Distribution and asymptotics under beta random scaling

الأصل · EN

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 Hₐ,b of X determines H. Based on that result we derive in this paper a recursive formula for calculation of H, if Hₐ,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 Hₐ,b, respectively, and the conditional limiting distribution of bivariate elliptical distributions.