Discrete semi-stable distributions |
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Authors: | Nadjib Bouzar |
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Affiliation: | (1) Department of Mathematics and Computer Science, University of Indianapolis, 1400 East Hanna Avenue, 46227-3697 Indianapolis, IN, USA |
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Abstract: | The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ +. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed. |
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Keywords: | Stability geometric stability infinite divisibility discrete distributions weak convergence |
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