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Extension of the κ-generalized distribution: new four-parameter models for the size distribution of income and consumption

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  • Masato Okamoto

Abstract

This paper studies a new kind of generalized beta distribution that is different from the GB1 and GB2 of McDonald (1984). This new four-parameter statistical distribution, the extended κ-generalized distribution of the second kind, abbreviated EκG2, is derived as one of two kinds of generalizations from the κ-generalized distribution of Clementi et al. (2007). By empirical comparison with the GB2 using the LIS income/consumption data, the EκG2 is found to be an overall better fit in terms of both frequency-based (FB) evaluation criteria, such as the likelihood, and money-amount-based (MAB) evaluation criteria, such as the accuracy of the estimated Lorentz curve. The EκG2 also overall outperforms the double Pareto-lognormal distribution (dPLN) of Reed (2003) in terms of FB criteria. Although not necessarily superior to the dPLN in terms of MAB criteria, the EκG2 is judged to be an overall better fit to the empirical distributions relative to the dPLN by a combined evaluation using both FB and MAB criteria. This paper also discusses similarities and differences in characteristics between the EκG2 and GB2, including the shapes of the distributions.

Suggested Citation

  • Masato Okamoto, 2013. "Extension of the κ-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.
    • Handle: RePEc:lis:liswps:600
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    References listed on IDEAS

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    1. Stephen P. Jenkins, 2007. "Inequality and the GB2 income distribution," Working Papers 73, ECINEQ, Society for the Study of Economic Inequality.
    2. 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.
    3. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    4. Brazauskas, Vytaras, 2002. "Fisher information matrix for the Feller-Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 159-167, September.
    5. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    6. William J. Reed & Fan Wu, 2008. "New Four- and Five-Parameter Models for Income Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 11, pages 211-223, Springer.
    7. 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.
    8. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    9. Kaniadakis, G. & Lissia, M. & Scarfone, A.M., 2004. "Deformed logarithms and entropies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 41-49.
    10. Ripsy Bandourian & Robert Turley & James McDonald, 2002. "A Comparison of Parametric Models of Income Distribution across Countries and over Time," LIS Working papers 305, LIS Cross-National Data Center in Luxembourg.
    11. 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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    Cited by:

    1. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    2. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    3. Wang, Frank Xuyan, 2021. "Shape factor asymptotic analysis II," MPRA Paper 110827, University Library of Munich, Germany.
    4. F. Clementi & M. Gallegati & G. Kaniadakis & S. Landini, 2016. "$\kappa$-generalized models of income and wealth distributions: A survey," Papers 1610.08676, arXiv.org.
    5. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.

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