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The Quality of Non-Uniform Random Numbers

  • Wolfgang Hörmann
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1993)

Summary

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.

Keywords

Transformation Method Uniform Method Uniform Random Number Uniform Generator Rejection Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

Die Qualität von nicht gleichverteilten Zufallszahlen wird nicht nur vom benützten Gleichverteilungsgenerator sondern auch von der verwendeten Transformationsmethode beeinflußt. Dieser Unterschied in der Qualität verschiedener “exakter” Transformationsmethoden wurde bisher in der Literatur fast völlig vernachlässigt. Darum vergleichen wir das Verhalten vier verschiedener Transformationsmethoden in Verbindung mit linearen Kongruenzgeneratoren (LKG). Heuristische Überlegungen, die Berechnung von zwei Maßen für die Approximation und ein statistischer Test zeigen, daß die Inversionsmethode am besten abschneidet. Unter den anderen Verfahren schneiden die Verwerfung — in Kombination mit einem LKG mit kleinem Multiplikator — und die Quotientenmethode am schlechtesten ab. Es ist nicht auszuschließen, daß ihre Verwendung die Resultate von Simulationsstudien verfälscht.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1994

Authors and Affiliations

  • Wolfgang Hörmann
    • 1
  1. 1.WU WienAustria

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