Models for Extremal Dependence Derived from Skew-symmetric Families

Skew-symmetric families of distributions such as the skew-normal and skew-t represent supersets of the normal and t distributions, and they exhibit richer classes of extremal behaviour. By defining a non-stationary skew-normal process, which allows the easy handling of positive definite, non-stationary covariance functions, we derive a new family of max-stable processes - the extremal skew-t process. This process is a superset of non-stationary processes that include the stationary extremal-t processes. We provide the spectral representation and the resulting angular densities of the extremal skew-t process and illustrate its practical implementation.

Scandinavian Journal of Statistics, 44(1), 21–45