Statistical analysis of extreme values
Statistical analysis of extreme values
Uniform distributions on spheres in finite dimensional L&agr; and their generalizations
Journal of Multivariate Analysis
Conditional limiting distribution of Type III elliptical random vectors
Journal of Multivariate Analysis
On decompositional algorithms for uniform sampling from n-spheres and n-balls
Journal of Multivariate Analysis
On Pearson-Kotz Dirichlet distributions
Journal of Multivariate Analysis
Scale mixtures of Kotz-Dirichlet distributions
Journal of Multivariate Analysis
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The paper deals with random vectors X in R^d,d=2, possessing the stochastic representation X=dARV, where R is a positive random radius independent of the random vector V and A@?R^d^x^d is a non-singular matrix. If V is uniformly distributed on the unit sphere of R^d, then for any integer m=0, such that W^2 is a beta distributed random variable with parameters m/2,(d-m)/2 and (U"1,...,U"m),(U"m"+"1,...,U"d) are independent uniformly distributed on the unit spheres of R^m and R^d^-^m, respectively. Assuming a more general stochastic representation for V in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors.