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A General Method to Create Lorenz Models

Author

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  • ZuXiang Wang
  • Russell Smyth
  • Yew-Kwang Ng

Abstract

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

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    1. Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
    2. ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Monash Economics Working Papers 20-07, Monash University, Department of Economics.
    3. 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.
    4. 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.
    5. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
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    Citations

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    Cited by:

    1. Gholamreza Hajargasht & William E. Griffiths, 2016. "Inference for Lorenz Curves," Department of Economics - Working Papers Series 2022, The University of Melbourne.
    2. Banica Logica & Stefan Liviu Cristian & Jurian Mariana, 2014. "Business Intelligence For Educational Purpose," Balkan Region Conference on Engineering and Business Education, Sciendo, vol. 1(1), pages 333-338, August.
    3. Wang, ZuXiang & Smyth, Russell, 2015. "A piecewise method for estimating the Lorenz curve," Economics Letters, Elsevier, vol. 129(C), pages 45-48.
    4. 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.
    5. Ruiz-Lozano, Mercedes & Tirado-Valencia, Pilar, 2016. "Do industrial companies respond to the guiding principles of the Integrated Reporting framework? A preliminary study on the first companies joined to the initiative," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(2), pages 252-260.
    6. Miguel Sordo & Jorge Navarro & José Sarabia, 2014. "Distorted Lorenz curves: models and comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 761-780, April.
    7. van Sluisveld, Mariësse A.E. & Worrell, Ernst, 2013. "The paradox of packaging optimization – a characterization of packaging source reduction in the Netherlands," Resources, Conservation & Recycling, Elsevier, vol. 73(C), pages 133-142.
    8. Collins, Alan R. & Hansen, Evan & Hendryx, Michael, 2012. "Wind versus coal: Comparing the local economic impacts of energy resource development in Appalachia," Energy Policy, Elsevier, vol. 50(C), pages 551-561.
    9. John Ogwang & Dennis Obote & Ursula Abwot, 2021. "A Technical Note on New Applications of Lorenz Curves in Business Based on Pareto Principles," International Journal of Applied Economics, Finance and Accounting, Online Academic Press, vol. 9(2), pages 76-81.
    10. Wang, ZuXiang & Smyth, Russell, 2015. "A hybrid method for creating Lorenz curves," Economics Letters, Elsevier, vol. 133(C), pages 59-63.
    11. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    12. Edyta Małecka-Ziembińska & Radosław Ziembiński, 2020. "Application of Genetic Algorithm to Optimal Income Taxation," JRFM, MDPI, vol. 13(11), pages 1-24, October.
    13. Songpu Shang & Songhao Shang, 2021. "Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve," Mathematics, MDPI, vol. 9(20), pages 1-11, October.

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    More about this item

    Keywords

    Lorenz curve; Gini index;

    JEL classification:

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

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