Conditional limiting distribution of beta-independent random vectors

Enkelejd Hashorva

Journal of Multivariate Analysis, 2008, vol. 99, issue 7, 1438-1459

Abstract: The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m =0, such that W2 is a beta distributed random variable with parameters m/2,(d-m)/2 and (U1,...,Um),(Um+1,...,Ud) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for 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.

Keywords: primary; 60F05 secondary; 60G70 Beta-independent random vectors Elliptical distributions Kotz Type I polar distributions Kotz approximation Conditional limiting distribution Estimation of conditional survivor function Max-domain of attractions (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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