Advanced Search
MyIDEAS: Login to save this paper or follow this series

A Constructive Representation of Univariate Skewed Distributions


Author Info

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


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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL:
Download Restriction: no

Bibliographic Info

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

as in new window
Length: 25 pages
Date of creation: 08 Mar 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0403002

Note: Type of Document - pdf; prepared on WinXP; pages: 25
Contact details of provider:
Web page:

Related research

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

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:


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.:
as in new window
  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.
  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. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
  5. 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.
Full references (including those not matched with items on IDEAS)


Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  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. A. Abtahi & J. Behboodian & M. Sharafi, 2012. "A general class of univariate skew distributions considering Stein’s lemma and infinite divisibility," Metrika, Springer, vol. 75(2), pages 193-206, February.
  3. Fischer, Matthias J., 2006. "The L-distribution and skew generalizations," Discussion Papers 75/2006, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  4. Klein, Ingo & Fischer, Matthias J., 2003. "Skewness by splitting the scale parameter," Discussion Papers 55/2003, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  5. Klein, Ingo, 2011. "Van Zwet ordering and the Ferreira-Steel family of skewed distributions," IWQW Discussion Paper Series 13/2011, Friedrich-Alexander-Universität Erlangen-Nürnberg, Institut für Wirtschaftspolitik und Quantitative Wirtschaftsforschung (IWQW).
  6. Rubio, F.J. & Steel, M.F.J., 2012. "On the Marshall–Olkin transformation as a skewing mechanism," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2251-2257.
  7. Ley, Christophe & Paindaveine, Davy, 2010. "Multivariate skewing mechanisms: A unified perspective based on the transformation approach," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1685-1694, December.
  8. De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
  9. Delicado, P. & Goria, M.N., 2008. "A small sample comparison of maximum likelihood, moments and L-moments methods for the asymmetric exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1661-1673, January.
  10. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer, vol. 71(1), pages 63-79, June.
  11. Alzaatreh, Ayman & Famoye, Felix & Lee, Carl, 2014. "The gamma-normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 67-80.
  12. Fischer, Matthias J., 2004. "The L-distribution and skew generalizations," Discussion Papers 63/2004, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  13. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
  14. A. Abtahi & M. Towhidi & J. Behboodian, 2011. "An appropriate empirical version of skew-normal density," Statistical Papers, Springer, vol. 52(2), pages 469-489, May.


This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


Access and download statistics


When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0403002. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.