Tail asymptotics under beta random scaling |
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Authors: | Enkelejd Hashorva Anthony G. Pakes |
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Affiliation: | a Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Extranef, UNIL-Dorigny, 1015 Lausanne, Switzerland b School of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, W.A., 6009, Australia |
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Abstract: | Let X,Y,B be three independent random variables such that X has the same distribution function as YB. Assume that B is a beta random variable with positive parameters α,β 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 Hα,β 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 Hα,β, respectively, and the conditional limiting distribution of bivariate elliptical distributions. |
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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 |
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