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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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