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gh-transformierte symmetrische Verteilungen


  • Klein, Ingo


Tukey (1960) derived via the technique of transformation of variables starting from the normal distribution a family of skewed and leptokurtic distributions. Skewness and leptokurtosis are determined by two parametersg and h. Therefore, the family was called gh-distributions. We modify Tukeys proposal such that other symmetric distributions will be taken as starting point for the transformation of variables. We speak about a family gh transformed symmetrical distributions. Especially, we condiser the Laplace distribution and the t-distribution with a fixed number of degrees. The aim ist to show, what kind of distribution take place between a leptokurtic symmetric distribution and the parameter g and . Because of numerical problems with maximum likelihood. Hoaglins (1983) technique of estimation by quantiles it used. We demonstrate how the three families of gh-transformed symmetrical distributions work fpr real financial data sets that stem from a skewed and leptokurtic distribution.

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  • Klein, Ingo, 2000. "gh-transformierte symmetrische Verteilungen," Discussion Papers 36/2000, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  • Handle: RePEc:zbw:faucse:362000

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    References listed on IDEAS

    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. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
    3. 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.
    4. Brian H. Boyer & Michael S. Gibson & Mico Loretan, 1997. "Pitfalls in tests for changes in correlations," International Finance Discussion Papers 597, Board of Governors of the Federal Reserve System (U.S.).
    5. Fortin, Ines & Kuzmics, Christoph, 2002. "Tail-Dependence in Stock-Return Pairs," Economics Series 126, Institute for Advanced Studies.
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