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

2006/04/18 by Ph . Barbe, Barbe, Ph ., W. P. McCormick +3
Mathematics · #41A60 #60F99 #60G50 #60K05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:41A60 #msc:60F99 #msc:60G50 #msc:60K05

paper · pdf · doi:10.48550/arxiv.math/0604378

13 pages

arxiv created 2006/04/18 · arxiv updated 2009/12/01

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.

Related

• Asympyotic expansions for infinite weighted convolutions of light subexponential distributions
• Tail asymptotics of light-tailed Weibull-like sums
• On Upper Bounds for the Tail Distribution of Geometric Sums of Subexponential Random Variables
• Asymptotics of summands I: square integrable independent random variables
• A conditional limit theorem for independent random variables