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A universal model for the Lorenz curve with novel applications for datasets containing zeros and/or exhibiting extreme inequality

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  • Thitithep Sitthiyot
  • Kanyarat Holasut

Abstract

Given that the existing parametric functional forms for the Lorenz curve do not fit all possible size distributions, a universal parametric functional form is introduced. By using the empirical data from different scientific disciplines and also the hypothetical data, this study shows that, the proposed model fits not only the data whose actual Lorenz plots have a typical convex segment but also the data whose actual Lorenz plots have both horizontal and convex segments practically well. It also perfectly fits the data whose observation is larger in size while the rest of observations are smaller and equal in size as characterized by 2 positive-slope linear segments. In addition, the proposed model has a closed-form expression for the Gini index, making it computationally convenient to calculate. Considering that the Lorenz curve and the Gini index are widely used in various disciplines of sciences, the proposed model and the closed-form expression for the Gini index could be used as alternative tools to analyze size distributions of non-negative quantities and examine their inequalities or unevennesses.

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  • Thitithep Sitthiyot & Kanyarat Holasut, 2023. "A universal model for the Lorenz curve with novel applications for datasets containing zeros and/or exhibiting extreme inequality," Papers 2304.13934, arXiv.org.
    • Handle: RePEc:arx:papers:2304.13934
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    1. Kakwani, N C & Podder, N, 1973. "On the Estimation of Lorenz Curves from Grouped Observations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 278-292, June.
    2. Ortega, P, et al, 1991. "A New Functional Form for Estimating Lorenz Curves," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(4), pages 447-452, December.
    3. Ogwang, Tomson & Gouranga Rao, U. L., 1996. "A new functional form for approximating the Lorenz curve," Economics Letters, Elsevier, vol. 52(1), pages 21-29, July.
    4. P. Ortega & G. Martín & A. Fernández & M. Ladoux & A. García, 1991. "A New Functional Form For Estimating Lorenz Curves," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(4), pages 447-452, December.
    5. Gupta, Manash Ranjan, 1984. "Functional Form for Estimating the Lorenz Curve," Econometrica, Econometric Society, vol. 52(5), pages 1313-1314, September.
    6. Kakwani, Nanak C & Podder, N, 1976. "Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations," Econometrica, Econometric Society, vol. 44(1), pages 137-148, January.
    7. Basmann, R. L. & Hayes, K. J. & Slottje, D. J. & Johnson, J. D., 1990. "A general functional form for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 77-90.
    8. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
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