Generating Gamma Distributed Variates for Computer Simulation Models

Compares two methods of generating random variates for simulation studies from gamma distributions with nonintegral shape parameters. The commonly used probability switch approximation method is examined for accuracy and computation costs, while Johnk's exact method is investigated for computation costs. The probability switch method approximates the gamma distribution very closely for shape parameters above 5.0, poorly between 1.0 and 5.0, and not at all below 1.0. Johnk's method, while exact, is 2.5 to 3 times slower in the shape parameter range of 1.0 to 5.0. Johnk's method is recommended for shape parameters below 5.0, and the probability switch method is recommended above 5.0. FORTRAN routines for the two methods are provided. The data used to investigate the accuracy of the probability switch method are appended, as are selected plots of the distributions and a discussion of methods to generate beta variates.