Symmetry and dependence properties within a semiparametric family of bivariate copulas

Abstract

In this paper, we study a semiparametric family of bivariate copulas. The family is generated by a univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence property (quadrant dependence, total positivity, \\ldots ) of the copulas. We provide bounds on different measures of association (such as Kendall's Tau, Spearman's Rho) for this family and several choices of generating functions for which these bounds can be reached.