Extreme value properties of multivariate \(t\) copulas
The authors deal with the extremal dependence behaviour of \(t\) copulas. The extreme value limiting copulas [\(t\)-EV-copulas, see \textit{H. Joe}, Multivariate models and dependence concepts. London: Chapman and Hall (1997; Zbl 0990.62517)] are derived explicitly using the introduced tail dependence and conditional tail dependence functions. The sharpness of the inequalities among three tail dependence parameters of a trivariate margin is proved. It is shown that the \(t\)-EV copulas yield the Hüsler-Reiss distribution and the Marshall-Olkinn distribution as the degrees of freedom go to infinity and zero, respectively. Several distributions are compared in the range of triplets of tail dependence parameters.
scientific article; zbMATH DE number 5855722