Reference Work Entry

International Encyclopedia of Statistical Science

pp 1625-1630

Date:

Uniform Random Number Generators

  • Pierre L’EcuyerAffiliated withUniversité de Montréal

Introduction

A growing number of modern statistical tools are based on Monte Carlo ideas; they sample independent random variables by computer to estimate distributions, averages, quantiles, roots or optima of functions, etc. These methods are developed and studied in the abstract framework of probability theory, in which the notion of an infinite sequence of independent random variables uniformly distributed over the interval (0, 1) (i.i.d. \(\mathcal{U}(0,1)\)), for example, is well-defined, and the theory is built under the assumption that such random variables can be sampled at will. But in reality, the notion of i.i.d. random variables cannot be implemented exactly on current computers. It can be approximated to some extent by physical devices, but these approximations are cumbersome, inconvenient, and not always reliable, so they are rarely used for computational statistics. Random number generators used for Monte Carlo applications are in reality deterministic algorit ...

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