Asymptotics of the Norm of Elliptical Random Vectors
Abstract
In this paper we consider elliptical random vectors X in Rd,d>1 with stochastic representation A R U where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of Rd and A is a given matrix. The main result of this paper is an asymptotic expansion of the tail probability of the norm of X derived under the assumption that R has distribution function is in the Gumbel or the Weibull max-domain of attraction.
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