Chapter 3 Uniform Random Number Generation

Abstract This chapter covers the basic design principles and methods for uniform random number generators used in simulation. We also briefly mention the connections between these methods and those used to construct highly-uniform point sets for quasi-Monte Carlo integration. The emphasis is on the methods based on linear recurrences modulo a large integer, or modulo 2. This reflects the fact that their mathematical structure is much better understood than other types of generators, and that most generators used in simulation have that form. We discuss the main requirements for a good generator, theoretical figures of merit for certain classes of linear-type generators, implementation issues, nonlinear generators, and statistical testing.

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