Conditional limiting distribution of beta-independent random vectors |
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Authors: | Enkelejd Hashorva |
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Institution: | aDepartment of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland |
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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<d we have the stochastic representations and , with W≥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. |
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Keywords: | AMS 2000 subject classifications: primary 60F05 secondary 60G70Beta-independent random vectors Elliptical distributions Kotz Type I polar distributions Kotz approximation Conditional limiting distribution Estimation of conditional survivor function Max-domain of attractions |
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