Hessian and increasing-Hessian orderings of scale-shape mixtures of multivariate skew-normal distributions and applications

In this work, we establish some stochastic comparison results for the class of scale-shape mixtures of multivariate skew-normal (SSSN) distributions. These multivariate stochastic comparisons involve Hessian and increasing-Hessian orderings as well as many of their special cases. We show that the supermodular and increasing-supermodular orderings are equivalent to the concordance and upper orthant orderings, respectively, as well as the …