Abstract
The hyperbolic secant distribution (HpSc) is one of six subfamilies of the natural exponential family with quadratic variance functions, NEF-QVF. The others are normal, gamma, Poisson, binomial and negative binomial distributions. It is, however, little-known and rarely used in applied statistics. In this paper, its properties are surveyed and graphically visualized; new facts on the moments, mode, and conjugate prior distribution are shown; ML estimation, generalized linear model and generalized additive model are explored. HpSc models are fitted to some data sets, and the results are preferable to the conventional ones. Some numerical procedures are to be developed, and further research will be promising.
