Automatic Nonuniform Random Variate Generation in R

Günter Tirler and Josef Leydold


Random variate genration is an important tool in statistical computing. Many programms for simulation or statistical computing (e.g. R) provide a collection of random variate generators for many standard distributions. However, as statistical modeling has become more sophisticated there is demand for larger classes of distributions. Adding generators for newly required distribution seems not to be the solution to this problem. Instead so called automatic (or black-box) methods have been developed in the last decade for sampling from fairly large classes of distributions with a single piece of code. For such algorithms a data about the distributions must be given; typically the density function (or probability mass function), and (maybe) the (approximate) location of the mode. In this contribution we show how such algorithms work and suggest an interface for R as an example of a statistical library.

Mathematics Subject Classification: 65C10 (Random Number Generation)

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

General Terms: Algorithms

Key Words: R, nonuniform random variate generation, universal algorithm, automatic code generator, transformed density rejection, continuous distribution

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