Hyperbolic Secant Distributions

Abstract

The hyperbolic secant distribution (HSD) has its origin in Fisher [1], Dodd [2], Roa [3] and Perks [4]. Additional properties are developed by Talacko [6, 7, 8]. It is symmetric and bell-shaped like the Gaussian distribution but has slightly heavier tails. However, in contrast, both probability density function, cumulative density function and quantile function, admit simple and closed-form expressions, which makes it appealing from a practical and a theoretical point of view. In particular, HSD can be used as starting distribution to obtain generalized distribution systems which exhibit skewness and heavier (or lighter) tails.