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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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2251-2257
    DOI: 10.1016/j.csda.2012.01.003
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    References listed on IDEAS

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    1. 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.
    2. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    3. 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.
    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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    Cited by:

    1. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.

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