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A flexible descriptive model for the size distribution of incomes


  • Masato Okamoto

    () (Statistical Research and Training Institute, Ministry of Internal Affairs and Communications)


There are four-parameter income distribution models that have good reputation for goodness-of-fit. In contrast, the existing models with five or more parameters fail to achieve a satisfactory level of goodness-of-fit. We propose a new seven-parameter model that is empirically shown to be substantially better fitted than the existing models by imposing an appropriate restriction on the parameter domain prior to the maximum likelihood estimation.

Suggested Citation

  • Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.
  • Handle: RePEc:ebl:ecbull:eb-14-00364

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    References listed on IDEAS

    1. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    2. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    3. Masato Okamoto, 2013. "Erratum to “Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation”," Economics Bulletin, AccessEcon, vol. 33(3), pages 2443-2444.
    4. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    5. 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.
    6. Masato Okamoto, 2013. "Extension of the ?-generalized distribution: new four-parameter models for the size distribution of income and consumption," LIS Working papers 600, LIS Cross-National Data Center in Luxembourg.
    7. Masato Okamoto, 2012. "Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation," Economics Bulletin, AccessEcon, vol. 32(4), pages 2969-2982.
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    More about this item


    income distribution; Lorenz curve; mixture distribution; model selection;

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • D6 - Microeconomics - - Welfare Economics


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