Reference Work Entry

International Encyclopedia of Statistical Science

pp 991-995


Non-uniform Random Variate Generations

  • Pierre L’EcuyerAffiliated withUniversité de Montréal


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 ...

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