The Generalized Discrete Linnik Distributions

by    G. Christoph, K. Schreiber

Preprint series: 97-24, Preprints

The paper is published: Advances in Stochastic Models for Reliability, Quality and Safety; W. Kahle (ed.) et al.,Birkhäuser, 1998, pp.3-18.

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-

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

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