Published

2014-07-01

The Graphical Representation of Inequality

La representación gráfica de la desigualdad

Keywords:

Bonferroni Curve, Inequality Index, Income Distribution, Lorenz Curve, Zenga Inequality Curve (en)
Curva de Bonferroni, Curva de Lorenz, Curva de Zenga, Distribución del ingreso, índice de desigualdad (es)

Downloads

Authors

  • Alberto Arcagni Università degli Studi di Milano-Bicocca
  • Francesco Porro Università degli Studi di Milano-Bicocca

As of the past century, the analysis and the graphical representation of inequality play a very important role in economics. In the literature, several curves have been proposed and developed to simplify the description of inequality. The aim of this paper is a review and a comparison of the most known inequality curves, evaluating the features of each, with a particular focus on interpretation.

Desde el siglo pasado el análisis y representación gráfica de la desigualdad juega un papel importante en la economía. En la literatura varias curvas han sido propuestas y desarrolladas para simplificar la descripción de la desigualdad. El objetivo de este artículo es revisar y comparar las curvas de la desigualdad más conocidas evaluando sus características y enfocándose en su interpretación.

Downloads

Download data is not yet available.

References

Arcagni, A. & Porro, F. (2013), ‘On the parameters of Zenga distribution’, Statistical Methods & Applications 22(3), 285–303.

Arcagni, A. & Zenga, M. (2013), ‘Application of Zenga’s distribution to a panel survey on household incomes of European Member States’, Statistica & Applicazioni 11(1), 79–102.

Bank of Italy (2012), ‘Indagine sui bilanci delle famiglie italiane’. *http://www.bancaditalia.it/statistiche/storiche

Bonferroni, C. (1930), Elementi di Statistica Generale, Seeber, Firenze.

Dagum, C. (1977), A New Model of Personal Income Distribution : Specification and Estimation, Cahier de recherche, University of Ottawa, Faculty of Social Sciences, Department of Economics.

*http://books.google.com.co/books?id=9eckNAEACAAJ

De Vergottini, M. (1940), ‘Sul significato di alcuni indici di concentrazione’, Annali di Economia Nuova Serie 2(5/6), 317–347.

Gastwirth, J. (1972), ‘The estimation of the Lorenz curve and Gini index’, The Review of Economics and Statistics 54(3), 306–316.

Gini, C. (1914), ‘Sulla misura della concentrazione e della variabilità dei caratteri’, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 73, 1203–1248.

Giorgi, G. & Crescenzi, M. (2001), ‘A look at Bonferroni inequality measure in a reliability framework’, Statistica 41, 571–583.

Greselin, F. & Pasquazzi, L. (2009), ‘Asymptotic confidence intervals for a new inequality measure’, Communications in Statistics-Simulation and Computation 38(8), 1742–1756.

Greselin, F., Pasquazzi, L. & Zitikis, R. (2013), ‘Contrasting the Gini and Zenga indices of economic inequality’, Journal of Applied Statistics 40(2), 282–297.

Langel, M. & Tillé, Y. (2012), ‘Inference by linearization for Zenga’s new inequality index: A comparison with the Gini index’, Metrika 75(8), 1093–1110.

Lorenz, M. (1905), ‘Methods of measuring the concentration of wealth’, Publications of the American Statistical Association 9(70), 209–219.

Pietra, G. (1915), ‘Delle relazioni fra indici di variabilità note I e II’, Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 74(2), 775–804.

Polisicchio, M. (2008), ‘The continuous random variable with uniform point inequality measure I(p)’, Statistica & Applicazioni 6(2), 137–151.

Polisicchio, M. & Porro, F. (2011), ‘A comparison between Lorenz L(p) curve and Zenga I(p) curve’, Statistica Applicata 21(3-4), 289–301.

Porro, F. (2008), Equivalence between partial order based on curve L(p) and partial order based on curve I(p), in ‘Proceedings of SIS 2008’, Padova.

Pundir, S., Arora, S. & Jain, K. (2005), ‘Bonferroni curve and the related statistical inference’, Statistics & Probability Letters 75(2), 140–150.

R Core Team (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.

*http://www.R-project.org/

Radaelli, P. (2010), ‘On the decomposition by subgroups of the Gini index and Zenga’s uniformity and inequality indexes’, International Statistical Review 78(1), 81–101.

Tarsitano, A. (1990), The Bonferroni index of income inequality, in ‘Income and Wealth Distribution, Inequality and Poverty’, C. Dagum and M. Zenga, Berlin, pp. 228–242.

Zenga, M. (1984), ‘Tendenza alla massima ed alla minima concentrazione per variabili casuali continue’, Statistica 44(4), 619–640.

Zenga, M. (2007), ‘Inequality curve and inequality index based on the ratios between lower and upper arithmetic means’, Statistica & Applicazioni 5(1), 3– 27.

Zenga, M. (2010), ‘Mixture of Polisicchio’s truncated Pareto distributions with beta weights’, Statistica & Applicazioni 8(1), 3–25.

Zenga, M. (2013), ‘Decomposition by sources of the Gini, Bonferroni and Zenga inequality indexes’, Statistica & Applicazioni 11(2), 133–161.