Generalized Hyperbolic Secant Distributions

Abstract

The two-parameter family of distributions having characteristic functions given by φ(t) = (sech αt)ρ, α > 0 ρ > 0, is introducted and their basic structural properties are derived. Examples of some random variables having this distribution are given and, as an application, the distribution of the geometric mean of the absolute values of Cauchy variables is obtained. Finally, estimation of the parameters α and ρ is considered.