Stochastic arrangement increasing property of skew-normal distributions

In this study, we investigate both sufficient and necessary conditions for bivariate skew-normal distributions to be stochastic arrangement increasing. The main results serve as either natural extension of or nice supplement to the characterization result of this property for bivariate normal distributions due to Cai and Wei (2015). Also, we generalize these results to multivariate skew-normal distributions. Numerical examples based on the theory and a real data are presented to illustrate the main results as well.