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1999-17

Positive Linnik and Discrete Linnik Distributions

by Christoph, G., Schreiber, K..


Series: 1999-17, Preprints

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

Abstract:
In the present paper (continuous) positive Linnik and
(nonnegative integer valued) discrete Linnik random
variables are discussed.
Rates of convergence and first terms of both the
Edgeworth expansions and the expansions in the exponent
of the distribution functions of certain sums of such
random variables with nonnegative strictly stable as well
as discrete limit laws are considered.

Keywords:
positive Linnik and discrete Linnik distributions, discrete self-decomposability, discrete stability, rates of convergence, Edgeworth expansions and expansions in the exponent with discrete stable limit law