Efficient Algorithm for Generating Maxwell Random Variables

A fast, easily implemented and high efficiency algorithm is derived for sampling from the Maxwell distribution. The algorithm is derived from the rejection-acceptance sampling method using the simple exponential decay function as an envelope function for the Maxwell distribution. The derived algorithm requires less number of random numbers per iteration, consumes less number of random numbers per sample and requires less expensive computation functions than the direct and Johnk's algorithms. The speed of the proposed algorithm is about 1.6 times that of the direct algorithm and is about 1.5 times that of Johnk's algorithm. Since the proposed algorithm for sampling from Maxwell distribution verified high efficiency and speed, Watt random variables can be generated by transforming Maxwell random variables generated by the proposed algorithm. The speed of generating Watt random variables using the proposed algorithm is about 1.1 times that generated from Kalos's algorithm.