Computer Generation of Gamma Random Variates with Non-integral Shape Parameters When the shape parameter, a, 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 Johnk. This paper presents a rejection method for exactly generating gamma random variables when a is greater than 1. The efficiency of the rejection method is shown to be better than the efficiency of Johnk's method. The paper concludes that when a is non-integral the following mix of procedures yields the best combination of accuracy and efficiency: (1) when a is less than 1, use Johnk's method; (2) when 1 is less than a and a is less than 5, use the rejection method; (3) when a is greater than 5, use the probability switch method. CACM December,1974 Wallace, N. D. simulation, gamma random variables, probability distribution, random numbers 5.5 8.1 CA741205 JB January 16, 1978 9:35 AM 2569 5 2569 2569 5 2569 2569 5 2569 2847 5 2569 2928 5 2569 3046 5 2569 3098 5 2569 3107 5 2569 1751 6 2569 2277 6 2569 2380 6 2569 2522 6 2569 2569 6 2569 2569 6 2569 2569 6 2569 2569 6 2569 2569 6 2569 2847 6 2569 2847 6 2569 3098 6 2569