Multivariate Lorenz Dominance Based On Zonoids

摘要

The classical Lorenz curve visualizes and measures the disparity of items which are characterized by a single variable: The more the curve bends, the more scatter the data. Recently a general approach has been proposed and investigated that measures the disparity of multidimensioned items regardless of their dimension.rnThis paper surveys various generalizations of Lorenz curve and Lorenz dominance for multidimensional data. Firstly, the Lorenz zonoid of multivariate data and, more general, of a random vector is introduced. Then three multivariate extensions of univariate Lorenz dominance are surveyed and contrasted, the set inclusion of lift zonoids, the scaled convex order, and the price Lorenz order. The latter is based on the set inclusion of extended Lorenz zonoids. Finally, a decomposition of the multivariate volume-Gini mean difference is given.