New properties and characterizations of the dispersive ordering

Abstract

New characterizations of the dispersive ordering are established. These include a characterization in terms of the stochastic ordering of the sample spacings, preservation of the ordering by monotone convex (concave) transformations, and preservation of the ordering by truncation at the same quantile. The question of when the sample spacings inherit the dispersive ordering is investigated and, for the important special case of F or G being the exponential distribution, it is shown that F and G are ordered in dispersion if and only if the sample spacings also have the same order.