On a Bivariate Copula for Modeling Negative Dependence

A new bivariate copula is proposed for modeling negative dependence between two random variables. We show that it complies with most of the popular notions of negative dependence reported in the literature and study some of its basic properties. Specifically, the Spearmans rho and the Kendalls tau for the proposed copula have a simple one-parameter form with negative values in the full range. Some important ordering properties comparing the strength of negative dependence with respect to the parameter involved are considered. Simple examples of the corresponding bivariate distributions with popular marginals are presented. Application of the proposed copula is illustrated using a real data set.