Random variate generation for unimodal and monotone densities

Abstract

We consider the problem of generating random variates with a monotone nonincreasing density on [0, ∞). No bounds are known that would allow a straightforward application of the rejection method, and the inverse of the distribution function is not explictly known either. We develop the inversion/rejection method, and show how it can be used for all monotone densities, even those with an infinite peak at 0 and unbounded support, provided only that the densityf and the distribution functionF can be computed for eachx. A theoretical analysis of the average time behaviaour of the algorithm is included.