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Histogram-based interpolation of the Lorenz curve and Gini index for grouped data
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 which takes the intra-class variability into account.
   
Keywords income distribution, inequality, Gini index, Lorenz curve
   
Citation Tillé, Y., & Langel, M. (2012). Histogram-based interpolation of the Lorenz curve and Gini index for grouped data. The American Statistician, 66(4), 225-231.
   
Type Journal article (English)
Date of appearance 1-10-2012
Journal The American Statistician
Volume 66
Issue 4
Pages 225-231
URL http://amstat.tandfonline.com/doi/full/10.1080/00031305.2...