On multivariate dispersion orderings based on the standard construction

We study the relationship between the multivariate dispersive orders based on the standard construction. In particular those given by Shaked and Shanthikumar [1998. Two variability orders. Probab. Eng. Inform. Sci. 12, 1–23] and Fernández-Ponce and Suárez-Llorens [2003. A multivariate dispersion ordering based on quantiles more widely separated. J. Multivariate Anal. 85, 40–53]. In order to reach our objective we define a new weaker multivariate dispersive notion. Random vectors with a common copula and positive dependence properties are analyzed.