A new class of copulas having dependence range larger than FGM-type copulas

We propose a new bivariate symmetric copula with positive and negative dependence properties. The main features of the proposed copula are its simple mathematical structure, wider dependence range compared to FGM copula and its generalizations, and no lower and upper tail dependence. The maximum range of Spearman's Rho of the proposed copula is [-0.5866,0.5866], which improves the dependence range of the FGM copula and its various generalizations. A new bivariate Rayleigh distribution is developed using the proposed copula, and some statistical properties have been studied. A real data set is analyzed to illustrate the proposed bivariate distribution's relevance in practical contexts.