Tail asymptotics under beta random scaling

Details

Serval ID
serval:BIB_96321E0F63DF
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Tail asymptotics under beta random scaling
Journal
Journal of Mathematical Analysis and Applications
Author(s)
Hashorva E., Pakes A.G.
ISSN
0022-247X
Publication state
Published
Issued date
2010
Peer-reviewed
Oui
Volume
372
Number
2
Pages
496-514
Language
english
Abstract
Let X, Y, B be three independent random variables such that X has the same distribution function as Y B. Assume that B is a beta random variable with positive parameters alpha, beta and Y has distribution function H with H(0) = 0. In this paper we derive a recursive formula for calculation of H, if the distribution function H(alpha,beta) of X is known. Furthermore, we investigate the relation between the tail asymptotic behaviour of X and Y, which is closely related to asymptotics of Weyl fractional-order integral operators. We present three applications of our asymptotic results concerning the extremes of two random samples with underlying distribution functions H and H(alpha,beta), respectively, and the conditional limiting distribution of bivariate elliptical distributions.
Keywords
Weyl fractional-order integral operator, Random scaling, Elliptical distribution, Max-domain of attraction, Asymptotics of sample maxima, Asymptotics of fractional integral, Conditional limiting results, Estimation of conditional distribution
Web of science
Open Access
Yes
Create date
03/09/2010 9:59
Last modification date
20/08/2019 14:58
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