The Barycenter of the Distribution and Its Application to the Measurement of Inequality: The Balance of Inequality, the Gini Index, and the Lorenz Curve

90 Pages Posted: 18 Mar 2022 Last revised: 23 Mar 2022

See all articles by Giorgio Di Maio

Giorgio Di Maio

University of Insubria - Department of Economics

Date Written: March 17, 2022

Abstract

This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable and explores its relation with the Gini index, the concentration area, and the Gini’s mean difference. The introduction of the barycenter allows for new economic, geometrical, physical, and statistical interpretations of these measures. For income distributions, the barycenter represents the expected recipient of one unit of income, as if the stochastic process that leads to the distribution of the total income among the population was observable as it unfolds. The barycenter splits the population into two groups, which can be considered as “the winners” and “the losers” in the income distribution, or “the rich” and “the poor”. We provide examples of application to thirty theoretical distributions and an empirical application with the estimation of personal income inequality in Luxembourg Income Study Database’s countries. We conclude that the barycenter is a new measure of the location or central tendency of distributions, which may have wide applications in both economics and statistics.

Keywords: Balance of Inequality, Balance of Inequality index, Barycenter, BOI index, Concentration, Concentration area, Concentration ratio, Gini index, Gini mean difference, Inequality, Income inequality, Lorenz curve, Pen parade, Quantile function.

JEL Classification: C10, C18, D31, D63

Suggested Citation

Di Maio, Giorgio, The Barycenter of the Distribution and Its Application to the Measurement of Inequality: The Balance of Inequality, the Gini Index, and the Lorenz Curve (March 17, 2022). University of Milan Bicocca Department of Economics, Management and Statistics Working Paper No. 493, Available at SSRN: https://ssrn.com/abstract=4060273

Giorgio Di Maio (Contact Author)

University of Insubria - Department of Economics ( email )

Via Monte Generoso 71
Varese, 21 100
Italy

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
35
Abstract Views
166
PlumX Metrics