Linear orderings of the scale mixtures of the multivariate skew-normal distribution

Abstract

In this paper, (positive) linear stochastic orderings of random vectors X and Y having scale mixtures of the multivariate skew-normal distribution are studied. Necessary and sufficient convenient conditions for a⊤X to be less than a⊤Y, when a is a vector of positive values, in the sense of usual, convex and increasing convex stochastic orders are grasped. The results are potentially applied to conduct some stochastic comparisons of weekly returns of developed markets and emerging markets. We demonstrate that the family of distributions is ordered in the stop-loss and the second degree stochastic dominance orders in terms of the correlation coefficients of the underlying random vectors. A possible application of one of the results in the reliability analysis of series and parallel systems is supplied.