Logarithmic transformation-based gamma random number generators

Developing efficient gamma variate generators is important for Monte Carlo methods. With a brief review of existing methods for generating gamma random numbers, this article proposes two simple gamma variate generators that are obtained from the ratio- of-uniforms method and based on two logarithmic transformations of the gamma random variable. One transformation allows for the generators to work for all shape parameter values. The other is introduced to have improved efficiency for shape parameters smaller than or equal to one.