Some Related Orderings

Abstract

In this chapter we consider certain partial orders defined on L (the class of non-negative random variables with positive finite expections) that are closely related to the Lorenz ordering (Chapter 3). The first, *-ordering, is often easier to deal with than Lorenz ordering, and can sometimes be used to verify Lorenz ordering which it implies. The other group of partial orderings to be discussed are those known as stochastic dominance of degree k, k=l,2,.... Degree 1 is just stochastic ordering. Degree 2 is intimately related to the Lorenz order, but distinct. Higher degree stochastic orders are most frequently encountered in economic contexts. The treatment provided here is brief.