  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.
