Probability in the Engineering & Informational Sciences
Multivariate analysis, Variables (Mathematics), Stochastic orders
To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.
Khaledi, E. and Kochar, S. (2005). Dependence, dispersiveness, and multivariate hazard rate ordering. Probability in the Engineering and Informational Sciences, 19, pp 427-446.