by Christoph, G..

**Series:** 1999-21, Preprints

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

**Abstract:**

Discrete stable disributions and their domains of attractions

were introduced in Steutel and van Harn (1979). Here asymptotic

expansions with discrete stable limit laws are considered. In one

case the Poisson distribution is the limit law, whereas the other

limit laws have infinite expectations. Therefore asymptotic

expansions for some infinitely divisible limit distributions with

infinite expectation are obtained, too. Examples demonstrate

the results.

**Keywords:**

Strictly stable and discrete stable distributions, discrete stability, Edgeworth expansions with discrete stable limit law.