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A note on gamma variate generators with shape parameter less than unity

Eine Bemerkung über Gamma-Zufallsgeneratoren mit Formparameter kleiner als Eins

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Abstract

A modification is given for an algorithm of Ahrens and Dieter [1] which generates random Gamma variates with shape parameter less than unity. The modified algorithm is substantially faster, although hardly more complex than the original one.

Zusammenfassung

Es wird eine Modifikation des Algorithmus von Ahrens und Dieter [1] angegeben, welcher gammaverteilte Zufallsvariable mit einem Formparameter kleiner Eins erzeugt. Der modifizierte Algorithmus ist deutlich schneller, obwohl er kaum komplexer ist als der ursprüngliche.

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References

  1. Ahrens, J. H., Dieter, U.: Computer methods for sampling from gamma, beta, Poisson and binomial distributions. Computing12, 223–246 (1974).

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  2. Atkinson, A. C., Pearce, M. C.: The computer generation of beta, gamma, and normal random variables (with discussion). J. Royal Stat. Soc.A139, 431–461 (1976).

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  3. Cheng, R. C. H., Feast, G. M.: Gamma variate generators with increased shape parameter range. Comm. ACM23, 389–394 (1980).

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Best, D.J. A note on gamma variate generators with shape parameter less than unity. Computing 30, 185–188 (1983). https://doi.org/10.1007/BF02280789

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  • DOI: https://doi.org/10.1007/BF02280789

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