Asymptotics of the Norm of Elliptical Random Vectors

Details Asymptotics of the Norm of Elliptical Random Vectors Asymptotics of the Norm of Elliptical Random Vectors

2008-12-22

arxiv.org/abs/0812.4105v2

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

Mathematics

Probability

11 pages

Scientific paper

10.1016/j.jmva.2009.10.004

In this paper we consider elliptical random vectors X in R^d,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 R^d 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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