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

AbstractThe hyperbolic secant distribution has several generalizations with applications in, for example, finance. In this study, we explore the dual geometric structure of one such generalization: the beta-logistic distribution. Within this family, two special cases of random variables, as examples, are of particular interests: their moments, by some recent results, give the Bernoulli and Euler polynomials, which are important objects in many areas of mathematics. This current study also uncovers that the beta-logistic distribution admits a <italic>α</italic>-parallel prior for any real number <italic>α</italic>, that has the potential for application in geometric statistical inference. [ABSTRACT FROM AUTHOR]