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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Veillette, Mark S.¹  Taqqu, Murad S.¹ 

[1] Boston Univ, Boston, MA 02215 USA

关键词: Berry-Esseen;    Edgeworth expansions;    Infinitely divisible distributions;    Rosenblatt distribution;   

DOI  :  10.1016/j.spa.2011.10.012

来源: Elsevier

【 摘 要 】

Consider the sum Z = Sigma(infinity)(n=1) lambda(n) (eta(n), - E eta(n)), where eta(n), are independent gamma random variables with shape parameters r(n) > 0, and the lambda(n)'s aree predetermined weights. We study the asymptotic behavior of the tail Sigma(infinity)(n=M) lambda(n)(eta(n) - E eta(n)), 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. The results we obtain are directly applicable to the study of double Wiener-Ito integrals and to the Rosenblatt distribution. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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