More on Stochastic Comparisons and Dependence among Concomitants of Order Statistics

For a sample of iid observations {(X_i, Y_i)} from an absolutely continuous distribution, the multivariate dependence of concomitants Y_[]=(Y_[1], Y_[2], …, Y_[n]) and the stochastic order of subsets of Y_[] are studied. If (X, Y) is totally positive dependent of order 2, Y_[] is multivariate totally positive dependent of order 2. If the conditional hazard rate function of Y given X, h_YX(yx), is decreasing in x for every y, Y_[] is multivariate right corner set increasing. And if Y is stochastically increasing in X, the concomitants are increasing in multivariate stochastic order.