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A Constructive Representation of Univariate Skewed Distributions

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Author Info
Jose T.A.S. Ferreira
Mark F.J. Steel

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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.

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Paper provided by EconWPA in its series Econometrics with number 0403002.

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Length: 25 pages
Date of creation: 08 Mar 2004
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Handle: RePEc:wpa:wuwpem:0403002

Note: Type of Document - pdf; prepared on WinXP; pages: 25
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Web page: http://129.3.20.41

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

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: 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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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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, vol. 13(1), pages 1-43, June. [Downloadable!] (restricted)
  2. Nadarajah, Saralees & Kotz, Samuel, 2003. "Skewed distributions generated by the normal kernel," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 269-277, November. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. Fernandez, C. & Steel, M.F.J., 1996. "On Bayesian modelling of fat tails and skewness," Discussion Paper 58, Tilburg University, Center for Economic Research. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Jose T.A.S. Ferreira & Mark F.J. Steel, 2004. "Model Comparison of Coordinate-Free Multivariate Skewed Distributions with an Application to Stochastic Frontiers," Econometrics 0404005, EconWPA. [Downloadable!]
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