The Barycenter of the Distribution and Its Application to the Measurement of Inequality : The Balance of Inequality, the Gini Index, and the Lorenz Curve
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
In: University of Milan Bicocca Department of Economics, Management and Statistics Working Paper No. 493
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments March 17, 2022 erstellt
Classification:
C10 - Econometric and Statistical Methods: General. General ; c18 ; D31 - Personal Income, Wealth and Their Distributions ; D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement