Chapter 4 Random Number Generation Pierre L'ecuyer

Random Number Generators and Empirical Tests

We recall some requirements for \good" random number generators and argue that while the construction of generators and the choice of their parameters must be based on theory, a posteriori empirical testing is also important. We then give examples of tests failed by some popular generators and examples of generators passing these tests.

Random Number Generators: Selection Criteria and Testing

Four Canadian Contributions to Stochastic Modeling

We outline the history, significance, and impact of four important contributions by Canadian researchers to stochastic modeling for operational research: the use of the uniformization method to compute transient probabilities for Markov chains, pioneered by Winfried K. Grassmann, contributions to Markov decision processes by Martin L. Puterman, contributions to the development of random number ...

Random Number Generation 1

Universit e de Montr eal 2 4.1 INTRODUCTION Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0; 1) random variables (i.e., continuous random variables distributed uniformly over the interval (0; 1)). These r...

Orbits and lattices for linear random number generators with composite moduli

In order to analyze certain types of combinations of multiple recursive linear congruential generators (MRGs), we introduce a generalized spectral test. We show how to apply the test in large dimensions by a recursive procedure based on the fact that such combinations are subgenerators of other MRGs with composite moduli. We illustrate this with the well-known RANMAR generator. We also design a...