Calculating a large number of tail probabilities or tail quantiles for a given distribution families becomes very challenging, if both the cumulative and the inverse distribution function are not available in closed form. In case of the Gaussian and Student t distribution, quantile...

Generalized autoregressive conditional heteroskedasticity (GARCH) processes have become very popular as models for financial return data because they are able to capture volatility clustering as well as leptokurtic unconditional distributions which result from the assumption of conditionally...

A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to...

A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to...

The H−family of distributions or H−distributions, introduced by Tukey (1960, 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes, MacGillivray and Mengersen (1997) generated...

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...