Models for extremal dependence derived from skew-symmetric families

Abstract

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 (Includes Supporting Information).