A tutorial on uniform variate generation

• Published in: Proceedings of the 21st conference on Winter simulation pp. 40 - 49
• Main Author: L'Ecuyer, P.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 01.10.1989
• Series: ACM Conferences
• Subjects: Computing methodologies > Modeling and simulation; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on matrices; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on polynomials; Mathematics of computing > Probability and statistics > Probabilistic reasoning algorithms > Random number generation
• ISBN: 0911801588; 9780911801583
• DOI: 10.1145/76738.76744

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in the appropriate way. In this tutorial, we examine practical ways of generating such variates on a computer. We compare them in terms of ease of implementation, efficiency, flexibility, theoretical support, and statistical robustness. We look in particular at the following classes of generators: linear congruential (in scalar and matrix form), lagged-Fibonacci (including generalized feedback shift register) and combined. We also mention others and give a bibliographic survey of the most recent papers on the subject.