Two New Ratio-of-Uniforms Gamma Random Number Generators

Two simple algorithms to generate gamma random numbers are proposed in this article. Both algorithms use the ratio-of-uniforms method and are based on logarithmic transformations of the gamma random variable. One algorithm applies to all positive shape parameter value without limitation. It has good performance compared with other existing algorithms for both shape parameter values greater than 1 and smaller than 1. The other algorithm is limited to shape parameter smaller or equal to 1, but it has better performance compared with the first algorithm in that limited shape parameter range. Furthermore, the proposed methods will gain more efficiency if the logarithmic scale is used for the generated Gamma random numbers.