The analysis of some algorithms for generating random variates with a given hazard rate

We analyze the expected time performance of two versions of the thinning algorithm of Lewis and Shedler for generating random variates with a given hazard rate on [0,∞]. For thinning with fixed dominating hazard rate g(x) = c for example, it is shown that the expected number of iterations is cE(X) where X is the random variate that is produced. For DHR distributions, we can use dynamic thinning by adjusting the dominating hazard rate as we proceed. With the aid of some inequalities, we show that this improves the performance dramatically. For example, the expected number of iterations is bounded by a constant plus E(log₊(h(0)X)) (the logarithmic moment of X).