On the interplay between variability and negative dependence for bivariate distributions

We investigate how increasing variability (in the sense of convex stochastic order) of the marginal distributions of negatively dependent bivariate random vectors (X1,X2) affects important characteristics of stochastic models like E max {X1,X2}. It will be shown that such a comparison result is possible under a negative dependence condition, which we call conditionally decreasing, and under the condition that the random vectors are comparable with respect to a suitable dependence order. Moreover, we give a counterexample demonstrating that a related result stated in Paul is true only for countermonotonic random vectors and not for RR2 random vectors as claimed.