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.
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.