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`)] / 2This distribution is not used much in applications, but it does have two curious features.

- Like the normal distribution, its density is proportional to
its characteristic function.
- The sample mean and median are equally efficient for this population distribution. See the page about efficiency for more on this.

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