On the extremal dependence coefficient of multivariate distributions

A measure called ‘extremal dependence coefficient’ (EDC) is introduced for studying the asymptotic dependence structure of the minimum and the maximum of a random vector. Some general properties of the EDC are derived and its relation to the tail dependence coefficient is examined. The extremal dependence structure of regularly varying elliptical random vectors is investigated and it is shown that the EDC is only determined by the tail index and by the pseudo-correlation coefficients of the elliptical distribution.