# Integral stochastic ordering of the multivariate normal mean-variance and the skew-normal scale-shape mixture models

### Abstract

In this paper, we introduce integral stochastic ordering of two most important classes of distributions that are commonly used to fit data possessing high values of skewness and (or) kurtosis. The first one is based on the selection distributions started by the univariate skew-normal distribution. A broad, flexible and newest class in this area is the scale and shape mixture of multivariate skew-normal distributions. The second one is the general class of Normal Mean-Variance Mixture distributions. We then derive necessary and sufficient conditions for comparing the random vectors from these two classes of distributions. The integral orders considered here are the usual, concordance, supermodular, convex, increasing convex and directionally convex stochastic orders. Moreover, for bivariate random vectors, in the sense of stop-loss and bivariate concordance stochastic orders, the dependence strength of random portfolios is characterized in terms of order of correlations.### References

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