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A combinatorial method for the generation of normally distributed random numbers

Eine kombinatorische Methode zur Erzeugung von normalverteilten Zufallszahlen

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Abstract

The proposed method generates standard normal variablesx. In 84.27% of all cases sampling from the centre\((|x| \leqslant \sqrt 2 )\) of the normal distribution is carried out using a variant ofJ. v. Neumann's algorithm for the generation of exponentially distributed random numbers. For sampling from the tails\((|x| > \sqrt 2 )\) the same method byJ. v. Neumann is combined with an acceptance-rejection approach ofG. Marsaglia.

Zusammenfassung

Die Methode erzeugt Zufallszahlen der standardisierten Normalverteilung. Für das Zentrum\(|x| \leqslant \sqrt 2 \) (84,27% aller Fälle) wird eine Variante des v.Neumannschen Vergleichsverfahrens zur Erzeugung exponentialverteilter Zufallszahlen vorgeschlagen. Für die Werte\(|x| > \sqrt 2 \) der Normalverteilung wird eine Verwerfungsmethode vonG. Marsaglia verwendet, bei der die majorisierende Funktion die Exponentialfunktion ist. Die dafür benötigten exponential-verteilten Zufallszahlen werden durch die ursprüngliche v.Neumann'sche Methode erzeugt.

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Authors and Affiliations

  1. Institut für Math. Statistik, Technische Hochschule Graz, Hammerlinggasse 6/VI, A-8010, Graz, Österreich

    U. Dieter

  2. Department of Applied Mathematics, Nova Scotia Technical College, Halifax, Nova Scotia, Canada

    J. H. Ahrens

Authors
  1. U. Dieter
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  2. J. H. Ahrens
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Additional information

Dedicated to Prof.H. Richter (München) on the occasion of his 60th birthday.

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Dieter, U., Ahrens, J.H. A combinatorial method for the generation of normally distributed random numbers. Computing 11, 137–146 (1973). https://doi.org/10.1007/BF02252903

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  • DOI: https://doi.org/10.1007/BF02252903

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