Information geometry and $\alpha$-parallel prior of the beta-logistic distribution

The hyperbolic secant distribution has several generalizations with applications in finance. In this study, we explore the dual geometric structure of one such generalization, namely the beta-logistic distribution. Recent findings also interpret Bernoulli and Euler polynomials as moments of specific random variables, treating them as special cases within the framework of the beta-logistic distribution. The current study also uncovers that the beta-logistic distribution admits an $\alpha$-parallel prior for any real number $\alpha$, that has the potential for application in geometric statistical inference.