When the shape parameter, &agr;, is integral, generating gamma random variables with a digital computer is straightforward. There is no simple method for generating gamma random variates with non-integral shape parameters. A common procedure is to approximately generate such random variables by use of the so-called probability switch method. Another procedure, which is exact, is due to Jöhnk. This paper presents a rejection method for exactly generating gamma random variables when &agr; is greater than 1. The efficiency of the rejection method is shown to be better than the efficiency of Jöhnk's method. The paper concludes that when &agr; is non-integral the following mix of procedures yields the best combination of accuracy and efficiency: (1) when &agr; is less than 1, use Jöhnk's method; (2) when 1 is less than &agr; and &agr; is less than 5, use the rejection method; (3) when &agr; is greater than 5, use the probability switch method.
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