## Tail dependence for elliptically contoured distributions.(English)Zbl 1015.62052

Summary: The relationship between the theory of elliptically contoured distributions and the concept of tail dependence is investigated. We show that bivariate elliptical distributions possess the so-called tail dependence property if the tail of their generating random variable is regularly varying, and we give a necessary condition for tail dependence which is somewhat weaker than regular variation of the latter tail. In addition, we discuss the tail dependence property for some well-known examples of elliptical distributions, such as the multivariate normal, $$t$$, logistic, and Bessel distributions.

### MSC:

 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62P05 Applications of statistics to actuarial sciences and financial mathematics 62E10 Characterization and structure theory of statistical distributions
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