Multidimensional inequalities and generalized quantile functions

Abstract

In this paper, we extend the generalized Yaari dual theory for multidimen-sional distributions, in the vein of Galichon and Henry's paper [6]. We show how a class of generalized quantiles-which encompasses Galichon and Henry's one or multivariate quantile transform [7] [4] [9]-allows to derive a general representation theorem. Moreover, we derive from this representation theorem a formula which could be applicable to multidimensional measure of inequality.