On the residual dependence index of elliptical distributions

Details On the residual dependence index of elliptical distributions On the residual dependence index of elliptical distributions

2008-11-21

arxiv.org/abs/0811.3552v2

Mathematics

Probability

11 pages, case \theta=1 now included

Scientific paper

10.1016/j.spl.2010.03.001

The residual dependence index of bivariate Gaussian distributions is determined by the correlation coefficient. This tail index is of certain statistical importance when extremes and related rare events of bivariate samples with asymptotic independent components are being modeled. In this paper we calculate the partial residual dependence indices of a multivariate elliptical random vector assuming that the associated random radius is in the Gumbel max-domain of attraction. Furthermore, we discuss the estimation of these indices when the associated random radius possesses a Weibull-tail distribution.

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