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Mikkel Meyer Andersen commented on MATH585:

I know that it is indeed important, and I will look into it as soon as time allows me to.
R is GPL, so using their implementation is a nogo. But the help file provides the methods
they have implemented:
{quote}
‘rgamma’ for ‘shape >= 1’ uses
Ahrens, J. H. and Dieter, U. (1982). Generating gamma variates by
a modified rejection technique. _Communications of the ACM_,
*25*, 4754,
and for ‘0 < shape < 1’ uses
Ahrens, J. H. and Dieter, U. (1974). Computer methods for
sampling from gamma, beta, Poisson and binomial distributions.
_Computing_, *12*, 223246.
{quote}
Again, thanks for reporting this  we'll do our best to improve our implementation.
> Very slow generation of gamma random variates
> 
>
> Key: MATH585
> URL: https://issues.apache.org/jira/browse/MATH585
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 2.2, 3.0
> Environment: All
> Reporter: Darren Wilkinson
> Labels: Gamma, Random
> Original Estimate: 6h
> Remaining Estimate: 6h
>
> The current implementation of gamma random variate generation works, but uses an inversion
method. This is wellknown to be a bad idea. Usually a carefully constructed rejection procedure
is used. To give an idea of the magnitude of the problem, the Gamma variate generation in
Parallel COLT is roughly 50 times faster than in Commons Math.

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