97-24
The Generalized Discrete Linnik Distributions
by Christoph, G.; Schreiber, K.
Preprint series: 97-24, Preprints
The paper is published: Advances in Stochastic Models for Reliability, Quality and \rSafety; W. Kahle (ed.) et al.,Birkhäuser, 1998, pp.3-18.
- 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 branching 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.
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