Published

2014-07-01

The Graphical Representation of Inequality

La representación gráfica de la desigualdad

DOI:

https://doi.org/10.15446/rce.v37n2spe.47947

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)

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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.

https://doi.org/10.15446/rce.v37n2spe.47947

The Graphical Representation of Inequality

La representación gráfica de la desigualdad

ALBERTO ARCAGNI1, FRANCESCO PORRO2

1Università degli Studi di Milano-Bicocca, Dipartimento di Statistica e Metodi Quantitativi, Italy. Professor. Email: alberto.arcagni@unimib.it
2Università degli Studi di Milano-Bicocca, Dipartimento di Statistica e Metodi Quantitativi, Italy. Professor. Email: francesco.porro1@unimib.it

Abstract

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.

Key words: Bonferroni Curve, Inequality Index, Income Distribution, Lorenz Curve, Zenga Inequality Curve.

Resumen

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.

Palabras clave: curva de Bonferroni, curva de Lorenz, curva de Zenga, distribución del ingreso, índice de desigualdad.

Texto completo disponible en PDF

References

1. Arcagni, A. & Porro, F. (2013), 'On the parameters of Zenga distribution', Statistical Methods & Applications 22(3), 285-303.

2. 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.

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

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

5. 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?id9eckNAEACAAJ

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

7. Gastwirth, J. (1972), 'The estimation of the Lorenz curve and Gini index', The Review of Economics and Statistics 54(3), 306-316.

8. 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.

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

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

11. Greselin, F., Pasquazzi, L. & Zitikis, Ri\vcardas (2013), 'Contrasting the Gini and Zenga indices of economic inequality', Journal of Applied Statistics 40(2), 282-297.

12. 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.

13. Lorenz, M. (1905), 'Methods of measuring the concentration of wealth', Publications of the American Statistical Association 9(70), 209-219.

14. 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.

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

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

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

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

19. R Core Team, (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. *http://www.R-project.org/

20. 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.

21. Tarsitano, A. (1990), The Bonferroni index of income inequality, 'Income and Wealth Distribution, Inequality and Poverty', C. Dagum and M. Zenga, Berlin, p. 228-242.

22. Zenga, M.M. (1984), 'Tendenza alla massima ed alla minima concentrazione per variabili casuali continue', Statistica 44(4), 619-640.

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

24. Zenga, M. (2010), 'Mixture of Polisicchio's truncated Pareto distributions with beta weights', Statistica & Applicazioni {8}(1), 3-25.

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

[Recibido en mayo de 2014. Aceptado en septiembre de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n2a09,
    AUTHOR  = {Arcagni, Alberto and Porro, Francesco},
    TITLE   = {{The Graphical Representation of Inequality}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {2},
    pages   = {419-437}
}

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.

How to Cite

APA

Arcagni, A. and Porro, F. (2014). The Graphical Representation of Inequality. Revista Colombiana de Estadística, 37(2Spe), 419–436. https://doi.org/10.15446/rce.v37n2spe.47947

ACM

[1]
Arcagni, A. and Porro, F. 2014. The Graphical Representation of Inequality. Revista Colombiana de Estadística. 37, 2Spe (Jul. 2014), 419–436. DOI:https://doi.org/10.15446/rce.v37n2spe.47947.

ACS

(1)
Arcagni, A.; Porro, F. The Graphical Representation of Inequality. Rev. colomb. estad. 2014, 37, 419-436.

ABNT

ARCAGNI, A.; PORRO, F. The Graphical Representation of Inequality. Revista Colombiana de Estadística, [S. l.], v. 37, n. 2Spe, p. 419–436, 2014. DOI: 10.15446/rce.v37n2spe.47947. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/47947. Acesso em: 7 jun. 2024.

Chicago

Arcagni, Alberto, and Francesco Porro. 2014. “The Graphical Representation of Inequality”. Revista Colombiana De Estadística 37 (2Spe):419-36. https://doi.org/10.15446/rce.v37n2spe.47947.

Harvard

Arcagni, A. and Porro, F. (2014) “The Graphical Representation of Inequality”, Revista Colombiana de Estadística, 37(2Spe), pp. 419–436. doi: 10.15446/rce.v37n2spe.47947.

IEEE

[1]
A. Arcagni and F. Porro, “The Graphical Representation of Inequality”, Rev. colomb. estad., vol. 37, no. 2Spe, pp. 419–436, Jul. 2014.

MLA

Arcagni, A., and F. Porro. “The Graphical Representation of Inequality”. Revista Colombiana de Estadística, vol. 37, no. 2Spe, July 2014, pp. 419-36, doi:10.15446/rce.v37n2spe.47947.

Turabian

Arcagni, Alberto, and Francesco Porro. “The Graphical Representation of Inequality”. Revista Colombiana de Estadística 37, no. 2Spe (July 1, 2014): 419–436. Accessed June 7, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/47947.

Vancouver

1.
Arcagni A, Porro F. The Graphical Representation of Inequality. Rev. colomb. estad. [Internet]. 2014 Jul. 1 [cited 2024 Jun. 7];37(2Spe):419-36. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/47947

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CrossRef citations19

1. Joseph L. Gastwirth. (2016). Measures of Economic Inequality Focusing on the Status of the Lower and Middle Income Groups. Statistics and Public Policy, 3(1), p.1. https://doi.org/10.1080/2330443X.2016.1213148.

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8. Shahryar Mirzaei, S. M. A. Jahanshahi. (2022). A New Goodness of Fit Measure Based on Income Inequality Curves. Journal of Modern Applied Statistical Methods, 19(1), p.2. https://doi.org/10.22237/jmasm/1619482080.

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