Generalized bivariate copulas and their properties

Copulas are useful devices to explain the dependence structure among variables by eliminating the influence of marginals. In this paper, we propose a new class of bivariate copulas to quantify dependency and incorporate it into various iterated copula families. We investigate properties of the new class of bivariate copulas and derive the measure of association, such as Spearman's ρ, Kendall's τ, and the regression function for the new class. We also provide the concept of directional dependence in bivariate regression setting by using copulas.