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Generating gamma variates by a modified rejection technique

By J. H. Ahrens, U. Dieter

Communications of the ACM, Vol. 25 No. 1, Pages 47-54

A suitable square root transformation of a gamma random variable with mean a ≥ 1 yields a probability density close to the standard normal density. A modification of the rejection technique then begins by sampling from the normal distribution, being able to accept and transform the initial normal observation quickly at least 85 percent of the time (95 percent if a ≥ 4). When used with efficient subroutines for sampling from the normal and exponential distributions, the resulting accurate method is significantly faster than competing algorithms.

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