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Kurtosis transformation and kurtosis ordering

Author

Listed:
  • Klein, Ingo
  • Fischer, Matthias J.

Abstract

Leptokurtic distributions can be generated by applying certain non-linear transformations to a standard normal random variable. Within this work we derive general conditions for these transformations which guarantee that the generated distributions are ordered with respect to the partial ordering of van Zwet for symmetric distributions and the partial ordering of MacGillivray for arbitrary distributions. In addition, we propose a general power transformation which nests the H-, J- and K-transformations which have already been proposed in the literature. Within this class of power transformations the above mentioned condition can be easily verified and the power can be interpreted as parameter of leptokurtosis.

Suggested Citation

  • Klein, Ingo & Fischer, Matthias J., 2003. "Kurtosis transformation and kurtosis ordering," Discussion Papers 53/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:532003
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    References listed on IDEAS

    as
    1. Fischer, Matthias J. & Horn, Armin & Klein, Ingo, 2003. "Tukey-type distributions in the context of financial data," Discussion Papers 52/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
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    1. Fischer, Matthias J. & Klein, Ingo, 2003. "Kurtosis modelling by means of the J-transformation," Discussion Papers 51/2003, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.

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