The Folded EGB2 distribution and its application to financial return data

In the literature there are several generalizations of the standard logistic distribution. Most of them are included in the generalized logistic distribution of type IV or EGB2 distribution. However, this four parameter family fails in modeling skewness absolutly greater than 2 and kurtosis higher than 9. To remove this shortcoming, an additional parameter is introduced. Unfortunately, there is now no closed form for the probability density function of the generalized EGB2, briefly called FEGB2 or genealized logistic distribution of type V. However, it can be approximated numerically, for example by saddlepoint approximation or numerical integration methods. Finally, FEGB2 is used for modeling returns of financial data.