Some positive dependence stochastic orders

In this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by restricting them to copulæ, we give a number of examples, and we study some positive dependence concepts that arise from the new positive dependence orders. We also discuss the relationship of the new orders to other positive dependence orders that have appeared in the literature.