2569	 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 . 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 when a is less than use Johnk s method when is less than a and a is less than use the rejection method when a is greater than use the probability switch method. simulation gamma random variables probability distribution random numbers
