On some features of the skewed families of max-stable processes

Abstract

Environmental phenomena are processes which are spatial by nature as a single extreme event (heat waves, floods, storms, etc.) often have repercussions at multiple locations. For risk management purposes it is important to have a good understanding of the dependence structure that links such events in order to make predictions on future phenomena, that can have a major impact on real life. Moreover available data at different sites can exhibit asymmetric distributions proving the necessity for max-stable processes that can handle skewness. The extremal-skew-$t$ process, constructed from a non-stationary skew-normal process is a solution that recently appeared in the literature. A generalisation of the discussion on the asymptotics of skewed families of extreme-value processes is provided, including skew-elliptical processes as well as the derivation of a skewed version of the well-known Gaussian extreme-value process. The challenge of simulating these processes is then tackled using the conditional simulation framework and simulated examples are provided to illustrate the method.