Generating Uniform Random Numbers
Generating Uniform Random Numbers
Christos Alexopoulos and Dave Goldsman
Georgia Institute of Technology, Atlanta, GA, USA
June 7, 2009
Alexopoulos and Goldsman
June 7, 2009 1 / 38
Outline
1 Introduction 2 Some Generators We Won't Use 3 Linear Congruential Generators 4 Tausworthe Generator 5 Generalizations of LCGs 6 Choosing a Good Generator -- Some Theory 7 Choosing a Good Generator -- Statistical Tests
2 Goodness-of-Fit Test Runs Tests for Independence
Alexopoulos and Goldsman
June 7, 2009 2 / 38
Introduction
Introduction
Uniform(0,1) random numbers are the key to random variate generation in simulation.
Goal: Give an algorithm that produces a sequence of pseudo-random numbers (PRN's) R1, R2, . . . that "appear" to be iid Unif(0,1).
Desired properties of algorithm output appears to be iid Unif(0,1) very fast ability to reproduce any sequence it generates
References: Banks, Carson, Nelson, and Nicol (2005); Bratley, Fox, and Schrage (1987); Knuth (2) (1981); Law (2007).
Alexopoulos and Goldsman
June 7, 2009 3 / 38
Introduction
Classes of Unif(0,1) Generators
output of random device table of random numbers midsquare (not very useful) Fibonacci (not very useful) linear congruential (most commonly used in practice) Tausworthe (linear recursion mod 2) hybrid
Alexopoulos and Goldsman
June 7, 2009 4 / 38
Outline
Some Generators We Won't Use
1 Introduction 2 Some Generators We Won't Use
3 Linear Congruential Generators
4 Tausworthe Generator
5 Generalizations of LCGs
6 Choosing a Good Generator -- Some Theory
7 Choosing a Good Generator -- Statistical Tests 2 Goodness-of-Fit Test Runs Tests for Independence
Alexopoulos and Goldsman
June 7, 2009 5 / 38
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