Rates of convergence to stable and discrete stable laws

by    G. Christoph, K. Schreiber

Preprint series: 98-36, Preprints

The paper is published: Probability Theory and Mathematical Statistics, Proceedings of the 7th Vilnius Conference (1998), Grigelionis, B. (ed.) et al., S. 147-156.

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

Abstract: Discrete analogues of self-decomposability and stability
were introduced in (Steutel and van Harn, 1979), where
discrete stable laws occur with discrete domains of
attraction.
In the present paper rates of convergence for the
distribution functions of certain sums or random sums of
non-negative integer valued random variables to discrete
stabel as well as (continuous) stable limit laws are
considered and discussed. Discrete Mittag-Leffler, discrete
Linnik as well as the Sibuya distributions are considered
as examples.




Keywords: Discrete self-decomposable, discrete stable and stable distributions, domains of attraction, rates of convergence, discrete Linnik and dicrete Mittag-Leffler distributions

Upload: 1999-01-27

Update: 2000-02-17


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