The Quality of Non-uniform Random Numbers

Wolfgang Hörmann


The quality of non-uniform random numbers is not only influenced by the quality of the uniform generator that is used but also by the transformation method applied to the uniform random numbers. This differences in quality between ``exact'' methods were almost entirely neglected in literature. So we compare the behaviour of four different transformation methods when combined with a linear congruential uniform generator (LCG). Heuristic considerations, the computation of two measures of approximation and a statistical test show that the inversion method performs best. Among the others rejection, when combined with a LCG with small multiplier, and ratio of uniforms perform worse. Their use could slightly change the results of some simulation studies.

Mathematics Subject Classification: 65C10 (Random Number Generation)

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

General Terms: Algorithms

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