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

Schmidt, Rafael

Math. Methods Oper. Res. 55, No. 2, 301-327 (2002).

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

Keywords:

elliptical distribution; spherical distribution; tail dependence; regular variation