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A Note on the Moments of the Skew-Normal Distribution

Author

Listed:
  • Markus Haas

    (Institute for Quantitative Business and Economics Research (QBER), University of Kiel)

Abstract

Azzalini's skew-normal distribution is an attractive tool for modeling the skewness observed in many economic and financial variables. Formulas for the odd moments of the skew-normal distribution have been given by Henze (1986) and, more recently, Martinez et al. (2008). This note provides a rather straightforward alternative approach to the calculation of the odd moments of the skew-normal distribution. It exploits a striking similarity between the density and the moment generating function of a skew-normal variable and leads to an attractive expression for the odd moments.

Suggested Citation

  • Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.
    • Handle: RePEc:ebl:ecbull:eb-12-00725
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2012/Volume32/EB-12-V32-I4-P318.pdf
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    References listed on IDEAS

    as
    1. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    2. Bernardi, Mauro, 2013. "Risk measures for skew normal mixtures," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1819-1824.
    3. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
    4. Adcock, C.J. & Shutes, K., 2005. "An analysis of skewness and skewness persistence in three emerging markets," Emerging Markets Review, Elsevier, vol. 6(4), pages 396-418, December.
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    Cited by:

    1. Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.

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    More about this item

    Keywords

    Moments; skewness; skew-normal distribution;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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