Conditionally ordered distributions

The concepts of conditionally more positively quadrant dependent, and conditionally more dispersed are introduced and studied. Based on these two concepts, new conditions are given for multivariate cdfs F and G so that EFh(X) >= EGh(X) for suitable h(X). Special cases include the multivariate normal distribution and elliptically contoured distributions. Conditional positive and negative dependence concepts as well as applications to the Farlie-Gumbel-Morgenstern distribution are also considered.