Estimating Lorenz Curves Using a Dirichlet Distribution
AbstractThe 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 InfoPaper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 802.
Length: 21 pages
Date of creation: 2001
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Gini coefficient; maximum likelihood estimation;
Other versions of this item:
- Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-95, April.
- Duangkamon Chotikapanich & William E. Griffiths, 2000. "Estimating Lorenz Curves Using a Dirichlet Distribution," Econometric Society World Congress 2000 Contributed Papers 1215, Econometric Society.
- C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
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