Tail dependence from a distributional point of view. (English) Zbl 1049.62055

Juri, Alessandro; Wüthrich, Mario V.

Extremes 6, No. 3, 213-246 (2003).

Summary: The dependence structure in the tails of bivariate random variables is studied by means of appropriate copulae. Weak convergence results show that these copulae are natural dependence structures for joint tail events. The results obtained apply to particular types of copulae such as archimedean copulae and the Gaussian copula. Further, connections to multivariate extreme value theory are investigated and a two-dimensional Pickands-Balkema-de Haan theorem type is derived. Finally, a counterexample showing that the tail dependence coefficients do not completely determine the dependence structure of bivariate rare events is provided.

MSC:

62G32	Statistics of extreme values; tail inference
62H20	Measures of association (correlation, canonical correlation, etc.)
62H10	Multivariate distribution of statistics

Keywords:

archimedean copula; dependent risks; extreme value theory; regular variation; tail dependence; invariance properties