FGM Copula's Extension Via Polynomial Function

This study is concerned with generalizing the well-known family of FGM copula in terms of a polynomial function. A general form of the FGM copula via a copula function is proposed in order to obtain a new FGM copula family. Various particular cases have been presented according to the degree of the polynomial function. Proofs of necessary and sufficient conditions of the created copulas have been explained so that we guarantee that the desire function is copula. We firstly propose and define a general form that associate the FGM copula with a polynomial function. Graphs and some extra properties are presented as explanatory tool of some degrees of the obtain copula. Finally, we present some important calculations related to the most popular dependences by means of the FGM copula extension.