New families of symmetric/asymmetric copulas

In 2004, Rodriguez-Lallena and Ubeda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In 2006, Dolati and Ubeda-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 Rodriguez-Lallena and Ubeda-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. (C) 2013 Elsevier B.V. All rights reserved.