Calculations in extension for copulas

In 2004, Rodríguez-Lallena and ´Ubeda-Flores have introduced a class of bivariate copulas which generalizes some known families such as the Farlie-Gumbel-Morgenstern distributions. In this study we generalize Rodríguez-Lallena and Úbeda-Flores’ study to a large number of copula families. Namely, we suggest new parametric copula families via extension of any given family. Then to describe the method, extensions of four well known Archimedean families will be shown.