Characterization of stochastic orders by L-functionals

Random variables may be compared with respect to their location by comparing certain functionals ad hoc, such as the mean or median, or by means of stochastic ordering based directly on the properties of the corresponding distribution functions. These alternative approaches are brought together in this paper. We focus on the class of L-functionals discussed by Bickel and Lehmann (1975) and characterize the comparison of random variables in terms of these measures by means of several stochastic orders based on iterated integrals, including the increasing convex order.