Computer generation of gamma random variables

Abstract

A new method for generating random variables from the gamma distribution with nonintegral shape parameter α is proposed. This method is similar to two other methods recently given by Wallace and Fishman. It is compared with Fishman's and Ahrens and Dieter's methods. The core storage requirements and programming effort for this method are similar to those of Fishman's method. The proposed method is the same as Fishman's method for 1 ≤ α < 2 and is faster than Fishman's method for 3 ≤ α ≤ 19. Also, the proposed method is much simpler than Ahrens and Dieter's method and is faster for α ≤ 8.