Symmetry and dependence properties within a semiparametric family of   bivariate copulas
  In this paper, we study a semiparametric family of bivariate copulas. The family is generated by an univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence property (quadrant dependence, total positivity, ...) 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 allowing to reach these bounds. 
C\'ecile Amblard and St\'ephane Girard
math.ST stat.TH