Hyperbolic-Secant distribution | Vose Software

Hyperbolic-Secant distribution

Format: HS(m, s)


The Hyperbolic-Secant distribution is a symmetric distribution similar to the Normal distribution and defined by its mean and standard deviation, but with a kurtosis of 5, so it is more peaked than the Normal. Examples of the Hyperbolic-Secant distribution are given below, together with Normal distributions with the same mean and standard deviation:


The Hyperbolic-Secant distribution can be used to fit data that seem to be approximately Normal in distribution but showing narrower shoulders, just as the Generalised Error and Student distributions are an option for data with wider shoulders than a Normal.


The Hyperbolic-Secant distribution gets its (rather awful) name from the sech function in its probability density function.


ModelRisk functions added to Microsoft Excel for the Hyperbolic Secant (HS) distribution

VoseHS generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseHSObject constructs a distribution object for this distribution.

VoseHSProb returns the probability density or cumulative distribution function for this distribution.

VoseHSProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseHSFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseHSFitObject constructs a distribution object of this distribution fitted to data.

VoseHSFitP returns the parameters of this distribution fitted to data.


Hyperbolic-Secant distribution equations