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Skewness by splitting the scale parameter

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  • Klein, Ingo
  • Fischer, Matthias J.

Abstract

There are several possibilities to introduce skewness into a symmetric distribution. One of these procedures applies two dfferent parameters of scale - with possibly different weights - to the positive and the negative part of a symmetric density. Within this work we show that this technique incorporates a well-defined parameter of skewness, i.e. that the generated distributions are skewed to the right (left) if the parameter of skewness takes values less (greater) than one. Secondly, we prove that the skewness parameter is compatible with the skewness ordering of van Zwet (1964) which is the strongest ordering in the hierarchy of orderings discussed by Oja (1981). Hence, the generated (skewed) distributions can be ordered by the skewness parameter.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:faucse:552003
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    References listed on IDEAS

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    1. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    2. Fischer, Matthias J. & Vaughan, David, 2002. "Classes of skew generalized hyperbolic secant distributions," Discussion Papers 45/2002, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    3. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
    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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