Computer methods for sampling from gamma, beta, poisson and bionomial distributions

@article{Ahrens2005ComputerMF,
  title={Computer methods for sampling from gamma, beta, poisson and bionomial distributions},
  author={J. H. Ahrens and Ulrich Dieter},
  journal={Computing},
  year={2005},
  volume={12},
  pages={223-246}
}
Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed for variable parameters. The known convenient methods are slow when the parameters are large. Therefore new procedures are introduced which can cope efficiently with parameters of all sizes. Some algorithms require sampling from the normal distribution as an intermediate step. In… Expand
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References

SHOWING 1-10 OF 23 REFERENCES
A combinatorial method for the generation of normally distributed random numbers
TLDR
The proposed method generates standard normal variablesx using a variant of J. v. Neumann's algorithm for the generation of exponentially distributed random numbers and an acceptance-rejection approach of G. Marsaglia. Expand
Pseudo-random numbers
TLDR
The included ALGOL and FORTRAN subroutines will enable programmers to make practical use of this paper and indicate that the factors 4a ≈2k ξ are superior. Expand
Von Neumann''s comparison method for random sampling from the normal and other distributions.
The author presents a generalization he worked out in 1950 of von Neumann''s method of generating random samples from the exponential distribution by comparisons of uniform random numbers on (0,1).Expand
A Simple Algorithm for Generating Binomial Random Variables When N is Large
Abstract This article proposes a simple algorithm for generating binomial (N, p) random variables when N is large. The method involves looking mainly at medians in uniform (0, 1) samples of sizeExpand
Extensions of Forsythe’s method for random sampling from the normal distribution
This article is an expansion of G. E. Forsythe's paper "Von Neumann's com- parison method for random sampling from the normal and other distributions" (5). It is shown that Forsythe's method for theExpand
Pseudo-random numbers. The exact distribution of pairs
4bstract. Pseudo-random numbers are usually generated by linear congruential methods. Starting with an integer yo, a sequence (y1 j is constructed by yi+1 _ ay; + r (mod m), m, a, r being integers.Expand
Computer methods for sampling from the exponential and normal distributions
TLDR
The authors' primary conwiba~ion is the rise of polynomiaI sampling (as ex~ p/tiffed in Section 2) to eliminate any dependency on standard&ruction programs. Expand
An exact determination of serial correlations of pseudo-random numbers
SummaryExact expressions for serial correlations of sequences of pseudo-random numbers are derived. The reduction to generalized Dedekind sums is of optimum simplicity and covers all cases of theExpand
A fast procedure for generating normal random variables
A technique for generating normally distributed random numbers is described. It is faster than those currently in general use and is readily applicable to both binary and decimal computers.
The Art of Computer Programming
TLDR
The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid. Expand
...
1
2
3
...