A Class of Copulas Derived from Residual Implications and Its Applications

Copulas are multivariate distribution functions with uniform marginal distributions. In this paper, we study a class of copulas called radial copulas, which is derived from residual implications where the extensions of level curves intersect at a point. This class of radial copulas is a comprehensive and asymmetric extension of a class of Archimedean copulas. We derive analytical formulas for key concordance measures, including Spearman’s rho and Kendall’s tau, and demonstrate that these formulas cover the entire range of positive and negative correlations. Furthermore, we estimate the parameters of radial copulas and evaluate their performance through a simulation study under various dependence structures. Finally, using two datasets, we compare the performance of the class of radial copulas to that of several well-known copula models.