On Mixture Methods for the Computer Generation of Random Variables

The general mixture method for the computer generation of random variables from a source of (pseudo) uniform (0, 1) random numbers is reviewed. It is shown that several of the general tools commonly used in generating random variables can be described as mixture methods. Such descriptions seem useful for illuminating and unifying the methods, and also for suggesting possible variations. The latter point is illustrated by a variation of the acceptance-rejection method that avoids repetition of steps.