On a Class of Variolinear Copulas

Abstract

We construct variolinear copulas with a given diagonal section, i.e. copulas that are linear on line segments connecting points on the diagonal to points on the boundary of the unit square. These line segments cover the unit square, two line segments can only intersect at (0,1) or (1,0), and the line segments may have a varying angle w.r.t. the main diagonal. The class of variolinear copulas covers the subclasses of semilinear, ortholinear and biconic copulas, whose construction has been reported before. We restrict the analysis to the case of symmetric variolinear copulas and we focus on the situation where the variability of the line segments is governed by two linear functions. For that subclass we provide the necessary and sufficient conditions on a diagonal function to obtain a variolinear copula. Some examples are provided.