Measuring inequality and social welfare from any arbitrary distribution

Abstract

Different measures of inequality such as the Lorenz curve, the generalised Lorenz curve (GLC) and the cumulated mean income curve (COMIC) are obtained for any univariate continuous distribution. GLC and COMIC are used to identify the best income distribution on welfare grounds when the ordinary Lorenz curves fail to work. Explicit expressions for the moments of a given Lorenz curve are also derived. The proposed method selects the appropriate generalised lambda distribution (GLD) representation corresponding to a given distribution under consideration and computes the different measures of inequality. A numerical illustration of the results, using per capita domestic product at current prices for various states/union territories of India for two periods 1994–95 and 2000–01, is also provided. © 2010, Brazilian Statistical Association. All rights reserved.