Asymptotic expansions for distributions of compound sums of light subexponential random variables

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We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an illustration of the main result. Complete calculations are done for a Weibull distribution, with which we derive, as examples and without any difficulties, 7 terms expansions.
13 pages

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Probability, 60F99, 60K05, 60G50, 41A60

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http://salesiana.dossiersoluciones.com/handle/123456789/111601

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604378
 http://arxiv.org/abs/math/0604378

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arXiv