Squeeze Methods for Generating Gamma Variates

Abstract

Two algorithms are given for generating gamma distributed random variables. The algorithms, which are valid when the shape parameter is greater than one, use a uniform majorizing function for the body of the distribution and exponential majorizing functions for the tails. The algorithms are self-contained, requiring only U (0, 1) variates. Comparisons are made to four competitive algorithms in terms of marginal execution times, initialization time, and memory requirements. Marginal execution times are less than those of existing methods for all values of the shape parameter, as implemented here in FORTRAN.

Key Words:

• Gamma distribution
• Simulation
• Random number generation
• Rejection methods
• Monte Carlo
• Distribution sampling