Asymptotic expansions for distributions of compound sums of light subexponential random variables
Ph . Barbe, W. P. McCormick, C. Zhang
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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