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Maximum entropy estimation of income share function from generalized Gini index

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  • N. Nakhaei Rad
  • G.R. Mohtashami Borzadaran
  • G.H. Yari

Abstract

Following Sir Anthony and Atkinson who started thinking about the insensitivity of the Gini index to income shares of the lower and the upper income groups, a generalization of the classical Gini index was introduced by Kakwani, Donaldson, Weymark and Yitzhaki which is sensitive to both high and low incomes. In this paper, the maximum entropy method is used to estimate the underlying true income share function based on the limited information of the generalized Gini index about the income shares of a population's percentiles. The income share function is estimated through maximizing both the Shannon entropy and the second-order entropy. In the end, through parametric bootstrap and analyzing a real dataset, the results are compared with the estimator of the share function, which is obtained based on the total information. In contrast to the classic Gini index, the derived share function based on the generalized Gini index provides more accurate approximations for income shares of the lower and the upper percentiles.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:16:p:2910-2921
    DOI: 10.1080/02664763.2016.1155112
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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. 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.

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