The classical Lorenz curve is often used to depict inequality in a population of incomes, and the associated Gini coefficient is relied upon to make comparisons between different countries and other groups. The sample estimates of these moment-based concepts are sensitive to outliers and so we investigate the extent to which quantile-based versions can capture income inequality and lead to robust procedures. Distribution-free interval estimates of the associated coefficients of inequality are obtained, as well as sample sizes required to estimate them to a given accuracy. Convexity, transference and robustness of the measures are examined and illustrated.
"Quantile versions of the Lorenz curve." Electron. J. Statist. 10 (2) 1896 - 1926, 2016. https://doi.org/10.1214/16-EJS1154