ABSTRACT
Random variables with exponential and gamma distributions are frequently used to model waiting times in queues of various kinds, and this is a natural consequence of the predictions of the Poisson process. This chapter provides some examples of particular methods for simulating non-uniform random variables. Particular rules may be exploited to simulate multivariate random variables. It is because of central limit theorems that the normal distribution is encountered so frequently, and forms the basis of much statistical theory. H. R. Neave showed that when the standard Box–Muller method is operated using pseudo-random numbers from a particular multiplicative congruential generator, the resulting numbers exhibit some strikingly non-normal properties. If the Box–Muller method were to be used regularly on a computer then it would be worth incorporating the following interesting modification, which avoids the use of time-consuming sine and cosine functions.
