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Shifted and Scaled Sibuya Distribution and Discrete Self-Decomposability

by Christoph, G., Schreiber, K..

Series: 1998-24, Preprints

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

The Sibuya distribution plays a crucial role in considering several discrete self-decomposable distributions which occure as stationary distribution in pure death processes with immigration. Here, some properties of the Sibuya distribution are studied.

Discrete Linnik distributions, discrete stable and discrete stable and discrete Mittag-Leffler distributions, discrete self-decomposable, Sibuya distributions, stable distributions.

This paper was published in:
Statistics & Probability Letters, 48 (2000), pp. 181 - 187