Histogram-Based Interpolation of the Lorenz Curve and Gini Index for Grouped Data

Yves Tillé and Matti Langel

The American Statistician, 2012, vol. 66, issue 4, 225-231

Abstract: In grouped data, the estimation of the Lorenz curve without taking into account the within-class variability leads to an overestimation of the curve and an underestimation of the Gini index. We propose a new strictly convex estimator of the Lorenz curve derived from a linear interpolation-based approximation of the cumulative distribution function. Integrating the Lorenz curve, a correction can be derived for the Gini index that takes the intraclass variability into account.

Date: 2012
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DOI: 10.1080/00031305.2012.734197

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