Generating gamma variates by a modified rejection technique

@article{Ahrens1982GeneratingGV,
  title={Generating gamma variates by a modified rejection technique},
  author={J. H. Ahrens and Ulrich Dieter},
  journal={Commun. ACM},
  year={1982},
  volume={25},
  pages={47-54}
}
A suitable square root transformation of a gamma random variable with mean a ≥ 1 yields a probability density close to the standard normal density. A modification of the rejection technique then begins by sampling from the normal distribution, being able to accept and transform the initial normal observation quickly at least 85 percent of the time (95 percent if a ≥ 4). When used with efficient subroutines for sampling from the normal and exponential distributions, the resulting accurate method… Expand
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References

SHOWING 1-10 OF 31 REFERENCES
Acceptance-Rejection Techniques for Sampling from The Gamma and Beta Distributions.
Abstract : John von Neumann's idea of sampling from a distribution by majorizing its probability density function is applied to gamma and beta distributions. Optimum envelopes are constructed… Expand
A survey of methods for sampling from the gamma distribution
TLDR
The current state of the art in gamma random variate generation is surveyed including the leading algorithms of Ahrens and Dieter, Atkinson, Cheng, Fishman, Marsaglia, Tadikamalla and Wallace. Expand
On computer generation of gamma random variables by rejection and composition procedures 2
The paper presents various algorithms for generating gamma random variables, by combining rejection and composition procedures. Two efficient algorithms are given for the case when the parameter of… Expand
Computer generation of gamma random variables
A new method for generating random variables from the gamma distribution with nonintegral shape parameter α is proposed. This method is similar to two other methods recently given by Wallace and… Expand
Computer Generation of Random Variables Using the Ratio of Uniform Deviates
TLDR
The ratio-of-uniforms method for generating random variables having continuous nonuniform distributions is presented and can be used for generating short and often as fast algorithms as well as longer algorithms. Expand
Sampling from the gamma distribution on a computer
TLDR
This paper describes a method of generating gamma variates that appears to be less costly than Wallace's recently suggested method, and which also dominates methods recently suggested by Dieter and Ahrens. Expand
Some Simple Gamma Variate Generators
SUMMARY Gamma variates with index a> 1 are produced by combining two adaptations of Kinderman and Monahan's technique for generating random variates by the use of the ratio of uniform variates.… Expand
An Easily Programmed Algorithm for Generating Gamma Random Variables
THIS note describes an easily programmed algorithm for generating gamma random variables with index ax greater than one which is intended to be complementary to the algorithms GO of Ahrens and Dieter… Expand
The squeeze method for generating gamma variates
Abstract This paper describes an exact method for computer generation of random variables with a gamma distribution. The method is based on the Wilson-Hilferty transformation and an improvement on… Expand
The Generation of Gamma Variables with Non‐Integral Shape Parameter
A rejection method is described for generating exact gamma variates with shape parameter α, where α > 1. The method is compared with previously published methods in terms of speed and program… Expand
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