On Generating a New Family of Distributions Using the Tangent Function

Abstract

In this paper, a method for generating a new family of univariate continuous distributions using the tangent function is proposed. Some general properties of this new family are discussed: hazard function, quantile function, Rényi and Shannon entropies, symmetry, and existence of the non-central n^th moment. Some new members as sub-families in the T-X family of distributions are provided. Three members of the new sub-families are defined and discussed: the five-parameter Normal-Generalized hyperbolic secant distribution (NGHS), the five-parameter Gumbel-Generalized hyperbolic secant distribution (GGHS), and the six-parameter Generalized Error-Generalized hyperbolic secant distribution (GEHS), the shapes of these distributions were found: skewed right, skewed left, or symmetric, and unimodal, bimodal, or trimodal. Finally, to demonstrate the usefulness and the capability of the distributions, two real data sets are used and the results are compared with other known distributions.