Numerical Inversion

Abstract

The inversion method (see Sect. 2.1) is one of the most important key-stones of random variate generation. In this chapter we try to demonstrate how the inversion principle can be applied to obtain universal algorithms. If the inverse of the cumulative distribution function F ^-1 is computable, we can generate variates of the desired distribution without any additional information. So we could speak of a “true” black-box algorithm in this case, as we simply can return F ^-1 (U). Unfortunately most important distributions have a cdf that cannot be expressed in terms of elementary functions and the inverse cdf is even more difficult. Hence the assumption that F ^-1 is available as a black-box is often of little practical relevance.