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

被引：5

作者：

Barbe, Ph. ^{[1
]}

McCormick, W. P. ^{[1
]}

Zhang, C. ^{[1
]}

机构：

[1] Univ Georgia, Dept Stat, Athens, GA 30602 USA

来源：

JOURNAL OF APPLIED PROBABILITY | 2007年 / 44卷 / 03期

关键词：

asymptotic expansion; convolution; tail area approximation; regular variation; subexponential distribution;

D O I：

10.1239/jap/1189717537

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：670 / 684

页数：15

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