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The hyperbolic secant distribution has several generalizations withapplications in finance. In this study, we explore the dual geometric structureof one such generalization, namely the beta-logistic distribution. Recentfindings also interpret Bernoulli and Euler polynomials as moments of specificrandom variables, treating them as special cases within the framework of thebeta-logistic distribution. The current study also uncovers that thebeta-logistic distribution admits an $\alpha$-parallel prior for any realnumber $\alpha$, that has the potential for application in geometricstatistical inference.

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