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Merging asymptotic expansions for semistable random variables

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Abstract

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.

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Authors and Affiliations

  1. Analysis and Stochastics Research Group of the Hungarian Academy of Sciences, Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, H–6720, Szeged, Hungary

    P. Kevei

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  1. P. Kevei
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Correspondence to P. Kevei.

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Kevei, P. Merging asymptotic expansions for semistable random variables. Lith Math J 49, 40–54 (2009). https://doi.org/10.1007/s10986-009-9035-y

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  • DOI: https://doi.org/10.1007/s10986-009-9035-y

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