183

arxiv created 2021/12/06 · arxiv updated 2021/12/07

Abstract

In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting processes, where the normalizations of the involved power series distributions can be expressed in terms of the Prabhakar function. The first example allows to consider the counting process in \citePoganyTomovski, the second one is inspired by a model studied in \citeGarraOrsingherPolito.

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