Rates of convergence to stable and discrete stable laws
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.
- 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
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