Random Variable Generation

Abstract

The methods developed in this book mostly rely on the possibility of producing (with a computer) a supposedly endless flow of random variables (usually iid) for well-known distributions. Such a simulation is, in turn, based on the production of uniform random variables. We thus provide in this chapter some basic methodology for doing this. In particular, we present a uniform random number generator and illustrate methods for using these uniform random variables to produce random variables from both standard and nonstandard distributions.

“Have you any thought,” resumed Valentin, “of a tool with which it could be done?”

“Speaking within modern probabilities, I really haven’t,” said the doctor.

— G.K. Chesterton, The Innocence of Father Brown