A non symmetric extension of Amblard-Girard copulas

A copula is a function that completely describes the dependence structure between the marginal distributions. One of the most important parametric family of copulas is the Farlie-Gumbel-Morgenstern (FGM) family. In practical applications this copula has been shown to be somewhat limited and a symmetric extension of this family, known as the Amblard-Girard copula, has been introduced. We propose a new non symmetric extension of this family.