  Although it is the generator distribution of the sixth natural exponential
family with quadratic variance function, the Hyperbolic-Secant distribution is
much less known than other distributions in the exponential families. Its lack
of familiarity is due to its isolation from many widely-used statistical
models. We fill in the gap by showing three examples naturally generating the
Hyperbolic-Secant distribution, including Fisher's analysis of similarity
between twins, the Jeffreys' prior for contingency tables, and invalid
instrumental variables.
