Could you please add the exact form of the distribution, because it's rather confusing in the current form.

In this url, the role of k and theta is precised with a formula :
[http://tinyurl.com/24jxfrk]*

It seems that in 
[http://docs.python.org/library/random.html#random.gammavariate] , alpha is playing the role of k and beta is playing the role of theta.

But it's still not clear, because one can confuse beta with 1/beta and vice et versa, like there is two usual representation for the gamma distribution [http://en.wikipedia.org/wiki/Gamma_distribution]

[http://docs.scipy.org/doc/numpy-1.5.x/reference/generated/numpy.random.gamma.html#numpy.random.gamma]*

Please update the documentation to avoid this ambiguity.

I provide an indicative patch which is updating the doc string in random.py

From reading the Wikipedia article, I might conclude that beta = 1/theta, but from reading random.py, beta=theta. I think this much should be clarified, but without giving the formula in a hard to read text form. Perhaps the random doc should give reference to the much more complete numpy.random (and Wikipedia and/or Mathworld) entries rather than merely 'any statistics text' (many of which will not describe all).

Yes I agree. Actually the parameters in the python code alpha, beta are corresponding respectively to k, theta in the first equation of [http://en.wikipedia.org/wiki/Gamma_distribution].

New changeset 42816be02b9b by Raymond Hettinger in branch '2.7':
Issue 10787: Document the probability density function for random.gammavariate.
http://hg.python.org/cpython/rev/42816be02b9b

New changeset e880020e7e6a by Raymond Hettinger in branch '3.1':
Issue 10787: Document the probability density function for random.gammavariate.
http://hg.python.org/cpython/rev/e880020e7e6a

New changeset f882b284d260 by Raymond Hettinger in branch '3.2':
Issue 10787: Document the probability density function for random.gammavariate.
http://hg.python.org/cpython/rev/f882b284d260

New changeset a892a0dd8190 by Raymond Hettinger in branch 'default':
Issue 10787: Document the probability density function for random.gammavariate.
http://hg.python.org/cpython/rev/a892a0dd8190