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The Asymptotic Distribution of the S–Gini Index

Author

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  • Ričardas Zitikis
  • Joseph L. Gastwirth

Abstract

Several generalizations of the classical Gini index, placing smaller or greater weights on various portions of income distribution, have been proposed by a number of authors. For purposes of statistical inference, the large sample distribution theory of the estimators of those measures of economic inequality is required. The present paper was stimulated by the use of bootstrap by Xu (2000) to estimate the variance of the estimator of the S–Gini index. It shows that the theory of L–statistics (Chernoff, Gastwirth & Johns, 1967; Shorack & Wellner, 1986) makes possible the construction of a consistent estimator for the S–Gini index and proof of its asymptotic normality. The paper also presents an explicit formula for the asymptotic variance. The formula should be helpful in planning the size of samples from which the S–Gini index can be estimated with a prescribed margin of error.

Suggested Citation

  • Ričardas Zitikis & Joseph L. Gastwirth, 2002. "The Asymptotic Distribution of the S–Gini Index," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(4), pages 439-446, December.
  • Handle: RePEc:bla:anzsta:v:44:y:2002:i:4:p:439-446
    DOI: 10.1111/1467-842X.00245
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    Citations

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    Cited by:

    1. Agostino Tarsitano, 2004. "A new class of inequality measures based on a ratio of L-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 137-160.
    2. Francis Bilson Darku & Frank Konietschke & Bhargab Chattopadhyay, 2020. "Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data," Econometrics, MDPI, vol. 8(2), pages 1-20, June.
    3. Andrew Leigh, 2005. "Can Redistributive State Taxes Reduce Inequality?," CEPR Discussion Papers 490, Centre for Economic Policy Research, Research School of Economics, Australian National University.
    4. 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.
    5. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    6. 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.
    7. Michael Beenstock & Daniel Felsenstein, 2007. "Mobility and Mean Reversion in the Dynamics of Regional Inequality," International Regional Science Review, , vol. 30(4), pages 335-361, October.
    8. N. Nakhaei Rad & G.R. Mohtashami Borzadaran & G.H. Yari, 2016. "Maximum entropy estimation of income share function from generalized Gini index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2910-2921, December.
    9. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.

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