A Convenient Method for Generating Normal Variables

Abstract

A normal random variable X may be generated in terms of uniform random variables $u_1 $, $u_2 $, in the following simple way: 86 percent of the time, put $X = 2(u_1 + u_2 + u_3 - 1.5)$,11 percent of the time, put $X = 1.5(u_1 + u_2 - 1)$, and the remaining 3 percent of the time, use a more complicated procedure so that the resulting mixture is correct. This method takes only half again as long as the very fastest methods, is much simpler, and requires very little storage space.