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gh-transformierte symmetrische Verteilungen

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  • Klein, Ingo

Abstract

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.

Suggested Citation

  • 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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