Expressing a Random Variable in Terms of Uniform Random Variables

This note suggests that expressing a distribution function as a mixture of suitably chosen distribution functions leads to improved methods for generating random variables in a computer. The idea is to choose a distribution function which is close to the original and use it most of the time, applying the correction only infrequently. Mixtures allow this to be done in probability terms rather than in the more elaborate ways of conventional numerical analysis, which must be applied every time.