Discrete semi-stable distributions
type: Item
instance of: scholarly article
title: Discrete semi-stable distributions
zbMATH Open document ID: 1065.60013
DOI: 10.1007/BF02530538
author: Nadjib Bouzar
published in: Annals of the Institute of Statistical Mathematics
publication date: 2005-03-14T00:00:00Z
review text: The author introduces and studies a concept of semi-stability for discrete distributions on the non-negative integers as a generalization of discrete stable distributions, which parallels the concept of semi-stable distributions on the real line. For discrete semi-stable random variables, a functional equation for the probability generating function is required to be fulfilled for a single parameter only. Discrete semi-stable distributions are shown to be infinitely divisible and to admit a certain canonical representation of their probability generating function. Further, a distributional equality using the Steutel and van Harn operator is shown to be characteristic for discrete semi-stability, from which the author deduces and studies discrete geometric semi-stable distributions by geometric randomization of a certain parameter, as well as corresponding limit theorems with discrete semi-stable limits. Examples based on Poisson mixtures with respect to a semi-stable distribution on the positive real line are also presented.
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 2144521
zbMATH Keywords: semi-stability
zbMATH Keywords: geometric semi-stability
zbMATH Keywords: infinite divisibility
zbMATH Keywords: discrete distributions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2144521