Asymptotic expansions of convolutions of regularly varying distributions

• Autores: Philippe Barbe, William P. McCormick
• Localización: Journal of the Australian Mathematical Society, ISSN 1446-7887, Vol. 78, Nº 3, 2005, págs. 339-371
• Idioma: inglés
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• Resumen

  • 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 a semiparametric 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.