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

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  • Veillette, Mark S.
  • Taqqu, Murad S.

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.

Suggested Citation

  • Veillette, Mark S. & Taqqu, Murad S., 2012. "Berry–Esseen and Edgeworth approximations for the normalized tail of an infinite sum of independent weighted gamma random variables," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 885-909.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:885-909
    DOI: 10.1016/j.spa.2011.10.012
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    References listed on IDEAS

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    1. 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;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 397-415, December.
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