In this paper we solve two open problems posed by Joe (1997) concerning the
supermodular order. First we give an example which shows that the supermodular order is
strictly stronger than the concordance order for dimension d= 3. Second we show that the
supermodular order fulfils all desirable properties of a multivariate positive dependence
order. We especially prove the non-trivial fact that it is closed with respect to weak
convergence. This is applied to give a complete characterization of the supermodular order …

In this paper we solve two open problems posed by Joe (1997) concerning the
supermodular order. First we give an example which shows that the supermodular order is
strictly stronger than the concordance order for dimension d= 3. Second we show that the
supermodular order fulfils all desirable properties of a multivariate positive dependence
order. We especially prove the non-trivial fact that it is closed with respect to weak
convergence. This is applied to give a complete characterization of the supermodular order …