Discrete Analogues of Self-Decomposability and Stability

Analogues are proposed for the concepts of self-decomposability and stability for distributions on the nonnegative integers. It turns out that these "discrete self-decomposable" and "discrete stable" distributions have properties that are quite similar to those of their continuou...

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Bibliographic Details
Published in:The Annals of probability 1979-10, Vol.7 (5), p.893-899
Main Authors: Steutel, F. W., van Harn, K.
Format: Article
Language:English
Subjects:
60E05
60F05
Discrete distribution
domain of attraction
Eigenfunctions
infinitely divisible
Mathematical lattices
Mathematical moments
Probability theory
Random variables
self-decomposable
Short Communications
stable
unimodal
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Description
Summary:Analogues are proposed for the concepts of self-decomposability and stability for distributions on the nonnegative integers. It turns out that these "discrete self-decomposable" and "discrete stable" distributions have properties that are quite similar to those of their continuous counterparts.
ISSN:0091-1798
2168-894X
DOI:10.1214/aop/1176994950