The Lorenz curve is a graphical tool that is widely used to characterize the concentration of a measure in a population, such as wealth. It is frequently the case that the measure of interest used to rank experimental units when estimating the empirical Lorenz curve, and the corresponding Gini coefficient, is subject to random error. This error can result in an incorrect ranking of experimental units which inevitably leads to a curve that exaggerates the degree of concentration (variation) in the population. We explore this bias and discuss several widely available statistical methods that have the potential to reduce or remove the bias in the empirical Lorenz curve. The properties of these methods are examined and compared in a simulation study. This work is motivated by a health outcomes application which seeks to assess the concentration of black patient visits among primary care physicians. The methods are illustrated on data from this study.
Health Services Research
Moskowitz, Chaya S.; Venkatraman, E. S.; Riedel, Elyn; and Begg, Colin B., "Estimating the Empirical Lorenz Curve and Gini Coefficient in the Presence of Error" (January 2007). Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series. Working Paper 12.