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Asymptotic Expansions with Discrete Stable Limit Laws

by Christoph, G..

Series: 1999-21, Preprints

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

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.

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