Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables

Details Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables

2010-10-19

arxiv.org/abs/1010.3948v1

Mathematics

Probability

19 pages, 2 figures

Scientific paper

Consider the sum $Z = \sum_{n=1}^\infty \lambda_n (\eta_n - \mathbb{E}\eta_n)$, where $\eta_n$ are i.i.d.~gamma random variables with shape parameter $r > 0$, and the $\lambda_n$'s are predetermined weights. We study the asymptotic behavior of the tail $\sum_{n=M}^\infty \lambda_n (\eta_n - \mathbb{E}\eta_n)$ which is asymptotically normal under certain conditions. We derive a Berry-Essen bound and Edgeworth expansions for its distribution function. We illustrate the effectiveness of these expansions on an infinite sum of weighted chi-squared distributions.

Affiliated with

Also associated with

No associations

Rating

Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-269184