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

Mark S. Veillette and Murad S. Taqqu

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 885-909

Abstract: Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηn are independent gamma random variables with shape parameters rn>0, and the λn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We derive a Berry–Esseen bound and Edgeworth expansions for its distribution function. We illustrate the effectiveness of these expansions on an infinite sum of weighted chi-squared distributions.

Keywords: Berry–Esseen; Edgeworth expansions; Infinitely divisible distributions; Rosenblatt distribution (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:3:p:885-909

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DOI: 10.1016/j.spa.2011.10.012

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