Introducing a new tangent distribution

Abstract

To date, only a limited number of basic unit distributions based on the tangent function have been considered. In this article, we expand this range by introducing a new candidate distribution and examining its key probabilistic properties, such as the cumulative distribution function, probability density function, quantile function, and moments. Particular emphasis is placed on analytical tractability. While potential applications fall outside the scope of this study, they could be investigated by specialists in relevant fields. Additionally, we highlight an open problem regarding the rigorous derivation of the second-order moment, which could stimulate further theoretical research.