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Merging asymptotic expansions for semistable random variables. (English) Zbl 1177.60031
Summary: Merging asymptotic expansions are established for distribution functions from the domain of geometric partial attraction of a semistable law. The length of the expansion depends on the exponent of the semistable law and on the characteristic function of the underlying distribution. We obtain sufficient conditions for the quantile function in order to get real infinite asymptotic expansion. The results are generalizations of the existing theory in the stable case.
MSC:
60F05Central limit and other weak theorems
60E07Infinitely divisible distributions; stable distributions
References:
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