The hyperbolic secant distribution is the probability distribution with density proportional to the hyperbolic secant function, which is the reciprocal of the hyperbolic cosine function, the hyperbolic cosine being defined by

cosh(x) = [exp(x) + exp(- x)] / 2

This distribution is not used much in applications, but it does have two curious features.

The hyperbolic secant density is shown in the Rweb plot below.