Two major generalizations of the hyperbolic secant distributionhave been proposed in the statistical literature which both introduce an additionalparameter that governs the kurtosis of the generalized distribution. Thegeneralized hyperbolic secant (GHS) distribution was introduced by Harknessand...

Leptokurtic distributions can be generated by applying certainnon-linear transformations to a standard normal random variable. Withinthis work we derive general conditions for these transformations which guaranteethat the generated distributions are ordered with respect to the partialordering of...

Using the Gaussian distribution as statistical model for data sets is widely spread, especiallyin practice. However, departure from normality seems to be more the rule than theexception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a singletransformation...

The H−family of distributions or H−distributions, introduced byTukey (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...

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

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

With the celebrated model of Black and Scholes in 1973 the development ofmodern option pricing models started. One of the assumptions of the Blackand Scholes model is that the risky asset evolves according to a geometricBrownian motion which implies normally distributed log-returns. As...

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...