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Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures

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  • Benito Frosini

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  • Benito Frosini, 2012. "Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures," Empirical Economics, Springer, vol. 43(1), pages 175-197, August.
    • Handle: RePEc:spr:empeco:v:43:y:2012:i:1:p:175-197
    DOI: 10.1007/s00181-011-0464-1
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    1. Zagier, Don, 1983. "Inequalities for the Gini coefficient of composite populations," Journal of Mathematical Economics, Elsevier, vol. 12(2), pages 103-118, October.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Bourguignon, Francois, 1979. "Decomposable Income Inequality Measures," Econometrica, Econometric Society, vol. 47(4), pages 901-920, July.
    4. Dagum, Camilo, 1997. "A New Approach to the Decomposition of the Gini Income Inequality Ratio," Empirical Economics, Springer, vol. 22(4), pages 515-531.
    5. Frank A. Cowell, 1980. "On the Structure of Additive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(3), pages 521-531.
    6. Deutsch, Joseph & Silber, Jacques, 1997. "Gini's "Transvariazione" and the Measurement of Distance between Distributions," Empirical Economics, Springer, vol. 22(4), pages 547-554.
    7. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    8. Benito V. Frosini, 2005. "Inequality measures for histograms," Statistica, Department of Statistics, University of Bologna, vol. 65(1), pages 27-40.
    9. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    10. Masato Okamoto, 2009. "Decomposition of gini and multivariate gini indices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(2), pages 153-177, June.
    11. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    12. Shlomo Yitzhaki & Robert I. Lerman, 1991. "Income Stratification And Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
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    Cited by:

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    2. Alex Cobham, Andy Sumner, 2013. "Is It All About the Tails? The Palma Measure of Income Inequality-Working Paper 343," Working Papers 343, Center for Global Development.
    3. E. Gómez-Déniz, 2016. "A family of arctan Lorenz curves," Empirical Economics, Springer, vol. 51(3), pages 1215-1233, November.
    4. Alex Cobham & Lukas Schlögl & Andy Sumner, 2016. "Inequality and the Tails: the Palma Proposition and Ratio," Global Policy, London School of Economics and Political Science, vol. 7(1), pages 25-36, February.
    5. Alex Cobham & Andrew Sumner, 2013. "Is it all about the tails? The Palma measure of income inequality," Working Papers 308, ECINEQ, Society for the Study of Economic Inequality.
    6. Muszyńska Joanna & Oczki Jarosław & Wędrowska Ewa, 2018. "Income Inequality in Poland and the United Kingdom. Decomposition of the Theil Index," Folia Oeconomica Stetinensia, Sciendo, vol. 18(1), pages 108-122, June.
    7. Delalić Adela & Čurković Maja & Antić Josipa, 2018. "The Croatian banking system total assets concentration dynamics: performing a variety of inequality measures," Croatian Review of Economic, Business and Social Statistics, Sciendo, vol. 4(1), pages 14-26, June.
    8. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    9. Michele Costa, 2016. "Overlapping component and inequality decomposition: a simulation study for the Gini index," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 193-205, August.
    10. Francesca Battisti & Francesco Porro, 2023. "A multi-decomposition of Zenga-84 inequality index: an application to the disparity in CO $$_2$$ 2 emissions in European countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 957-981, September.
    11. Ausloos, Marcel, 2020. "Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. Francesco Porro & Mariangela Zenga, 2023. "Decompositions by sources and by subpopulations of the Pietra index: two applications to professional football teams in Italy," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 73-100, March.
    13. M. Costa, 2019. "The evaluation of gender income inequality by means of the Gini index decomposition," Working Papers wp1130, Dipartimento Scienze Economiche, Universita' di Bologna.
    14. Maria Giovanna Monti & Simone Pellegrino & Achille Vernizzi, 2015. "On Measuring Inequity in Taxation Among Groups of Income Units," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(1), pages 43-58, March.
    15. Francesco Porro & Michele Zenga, 2020. "Decomposition by subpopulations of the Zenga-84 inequality curve and the related index $$\zeta $$ζ: an application to 2014 Bank of Italy survey," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 187-207, March.
    16. Michele Zenga, 2016. "On the decomposition by subpopulations of the point and synthetic Zenga (2007) inequality indexes," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 375-405, December.

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    More about this item

    Keywords

    Income inequality; Gini; Pietra–Ricci and Theil indices; Decomposition of inequality measures; C46; D31;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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