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.

翻译：本文提出了一种具有正负依赖特性的二元对称连接函数。该连接函数的主要特征包括：简洁的数学结构、相较于FGM连接函数及其推广形式更宽的依赖范围，以及无上下尾依赖性。所提连接函数的Spearman秩相关系数最大范围为[-0.5866,0.5866]，改进了FGM连接函数及其多种推广形式的依赖范围。基于该连接函数，我们构建了一种新的二元瑞利分布，并研究了其若干统计性质。通过分析实际数据集，验证了所提二元分布在实际应用中的相关性。