Variability orders and mean differences

Abstract

Several well-known stochastic orderings are defined in terms of iterated integrals of distribution or survival functions. In this note we will provide necessary conditions for some variability orderings of the above type. These conditions will be based on the comparison of mean differences, which will be written by using the iterated integrals of survival and distribution functions. An interesting by-product of this idea is a curious formula for the variance. A bivariate version of the above results will be provided, as well.