We propose a new family of copulas generalizing the Farlie-Gumbel-Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman's Rho is [-3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided
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