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Calculating the Extended Gini Coefficient From Grouped Data - A Covariance Presentation

Edna Schechtman, Shlomo Yitzhaki

Abstract


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).

Keywords


Gini index, Lorenz curve, Grouped data

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