No Crystal Ball function
The Error distribution goes by a variety of names:
Exponential Power Distribution
Generalised Error Distribution (GED)
Generalised Gaussian distribution (GGD)
To add to the confusion, you will also see a wide range of parameterizations. We have chosen to use the mean m, standard deviation s and power index n to parameterize the distribution, because it makes comparisons with the Normal and Laplace distributions (special case of the GED) easier.
This three parameter distribution offers a variety of symmetric shapes, as shown in the figures below. The first pane shows the effect on the distribution's shape of varying parameter n. Note n = 2 is a Normal distribution, n =1 is a Laplace distribution and the distribution approaches a Uniform as n approaches infinity. The second pane shows the change in the distribution's spread by varying parameter s, its standard deviation. Parameter m is simply the location of the distribution's peak, and the distribution's mean.
Uses and generation
The Error distribution finds quite a lot of use as a prior distribution in Bayesian inference because it has greater flexibility than a Normal prior, in that the Error distribution is flatter than a Normal (platykurtic) when n > 2, and more peaked than a Normal distribution (leptokurtic) when n < 2. Thus, using the GED allows one to maintain the same mean and variance, but vary the distribution's shape (via the parameter n) as required.
We have also seen the Error distribution being used to model variations in historic UK property market returns.
It is not easy to generate values from the Error Distribution using any direct algorithm. However, one simple method is to construct a General distribution from the equation for the probability density function, as shown in the model ErrorThis method has the advantage of retaining the benefits of Latin Hypercube sampling if used.
The error distribution is also referred to as the exponential power distribution, the Subbotin distribution, or the general error distribution.
The links to the Error software specific models are provided here: