Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 36/2000
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.