CALCULATING THE EXTENDED GINI COEFFICIENT FROM GROUPED DATA - A COVARIANCE PRESENTATION.

The basic approach to estimating the Gini and extended Gini indices is to approximate the Lorenz curve by a number of linear segments, and then estimate the Gini coefficients as the areas (or weighted areas) between the linear segments and the 45-degree line. We show that the estimator for the extended Gini, obtained from the Lorenz curve (Chotikapanich and Griffiths, 2001) is algebraically identical to a covariance-based estimator. The advantages of the covariance-based estimators are twofold; first, they are easy to compute, using any standard statistical software, and second, the covariance-based estimators allow for the decomposition of the Gini index of a sum of variables (or populations). [ABSTRACT FROM AUTHOR]