Berry–Esseen and Edgeworth approximations for the normalized tail of an infinite sum of independent weighted gamma random variables
AbstractConsider 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 122 (2012)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- Antonia Castaño-Martínez & Fernando López-Blázquez, 2005. "Distribution of a sum of weighted noncentral chi-square variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 14(2), pages 397-415, December.
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