Asymptotic expansions for distributions of compound sums of random variables with rapidly varying subexponential distribution

@inproceedings{Barbe2007AsymptoticEF,
  title={Asymptotic expansions for distributions of compound sums of random variables with rapidly varying subexponential distribution},
  author={Philippe Barbe and W. P. Mccormick and Cuiping Zhang},
  year={2007}
}
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same rapidly varying 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, seven-term expansions. In this paper we construct asymptotic expansions for the tail area of a… CONTINUE READING

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