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Skewness and Kurtosis Properties of Income Distribution Models

Author

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  • James McDonald

    ()

  • Patrick A. Turley

    ()

  • Jeff Sorensen

    ()

Abstract

This paper explores the ability of some popular income distributions to model observed skewness and kurtosis. We present the generalized beta type 1 (GB1) and type 2 (GB2) distributions’ skewness-kurtosis spaces and clarify and expand on previously known results on other distributions’ skewness-kurtosis spaces. Data from the Luxembourg Income Study are used to estimate sample moments and explore the ability of the generalized gamma, Dagum, Singh-Maddala, beta of the first kind, beta of the second kind, GB1, and GB2 distributions to accommodate the skewness and kurtosis values. The GB2 has the flexibility to accurately describe the observed skewness and kurtosis.

Suggested Citation

  • James McDonald & Patrick A. Turley & Jeff Sorensen, 2011. "Skewness and Kurtosis Properties of Income Distribution Models," LIS Working papers 569, LIS Cross-National Data Center in Luxembourg.
  • Handle: RePEc:lis:liswps:569
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    References listed on IDEAS

    as
    1. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    2. McDonald, James B. & Ransom, Michael R., 1981. "An analysis of the bounds for the Gini coefficient," Journal of Econometrics, Elsevier, vol. 17(2), pages 177-188, November.
    3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    4. Erich Battistin & Richard Blundell & Arthur Lewbel, 2009. "Why Is Consumption More Log Normal than Income? Gibrat's Law Revisited," Journal of Political Economy, University of Chicago Press, vol. 117(6), pages 1140-1154, December.
    5. Thurow, Lester C, 1970. "Analyzing the American Income Distribution," American Economic Review, American Economic Association, vol. 60(2), pages 261-269, May.
    6. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
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    Citations

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    Cited by:

    1. David Mauler & James McDonald, 2015. "Option Pricing and Distribution Characteristics," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 579-595, April.
    2. Hang K. Ryu & Daniel J. Slottje & Michael McAleer, 2017. "A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries," Documentos de Trabajo del ICAE 2017-25, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Jones, A. & Lomas, J. & Rice, N., 2014. "Going Beyond the Mean in Healthcare Cost Regressions: a Comparison of Methods for Estimating the Full Conditional Distribution," Health, Econometrics and Data Group (HEDG) Working Papers 14/26, HEDG, c/o Department of Economics, University of York.
    4. Andrew M. Jones & James Lomas & Peter T. Moore & Nigel Rice, 2016. "A quasi-Monte-Carlo comparison of parametric and semiparametric regression methods for heavy-tailed and non-normal data: an application to healthcare costs," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(4), pages 951-974, October.
    5. repec:gam:jecnmx:v:6:y:2018:i:2:p:21-:d:141682 is not listed on IDEAS
    6. repec:eee:ecoedu:v:59:y:2017:i:c:p:87-104 is not listed on IDEAS
    7. Jingjing Bai & Wei Gu & Xiaodong Yuan & Qun Li & Feng Xue & Xuchong Wang, 2015. "Power Quality Prediction, Early Warning, and Control for Points of Common Coupling with Wind Farms," Energies, MDPI, Open Access Journal, vol. 8(9), pages 1-18, August.

    More about this item

    Keywords

    skewness; kurtosis; generalized beta type 2 distribution; generalized gamma distribution;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E25 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Aggregate Factor Income Distribution

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