Stochastic Comparisons of Some Distances between Random Variables

Abstract

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

On the second-order excess wealth order and its properties

“…Furthermore, Fernández-Ponce et al [16] proposed and studied a multivariate generalization of the excess wealth function and used it for a multivariate stochastic comparison. Ortega-Jiménez et al [28] have used the excess wealth order in providing sufficient conditions for comparing several distances between pairs of random variables.…”