# 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

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 10:59

Last modification date

20/08/2019 15:58