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A General Method to Create Lorenz Models


  • ZuXiang Wang
  • Russell Smyth
  • Yew-Kwang Ng


There are currently about two dozen Lorenz models available in the literature for fitting grouped income distribution data. A general method to construct parametric Lorenz models of the weighted product form is offered in this paper. First, a general result to describe the conditions for the weighted product model to be a Lorenz curve, created by using several component parametric Lorenz models, is given. We show that the key property for an ideal component model is that the ratio between its second derivative and its first derivative is increasing. Then, a set of Lorenz models, consisting of a basic group of models along with their convex combinations, is proposed, and it is shown that any model in the set possesses this key property. Equipped with this general result and the model set, we can create a range of different weighted product Lorenz models. Finally, test results are presented which demonstrate that there may be many satisfactory models among those created. The proposed method can be generalized by finding other models with this key property.

Suggested Citation

  • ZuXiang Wang & Russell Smyth & Yew-Kwang Ng, 2009. "A General Method to Create Lorenz Models," Monash Economics Working Papers 06-09, Monash University, Department of Economics.
  • Handle: RePEc:mos:moswps:2009-06

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    References listed on IDEAS

    1. ZuXiang Wang & Yew-Kwang Ng & Russell Smyth, 2007. "Revisiting The Ordered Family Of Lorenz Curves," Monash Economics Working Papers 19-07, Monash University, Department of Economics.
    2. 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.
    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. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    5. ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Monash Economics Working Papers 20-07, Monash University, Department of Economics.
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    Cited by:

    1. Banica Logica & Stefan Liviu Cristian & Jurian Mariana, 2014. "Business Intelligence For Educational Purpose," Balkan Region Conference on Engineering and Business Education, De Gruyter Open, vol. 1(1), pages 333-338, August.
    2. Caliskan, Hakan & Hepbasli, Arif, 2010. "Energy and exergy prices of various energy sources along with their CO2 equivalents," Energy Policy, Elsevier, vol. 38(7), pages 3468-3481, July.

    More about this item


    Lorenz curve; Gini index;

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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