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

Ph . Barbe; W. P. McCormick; C. Zhang

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

Ph . Barbe·W. P. McCormick·C. Zhang

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Abstract

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.

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Ph . Barbe, W. P. McCormick, C. Zhang. 2006-04-18. Asymptotic expansions for distributions of compound sums of light subexponential random variables. https://arxiv.org/abs/math/0604378

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