Tail asymptotics under beta random scaling

[摘要] 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,H-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,H-beta, respectively, and the conditional limiting distribution of bivariate elliptical distributions. (C) 2010 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-15

[关键词] 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