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A characterization of income distributions in terms of generalized Gini coefficients

Author

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  • Samuel Kotz

    (Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC, USA)

  • Christian Kleiber

    (Fachbereich Statistik, Universität Dortmund, D-44221 Dortmund, Germany)

Abstract

Most commonly used parametric models for the size distribution of incomes possess only a few finite moments, and hence cannot be characterized by the sequence of their moments. However, all income distributions with a finite mean can be characterized by the sequence of first moments of the order statistics. This is an attractive feature since the generalized Gini coefficients of Kakwani (1980), Donaldson and Weymark (1980, 1983) and Yitzhaki (1983) are simple functions of expectations of sample minima. We present results which streamline these characterizations motivated by Aaberge (2000).

Suggested Citation

  • Samuel Kotz & Christian Kleiber, 2002. "A characterization of income distributions in terms of generalized Gini coefficients," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(4), pages 789-794.
    • Handle: RePEc:spr:sochwe:v:19:y:2002:i:4:p:789-794
    Note: Received: 8 March 2001/Accepted: 31 July 2001
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    Citations

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    Cited by:

    1. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2017. "Maximum Tsallis entropy with generalized Gini and Gini mean difference indices constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 554-560.
    2. Giovanni Maria Giorgi & Paola Palmitesta & Corrado Provasi, 2006. "Asymptotic and bootstrap inference for the generalized Gini indices," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 107-124.
    3. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, Jafar, 2018. "New functional forms of Lorenz curves by maximizing Tsallis entropy of income share function under the constraint on generalized Gini index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 280-288.
    4. Tam'as S. Bir'o & Zolt'an N'eda, 2020. "Gintropy: Gini index based generalization of Entropy," Papers 2007.04829, arXiv.org.
    5. Kleiber, Christian, 2005. "The Lorenz curve in economics and econometrics," Technical Reports 2005,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Florent Bresson, 2010. "A general class of inequality elasticities of poverty," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(1), pages 71-100, March.
    7. José Manuel Gavilan-Ruiz & África Ruiz-Gándara & Francisco Javier Ortega-Irizo & Luis Gonzalez-Abril, 2024. "Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index," Stats, MDPI, vol. 7(4), pages 1-12, November.
    8. Meishu Wang & Hui Gong, 2019. "Expected Rural Wastewater Treatment Promoted by Provincial Local Discharge Limit Legislation in China," Sustainability, MDPI, vol. 11(10), pages 1-13, May.
    9. Marta Cardin & Bennett Eisenberg & Luisa Tibiletti, 2012. "Bid and Ask Prices Tailored to Traders' Risk Aversion and Gain Propension: a Normative Approach," International Journal of Business Research and Management (IJBRM), Computer Science Journals (CSC Journals), vol. 3(6), pages 294-306, December.
    10. Meishu Wang & Hui Gong, 2018. "Imbalanced Development and Economic Burden for Urban and Rural Wastewater Treatment in China—Discharge Limit Legislation," Sustainability, MDPI, vol. 10(8), pages 1-12, July.
    11. Christian Kleiber, 2014. "The Generalized Lognormal Distribution and the Stieltjes Moment Problem," Journal of Theoretical Probability, Springer, vol. 27(4), pages 1167-1177, December.
    12. Haim Shalit & Shlomo Yitzhaki, 2010. "How does beta explain stochastic dominance efficiency?," Review of Quantitative Finance and Accounting, Springer, vol. 35(4), pages 431-444, November.
    13. Xiao-jun Wang & Jian-yun Zhang & Shamsuddin Shahid & Amgad ElMahdi & Rui-min He & Xin-gong Wang & Mahtab Ali, 2012. "Gini coefficient to assess equity in domestic water supply in the Yellow River," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 17(1), pages 65-75, January.
    14. E. Schechtman & S. Yitzhaki, 2003. "A Family of Correlation Coefficients Based on the Extended Gini Index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(2), pages 129-146, August.
    15. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2015. "Entropy maximization under the constraints on the generalized Gini index and its application in modeling income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 657-666.
    16. Yuan, Qiang & McIntyre, Neil & Wu, Yipeng & Liu, Yichao & Liu, Yi, 2017. "Towards greater socio-economic equality in allocation of wastewater discharge permits in China based on the weighted Gini coefficient," Resources, Conservation & Recycling, Elsevier, vol. 127(C), pages 196-205.
    17. Shlomo Yitzhaki & Edna Schechtman, 2005. "The properties of the extended Gini measures of variability and inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 401-433.

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