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Skewness–kurtosis bounds for the skewed generalized T and related distributions

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  • Kerman, Sean C.
  • McDonald, James B.

Abstract

Bounds for the skewness–kurtosis space corresponding to the skewed generalized t, skewed generalized error, skewed t, and some other distributions are presented and contrasted with the bounds reported by Klaassen et al. (2000) for unimodal probability density functions. The skewed generalized T and skewed generalized error distributions have the greatest flexibility of the distributions considered.

Suggested Citation

  • Kerman, Sean C. & McDonald, James B., 2013. "Skewness–kurtosis bounds for the skewed generalized T and related distributions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2129-2134.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:2129-2134
    DOI: 10.1016/j.spl.2013.05.028
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    References listed on IDEAS

    as
    1. Hansen, Christian & McDonald, James B. & Newey, Whitney K., 2010. "Instrumental Variables Estimation With Flexible Distributions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 13-25.
    2. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    3. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    4. Theodossiou, Panayiotis & McDonald, James B. & Hansen, Christian B., 2007. "Some Flexible Parametric Models for Partially Adaptive Estimators of Econometric Models," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 1, pages 1-20.
    5. Klaassen, Chris A. J. & Mokveld, Philip J. & van Es, Bert, 2000. "Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 131-135, November.
    6. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
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    More about this item

    Keywords

    Skewed generalized T; Kurtosis; Skewness;

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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