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A Constructive Representation of Univariate Skewed Distributions

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  • Jose T.A.S. Ferreira
  • Mark F.J. Steel

Abstract

We introduce a general perspective on the introduction of skewness into symmetric distributions. Making use of inverse probability integral transformations we provide a constructive representation of skewed distributions, where the skewing mechanism and the original symmetric distributions are specified separately. We study the effects of the skewing mechanism on \emph{e.g.} modality, tail behaviour and the amount of skewness generated. In light of the constructive representation, we review a number of characteristics of three classes of skew distributions previously defined in the literature. The representation is also used to introduce two novel classes of skewed distributions. Finally, we incorporate the different classes of distributions into a Bayesian linear regression framework and analyse their differences and similarities.

Suggested Citation

  • Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "A Constructive Representation of Univariate Skewed Distributions," Econometrics 0403002, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0403002
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    References listed on IDEAS

    as
    1. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    2. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November.
    3. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
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    More about this item

    Keywords

    Arnold and Groeneveld skewness measure; Bayesian regression model; inverse probability integral transformation; modality; skewing mechanism; tail behaviour;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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