generating a gamma random variable

Faheem Mitha wrote:

Dear R People,

This question has nothing to do with R directly, but it is a simulation
question. I need to generate a random variable distributed as
gamma(\alpha,\beta), with the additional proviso that it must be a
function of random variable(s) which do not depend on \alpha, \beta. In
this case, I have \alpha = (T-1)/2, where T is a positive integer.

So, it seems reasonable to first simulate from a chi-squared distribution
with T-1 degrees of freedom. Then multiply by the appropriate scale
factor.

Is there a reason why you don't want to use either rgamma or rchisq?

Come to think of it, there is no reason why I should not use rchisq. This
would depend on T, but that is Ok, since T is a constant within the
calculation, and the method I'm using above depends on T being fixed
anyway. This would probably be the most efficient way, since to get a
gamma distribution would then just involve multiplying by a constant.

Background: I'm using this simulation to run coupled Markov chains. T is a
contant within the calculation.

There seem to be at least two different ways to simulate from a
chi-squared distribution with n degrees of freedom.

There are much quicker ways than you suggested.  A rejection algorithm
is one choice.  I'll save him the embarrassment of having to indulge in
self promotion by suggesting that the classic text is Brian Ripley's
1987 book 'Stochastic Simulation'. There is also an algorithm in Press
et al.'s 'Numerical Recipes in C'.

Yes, actually Stochastic Simulation is on my desk as I write, and it
suggests the methods I outlined above for simulating from chisq/gamma.

I'm still wondering about how to check (in general) whether a bunch of rvs
are distributed as gamma or not. How do people check such things in
practice?

Thanks for your reply.
                                      Sincerely, Faheem Mitha.

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