In this paper, we shall construct a large class of new bivariate copulas. This class happens to contain several known classes of copulas, such as Farlie-Gumbel-Morgenstern, Ali-Mikhail-Haq and Barnett-Gumbel, as its especial members. It is shown that the proposed copulas improve the range of values of correlation coefficient and thus they are more applicable in data modeling. We shall also reveal that the dependent properties of the base copula are preserved by the generated copula under certain conditions. Several members of the new class are introduced as instances and their range of correlation coefficients are computed.

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