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Classes of skew generalized hyperbolic secant distributions

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  • Fischer, Matthias J.
  • Vaughan, David

Abstract

A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For that reason, we additionally introduce a skewness parameter by means of splitting the scale parameter and show that most of the nice properties are preserved. Finally, we compare both families with respect to their ability to model financial return distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:faucse:452002
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    References listed on IDEAS

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    1. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 99-128, May.
    2. McDonald, James B., 1991. "Parametric models for partially adaptive estimation with skewed and leptokurtic residuals," Economics Letters, Elsevier, vol. 37(3), pages 273-278, November.
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    Cited by:

    1. 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.
    2. Hakan Savaş Sazak & Melis Zeybek, 2022. "The modified maximum likelihood estimators for the parameters of the regression model under bivariate median ranked set sampling," Computational Statistics, Springer, vol. 37(3), pages 1069-1109, July.

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