New families of symmetric/asymmetric copulas

In 2004, Rodríguez-Lallena and Úbeda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie–Gumbel–Morgenstern distributions. In 2006, Dolati and Úbeda-Flores presented multivariate generalizations of this class, also they investigated symmetry, dependence concepts and measuring the dependence among the components of each classes. In this paper, a new method of constructing binary copulas is introduced, extending the original study of Rodríguez-Lallena and Úbeda-Flores to new families of symmetric/asymmetric copulas. Several properties and parameters of newly introduced copulas are included. Among others, relationship of our construction method with several kinds of ordinal sums of copulas is clarified.