ASSESSMENT AND APPLICATION OF THIRD AND FOURTH ORDER GAUGE FUNCTIONS IN EXTREME VALUE ANALYSIS TOWARD ENHANCED GEOMETRIC MODELING

The gauge function is the basis for modeling the dependence of multivariate extremes using the so-called geometric approach developed in [1] and [12], and many others in recent literature. The work of Wadsworth and Campbell [12] as well as Nolde and Zhang [9] establishes a relationship between the domain G described by a function known as the gauge function and the dependence of the extreme values found there. In this paper, we propose two new candidates of gauge functions for modeling by the geometric approach of multivariate extremes. These functions are constructed through the decompositions of densities D-vine of orders 3 and 4 in connection with the form proposed in [12]. These theoretical constructions are followed by practical simulations, including probability estimation in extreme regions, as well as an application to real-world data.