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Non-uniform Random Variate Generations

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International Encyclopedia of Statistical Science

Introduction

As explained in the entry Uniform Random Number Generators, the simulation of random variables on a computer operates in two steps: In the first step, uniform random number generators produce imitations of i.i.d. \(U(0,1)\) (uniform over (0,1)) random variables, and in the second step these numbers are transformed in an appropriate way to imitate random variables from other distributions than the uniform ones, and other types of random objects. Here we discuss the second step only, assuming that infinite sequences of (truly) i.i.d. \(U(0,1)\) random variables are available from the first step. This assumption is not realized exactly in software implementations, but good-enough approximations are available (L’Ecuyer 2004).

For some distributions, simple exact transformations from the uniform to the target distribution are available, usually based on the inversion method. But for many types of distributions and processes, in particular those having shape parameters, and...

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Author information

Authors and Affiliations

  1. Université de Montréal, Montréal, QC, Canada

    Pierre L’Ecuyer (Professor, DIRO)

Authors
  1. Pierre L’Ecuyer
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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L’Ecuyer, P. (2011). Non-uniform Random Variate Generations. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_408

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