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1997-24

The Generalized Discrete Linnik Distributions

by Christoph, G., Schreiber, K..


Series: 1997-24, Preprints

MSC:
60E05 Distributions: general theory
60F05 Central limit and other weak theorems
60E07 Infinitely divisible distributions; stable distributions

Abstract:
Discrete self-decomposable random variables play an important role in branch-
ing processes. Here the generalized discrete Linnik distributions, which are discrete
self-decomposable and include the discrete stable as well as the discrete Mittag--
Leffler distributions, are introduced and some properties of their probabilities are
investigated. Further, the family of survival distributions of a generalized discrete
Linnik distributed original observation subjected to a destructive process is deter-
mined.

Keywords:
Discrete Linnik distribution, discrete stable and discrete Mittag--Lefflerdistribution, discrete self-decomposable, stable distributions, survival distribution.

This paper was published in:
Advances in Stochastic Mode