Abstract: The purpose of this paper is to derive analytic expressions for the multivariate Lorenz
surface for a relevant type of models based on the class of distributions with given marginals described
by Sarmanov and Lee. The expression of the bivariate Lorenz surface can be conveniently interpreted
as the convex linear combination of products of classical and concentrated univariate Lorenz curves.
Thus, the generalized Gini index associated with this surface is expressed as a function of marginal
Gini indices and concentration indices. This measure is additively decomposable in two factors,
corresponding to inequality within and between variables. We present different parametric models
using several marginal distributions including the classical Beta, the GB1, the Gamma, the lognormal
distributions and others. We illustrate the use of these models to measure multidimensional inequality
using data on two dimensions of well-being, wealth and health, in five developing countries
