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arXiv · 1010.3948

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

Mark S. Veillette·Murad S. Taqqu
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Abstract

Consider the sum $Z = \sum_{n=1}^\infty λ_n (η_n - \mathbb{E}η_n)$, where $η_n$ are i.i.d.~gamma random variables with shape parameter $r > 0$, and the $λ_n$'s are predetermined weights. We study the asymptotic behavior of the tail $\sum_{n=M}^\infty λ_n (η_n - \mathbb{E}η_n)$ 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.

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Mark S. Veillette, Murad S. Taqqu. 2010-10-19. Berry-Esseen and Edgeworth approximations for the tail of an infinite sum of weighted gamma random variables. https://arxiv.org/abs/1010.3948

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