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Estimating Lorenz Curves Using a Dirichlet Distribution

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  • Chotikapanich, Duangkamon
  • Griffiths, William E

Abstract

The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares, estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology that recognises the cumulative proportional nature of the Lorenz curve data by assuming that the income proportions are distributed as a Dirichlet distribution. Five Lorenz-curve specifications are used to demonstrate the technique. Maximum likelihood estimates under the Dirichlet distribution assumption provide better-fitting Lorenz curves than nonlinear least squares and another estimation technique that has appeared in the literature.

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Bibliographic Info

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 20 (2002)
Issue (Month): 2 (April)
Pages: 290-95

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Handle: RePEc:bes:jnlbes:v:20:y:2002:i:2:p:290-95

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References

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Cited by:
  1. Chiara Gigliarano & Pietro Muliere, 2013. "Estimating the Lorenz curve and Gini index with right censored data: a Polya tree approach," METRON, Springer, vol. 71(2), pages 105-122, September.
  2. Heshmati, Almas, 2004. "A Review of Decomposition of Income Inequality," IZA Discussion Papers 1221, Institute for the Study of Labor (IZA).
  3. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
  4. Heshmati, Almas, 2004. "Inequalities and Their Measurement," IZA Discussion Papers 1219, Institute for the Study of Labor (IZA).
  5. T. Kämpke & R. Pestel & F.J. Radermacher, 2003. "A Computational Concept for Normative Equity," European Journal of Law and Economics, Springer, vol. 15(2), pages 129-163, March.
  6. José M.R. Murteira & Joaquim J.S. Ramalho, 2013. "Regression Analysis of Multivariate Fractional Data," CEFAGE-UE Working Papers 2013_05, University of Evora, CEFAGE-UE (Portugal).

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