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Consider the following code:

sampling = 
 Compile[{{T, _Real}, {nparticles, _Integer}}, 
  RandomVariate[GammaDistribution[3, T], nparticles], 
  CompilationTarget -> "C"]

It will be a part of another compiled code, so it is crucial for me to keep everything compiled. However, it calls MainEvaluate, probably because GammaDistribution is not compilable. Is there a workaround here?

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Is UniformDistribution compilable? (Or maybe RandomReal?) If so, then making use of the fact that a Gamma[3, t] has the same distribution as a sum of 3 Exponential random variables with parameter $t$ might help:

nparticles = 1000000;
t = 4.5;
x = -t  Total[Log[#]] & /@ RandomVariate[UniformDistribution[{0, 1}], {n, 3}];
Show[Histogram[x, "FreedmanDiaconis", "PDF"],
 Plot[PDF[GammaDistribution[3, t], z], {z, 0, 50}]]

PDF of gamma distribution and histogram of a random sample from that distribution

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