Over the summer of 2009–2010 I undertook a summer studentship at the University of Auckland Department of Statistics. The project I undertook was to create a new package called GeneralizedHyperbolic based on David Scott’s HyperbolicDist package.

What the GeneralizedHyperbolic package does is it provides functions for use with the generalised hyperbolic distribution and related distributions. These functions include probability, density, quantile, fitting, checking and random observation generating functions.

The result of my work has been posted up on GeneralizedHyperbolic. Since undertaking this work GeneralizedHyperbolic has become available on CRAN. To install the package run the following command within R: install.packages("GeneralizedHyperbolic").

Once the package has been installed, using it is as simple as running R, then loading the package using library(GeneralizedHyperbolic). Example usage is as follows:

> library(GeneralizedHyperbolic)
> dghyp(2)
[1] 0.08878272
> dghyp(0)
[1] 0.3055948
> dghyp(3, mu = 4)
[1] 0.2019553
> dghyp(3, mu = 4, alpha = 3)
[1] 0.1789202
> ghypdata <- rghyp(1000)
> fitteddata <- hyperbFit(ghypdata, hessian = TRUE)
> summary(fitteddata) # Printing fitted parameters & std errors

Data:      ghypdata
Parameter estimates:
       mu        delta       alpha        beta
   -0.02921     0.57314     0.94262    -0.03066 
  ( 0.08689)  ( 0.19332)  ( 0.05222)  ( 0.03881)
Likelihood:         -1852.273
Method:             Nelder-Mead
Convergence code:   0
Iterations:         169

I have created some extra code to go with this package that allows visualisation of the generalised hyperbolic distribution. Note, the slider tool was sourced from the fBasics package. With this tool, you can modify each parameter by moving a slider and noting the effects that this has. You can grab the code to do this at my GHyp Slider gist.

Here is an example of the visualisation:

Generalised hyperbolic distribution visualisation