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 allow for skewness. For that reason, we additionally introduce a skewness parameter by means of splitting the scale parameter and show that most of the nice properties are preserved. Finally, we compare both families with respect to their ability to model financial return distributions.
Skewed hyperbolic secant NEF-GHS distribution GSH distribution skewness return data