This is an example of using Regress+ to generate a sample of random variates from a specified distribution.

Regress+ has this capability because it must be able to assess the goodness-of-fit of the data to a chosen model. It performs that test by means of a parametric bootstrap, a kind of Monte Carlo simulation. It should be apparent that the synthetic sample (histogram) is a very good fit to the theoretical model (solid line).


Gamma(A,B,C) = (1/(B Gam (C))) ((y − A)/B)^(C − 1) exp ((A − y)/B)

where Gam (·) is the complete Gamma function.


The curve shown in the plot is the theoretical, not fitted model, obtained by specifying the initial parameters and setting them all Constant. When this dataset is considered to be a Gamma sample with unknown parameters, the maximum-likelihood parameters are found to be as follows:

The differences, from (1, 2, 3), are due to the natural variation inherent in drawing a sample of size 10,000 from this particular parent population.