Measuring the extremal dependence

Statistics & Probability Letters, 73(2) (2005), 99-103
http://dx.doi.org/10.1016/j.spl.2005.02.015

We deal with the problem of how to measure the strength of the dependence in the extremes. Probabilistic and statistical methods for multivariate extreme values motivate an adjustment in the definition of the extremal coefficient. We point out that the available extremal coefficient does not measure correctly the dependence in the limiting distribution of maxima when a multivariate extremal index is present and propose an adjustment of this coefficient in order to cover this case and preserve its main properties. We will present a new definition for the extremal coefficient and relate it with the tail dependence. Finally, we illustrate this contribution with examples.