Asymptotics of the norm of elliptical random vectors

Enkelejd Hashorva

Journal of Multivariate Analysis, 2010, vol. 101, issue 4, 926-935

Abstract: In this paper we consider elliptical random vectors in with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of and is a given matrix. Denote by ||[dot operator]|| the Euclidean norm in , and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability for F in the Gumbel or the Weibull max-domain of attraction. In the special case that is a mean zero Gaussian random vector our result coincides with the one derived in Hüsler et al. (2002) [1].

Keywords: Elliptical; distribution; Gaussian; distribution; Kotz; Type; distribution; Gumbel; max-domain; of; attraction; Tail; approximation; Density; convergence; Weak; convergence (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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