Distribution and asymptotics under beta random scaling

Details Distribution and asymptotics under beta random scaling Distribution and asymptotics under beta random scaling

2008-12-04

arxiv.org/abs/0812.0881v2

Mathematics

Probability

12 pages

Scientific paper

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 a,b and Y has distribution function H. Pakes and Navarro (2007) show under some mild conditions that the distribution function H_{a,b} of X determines H. Based on that result we derive in this paper a recursive formula for calculation of H, if H_{a,b} is known. Furthermore, we investigate the relation between the tail asymptotic behaviour of X and Y. We present three applications of our asymptotic results concerning the extremes of two random samples with underlying distribution functions H and H_{a,b}, respectively, and the conditional limiting distribution of bivariate elliptical distributions.

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