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Asymptotic expansions of convolutions of regularly varying distributions

Published online by Cambridge University Press:  09 April 2009

Philippe Barbe
Affiliation:
CNRS 90 rue de Vaugirard 75006 Paris, France
William P. McCormick
Affiliation:
Department of StatisticsUniversity of Georgia Athens, GA 30602USA e-mail: [email protected]
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Abstract

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In this paper we derive precise tail-area approximations for the sum of an arbitrary finite number of independent heavy-tailed random variables. In order to achieve second-order asymptotics, a mild regularity condition is imposed on the class of distribution functions with regularly varying tails.

Higher-order asymptotics are also obtained when considering asemiparametric subclass of distribution functions with regularly varying tails. These semiparametric subclasses are shown to be closed under convolutions and a convolution algebra is constructed to evaluate the parameters of a convolution from the parameters of the constituent distributions in the convolution. A Maple code is presented which does this task.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

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