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Revisiting The Ordered Family Of Lorenz Curves

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  • ZuXiang Wang
  • Yew-Kwang Ng
  • Russell Smyth

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Bibliographic Info

Paper provided by Monash University, Department of Economics in its series Monash Economics Working Papers with number 19-07.

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Length: 28pages
Date of creation: 2007
Date of revision:
Handle: RePEc:mos:moswps:2007-19

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Related research

Keywords: Lorenz curve; Gini index Abstract: Sarabia et al. (1999) present a basic model to create ordered families of Lorenz curves; along with basic theorems that describe the conditions for the models to satisfy the definition of the Lorenz curve. Using these basic models; they suggest a family which includes several well-known Lorenz models as special cases. This paper first shows that their basic theorems can be generalized. The paper then proceeds to propose additional families of Lorenz models. Finally the performance of some of the models is compared and it is shown that more efficient Lorenz models are possible with the assistance of our generalized result of the Sarabia et al. (1999) basic model.;

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References

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  1. 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 447-52, December.
  2. Rasche, R H, et al, 1980. "Functional Forms for Estimating the Lorenz Curve: Comment," Econometrica, Econometric Society, vol. 48(4), pages 1061-62, May.
  3. Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
  4. 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.
  5. Sarabia, José María & Castillo, Enrique & Pascual, Marta & Sarabia, María, 2005. "Mixture Lorenz curves," Economics Letters, Elsevier, vol. 89(1), pages 89-94, October.
  6. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
  7. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
  8. 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.
  9. 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.
  10. Gupta, Manash Ranjan, 1984. "Functional Form for Estimating the Lorenz Curve," Econometrica, Econometric Society, vol. 52(5), pages 1313-14, September.
  11. Rossi, Jose W., 1985. "Notes on a new functional form for the Lorenz curve," Economics Letters, Elsevier, vol. 17(1-2), pages 193-197.
  12. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
  13. Kwang Soo Cheong, 2002. "An empirical comparison of alternative functional forms for the Lorenz curve," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 171-176.
  14. Holm, Juhani, 1993. "Maximum entropy Lorenz curves," Journal of Econometrics, Elsevier, vol. 59(3), pages 377-389, October.
  15. 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.
  16. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
  17. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-86, September.
  18. 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.
  19. Jose-Mari Sarabia, 1997. "A hierarchy of lorenz curves based on the generalized tukey's lambda distribution," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 305-320.
  20. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
  21. José-María Sarabia & Enrique Castillo & Daniel J. Slottje, 2001. "An Exponential Family of Lorenz Curves," Southern Economic Journal, Southern Economic Association, vol. 67(3), pages 748-756, January.
  22. 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.
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Cited by:
  1. ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Development Research Unit Working Paper Series 20-07, Monash University, Department of Economics.
  2. ZuXiang Wang & Russell Smyth & Yew-Kwang Ng, 2009. "A General Method to Create Lorenz Models," Development Research Unit Working Paper Series 06-09, Monash University, Department of Economics.

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