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.
- 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.
