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On the Marshall–Olkin transformation as a skewing mechanism

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  • Rubio, F.J.
  • Steel, M.F.J.

Abstract

The use of the Marshall–Olkin transformation as a skewing mechanism is investigated. The distributions obtained when this transformation is applied to several classes of symmetric and unimodal distributions are analysed. It is shown that most of the resulting distributions are not flexible enough to model data presenting high or moderate skewness. The only case encountered where the Marshall–Olkin transformation can be considered a useful skewing mechanism is when applied to Student-t distributions with Cauchy or even heavier tails.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 7 ()
Pages: 2251-2257

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Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2251-2257

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Web page: http://www.elsevier.com/locate/csda

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Keywords: Moment; Skewness measure; Student-t; Tail behaviour;

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  1. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
  2. 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.
  3. Richard A. Groeneveld & Glen Meeden, 2009. "An improved skewness measure," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 325-337.
  4. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
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