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Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation


  • Masato Okamoto

    () (Ministry of Internal Affairs and Communications)


This paper compares the goodness-of-fit of two new types of parametric income distribution models (PIDMs), the kappa-generalized (kG) and double-Pareto lognormal (dPLN) distributions, with that of beta-type PIDMs using US and Italian data for the 2000s. A three-parameter model kG tends to estimate the Lorenz curve and income inequality indices more accurately when the likelihood value is similar to that of the beta-type PIDMs. For the first half of the 2000s in the USA, the kG outperforms the other PIDMs in goodness-of-fit evaluated by both frequency-based criteria (such as the maximum likelihood value) and money-amount-based criteria (such as accuracy of estimation of the Lorenz curve). A four-parameter model dPLN generally outperforms the GB2 in both criteria. Furthermore, when the overall income distribution is approximated by a mixture of distributions fitted separately for each age class of the household heads (the ‘MLE-by-Age' method), the goodness-of-fit of the dPLN mixture model is found to be comparable to or higher than that of all of the PIDMs in the ordinary MLE fit, and, in the overall evaluation, this mixture model outperforms all of the single PIDMs in the sense that it is better fitted according to at least in one of the two criteria in almost all cases. The dPLN and its mixture model are found to have an explicit analytic expression for the Gini coefficient. The dPLN is therefore also suitable for the MLE-by-Age method in this respect.

Suggested Citation

  • 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.
  • Handle: RePEc:ebl:ecbull:eb-12-00636

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    References listed on IDEAS

    1. 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.
    2. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075,, revised Feb 2009.
    3. 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.
    4. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    5. Masato Okamoto, 2012. "The Relationship between the Equivalence Scale and the Inequality Index and its Impact on the Measurement of Income Inequality," LIS Working papers 575, LIS Cross-National Data Center in Luxembourg.
    6. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
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    Cited by:

    1. repec:aes:jsesro:v:6:y:2017:i:1:p:1-15 is not listed on IDEAS
    2. 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.
    3. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.
    4. F. Clementi & M. Gallegati, 2016. "New economic windows on income and wealth: The k-generalized family of distributions," Papers 1608.06076,
    5. Masato Okamoto, 2016. "Mincer earnings regression in the form of the double Pareto-lognormal model," Working Papers 407, ECINEQ, Society for the Study of Economic Inequality.

    More about this item


    income distribution; mixture model; double-Pareto lognormal distribution; kappa-generalized distribution;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty


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