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Asymptotic Expansions for Distributions of Compound Sums of Random Variables with Rapidly Varying Subexponential Distribution

  • Ph. Barbe (a1), W. P. McCormick (a2) and C. Zhang (a2)

Abstract

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.

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Copyright

Corresponding author

Postal address: 90 rue de Vaugirard, 75006 Paris, France.
∗∗ Postal address: Department of Statistics, University of Georgia, Athens, GA 30602, USA.
∗∗∗ Email address: bill@stat.uga.edu

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