The q-Deformed Hyperbolic Secant Family

Abstract

In this paper, by virtue of deformed hyperbolic functions, a q-deformed hyperbolic secant (q-DHS) distribution for the symmetric hyperbolic secant (HS (distribution is constructed. The introduced parameter q. Based on this distribution, the moment-generating function (mgf), the characteristic function (cf), the score function, the cumulant-generating function (cgf) and some corresponding important characteristics are derived. The maximum likelihood (ML) method is illustrated to determine the corresponding maximum likelihood estimates (MLE) for the introducing parameter q. According to the values of the proposed parameter, some calculations are reviewed and tabulated.