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

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

2006-04-18

arxiv.org/abs/math/0604378v1

Mathematics

Probability

13 pages

Scientific paper

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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