Multivariate Lorenz dominance based on zonoids

Multivariate Lorenz order, Directional majorization, Price Lorenz order, Generalized Lorenz function, Multidimensioned Gini index,

Multivariate Gini Indices

Two extensions of the univariate Gini index are considered:RD, based on expected distance between two independent vectors from the same distribution with finite mean[mu][set membership, variant]d; andRV, related to the expected volume of the simplex formed fromd+1 independent such vectors. A new characterization ofRDas proportional to a univariate Gini index for a particular linear combination of attributes relates it to the Lorenz zonoid. TheLorenz zonoidwas suggested as a multivariate generalization of the Lorenz curve.RVis, up to scaling, the volume of the Lorenz zonoid plus a unit cube of full dimension. Whend=1, bothRDandRVequal twice the area between the usual Lorenz curve and the line of zero disparity. Whend>1, they are different, but inherit properties of the univariate Gini index and are related via the Lorenz zonoid:RDis proportional to the average of the areas of some two-dimensioned projections of the lift zonoid, whileRVis the average of the volumes of projections of the Lorenz zonoid over all coordinate subspaces.dilation disparity measurement Gini mean difference lift zonoid Lorenz order

Restricted Lorenz dominance of economic inequality in one and many dimensions

The paper investigates Lorenz dominance and generalized Lorenz dominance to compare distributions of economic status in one and several attributes. Restrictions of these dominance relations are developed that focus on central parts of the distributions and facilitate their comparison. Copyright Kluwer Academic Publishers 2005inequality measurement, lift zonoid order, Lorenz order, majorization, multivariate inequality ordering,

Restricted Lorenz dominance of economic inequality in one and many dimensions

The paper investigates Lorenz dominance and generalized Lorenz dominance to compare distributions of economic status in one and several attributes. Restrictions of these dominance relations are developed that focus on central parts of the distributions and facilitate their comparison. Copyright Kluwer Academic Publishers 2004inequality measurement, lift zonoid order, Lorenz order, majorization, multivariate inequality ordering,

A vector valued bivariate gini index for truncated distributions

Disparity measurement, Gini index, Vector valued failure rate, Truncated distributions, Characterization of probability distributions,

Constructing indices of multivariate polarization

Polarization index, Decomposable inequality indices, Multidimensional inequality, Multivariate social evaluation, C43, D63,