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Copulas are useful mathematical tools in probabilistic modelling and simulation; they allow the construction or understanding of various dependence structures in random processes. As a result, constructing various types of copulas is quite important. In this paper, we first present and investigate a new copula based on a simple but original ratio function. Among the properties, we show that it does not belong to the Archimedean family, it is symmetric, it is not radially symmetric, it has interesting quadrant dependence properties, it has the tail independence property, and it satisfies comprehensive concordance properties with the famous Farlie-Gumbel-Morgenstern copula. Secondly, in order to make it more flexible, we propose and develop some parametric generalizations of this copula. One generalization is of particular interest; it can be considered as a new generalized version of the Farlie-Gumbel-Morgenstern copula involving a weighted ratio function. Some graphical illustrations illustrate the findings. 

Farlie-Gumbel-Morgenstern copula, spearman measure, tail dependence.