On the residual dependence index of elliptical distributions

Abstract

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.

11 pages, case θ=1 now included

References in corpus (3)

• Estimation of bivariate excess probabilities for elliptical models
• Conditional Limit Results for Type I Polar Distributions
• Conditional Limits of W_p scale Mixture Distributions

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• Tail asymptotic of Weibull-type risks
• Asymptotics for Kotz Type III Elliptical Distributions
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• Efficient simulation for dependent rare events with applications to extremes
• Bridging Asymptotic Independence and Dependence in Spatial Extremes Using Gaussian Scale Mixtures