On modeling directional dependence by using copulas

Understanding and modeling multivariate dependence structures depending upon the direction are challenging but an interest of theoretical and applied researchers. In this article, we introduce a way of looking at directional dependence by using a direction parameter, possibly random in Bayesian setting, expressed as an angle. This construction allows us to model and measure directional dependence in a meaningful way and leads to informative graphical displays. Our focus in this paper will be on the 3-dimensional case.