  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.
