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 assuming that 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 which recognizes the cumulative proportional nature of the Lorenz curve data by assuming that the proportion of income is distributed as a Dirichlet distribution. Five Lorenz-curve specifications were used to demonstrate the technique. Once a likelihood function and the posterior probability density function for each specification are derived we can use maximum likelihood or Bayesian estimation to estimate the parameters. Maximum likelihood estimates and Bayesian posterior probability density functions for the Gini coefficient are also obtained for each Lorenz-curve specification.
Download InfoTo our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of Business and Economic Statistics.
Volume (Year): 20 (2002)
Issue (Month): 2 (April)
Contact details of provider:
Web page: http://www.amstat.org/publications/jbes/index.cfm?fuseaction=main
Other versions of this item:
- Duangkamon Chotikapanich & William E. Griffiths, 2000. "Estimating Lorenz Curves Using a Dirichlet Distribution," Econometric Society World Congress 2000 Contributed Papers 1215, Econometric Society.
- Chotikapanich, D. & Griffiths, W., 2001. "Estimating Lorenz Curves Using a Dirichlet Distribution," Department of Economics - Working Papers Series 802, The University of Melbourne.
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- McDonald, James B. & Xu, Yexiao J., 1995.
"A generalization of the beta distribution with applications,"
Journal of Econometrics,
Elsevier, vol. 66(1-2), pages 133-152.
- McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
- Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
- Whitney K. Newey & Kenneth D. West, 1986.
"A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix,"
NBER Technical Working Papers
0055, National Bureau of Economic Research, Inc.
- Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- 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 278-92, June.
- Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 723-35, October.
- Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-27, November.
- 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 137-48, January.
- Kakwani, Nanak, 1980. "On a Class of Poverty Measures," Econometrica, Econometric Society, vol. 48(2), pages 437-46, March.
- Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-16, August.
- Rasche, R H, et al, 1980. "Functional Forms for Estimating the Lorenz Curve: Comment," Econometrica, Econometric Society, vol. 48(4), pages 1061-62, May.
- Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
- Datt, Gaurav, 1998. "Computational tools for poverty measurement and analysis," FCND discussion papers 50, International Food Policy Research Institute (IFPRI).
- Woodland, A. D., 1979. "Stochastic specification and the estimation of share equations," Journal of Econometrics, Elsevier, vol. 10(3), pages 361-383, August.
- Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
- McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
- Ryu, Hang K. & Slottje, Daniel J., 1996. "Two flexible functional form approaches for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 251-274.
- T. KÃ¤mpke & 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.
- Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
- 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).
- 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.
- Heshmati, Almas, 2004. "A Review of Decomposition of Income Inequality," IZA Discussion Papers 1221, Institute for the Study of Labor (IZA).
- Heshmati, Almas, 2004. "Inequalities and Their Measurement," IZA Discussion Papers 1219, Institute for the Study of Labor (IZA).
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.