Quantile Versions of the Lorenz Curve

TL;DR

This paper introduces quantile-based versions of the Lorenz curve and Gini coefficient to provide more robust measures of income inequality less sensitive to outliers, with distribution-free estimation methods and analysis of their properties.

Contribution

It develops distribution-free, quantile-based inequality measures and investigates their convexity, transference, robustness, and sample size requirements, offering an alternative to classical moment-based methods.

Findings

Quantile-based inequality measures are more robust to outliers.

Distribution-free estimates of these measures are derived.

Sample size requirements for accurate estimation are provided.

Abstract

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 definitions can capture income inequality and lead to more robust procedures. Distribution-free estimates of the corresponding 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.