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von Neumann's comparison method for random sampling from the normal and other distributions

Author: George E. Forsythe
Journal: Math. Comp. 26 (1972), 817-826
MSC: Primary 65C10
MathSciNet review: 0315863
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Abstract: 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). It is shown how to generate samples from any distribution whose probability density function is piecewise both absolutely continuous and monotonic on $ ( - \infty ,\infty )$. A special case delivers normal deviates at an average cost of only 4.036 uniform deviates each. This seems more efficient than the Center-Tail method of Dieter and Ahrens, which uses a related, but different, method of generalizing the von Neumann idea to the normal distribution.

References [Enhancements On Off] (What's this?)

  • [1] J. H. Ahrens and U. Dieter, Computer methods for sampling from the exponential and normal distributions, Comm. ACM 15 (1972), 873–882. MR 0336955,
  • [2] U. Dieter and J. H. Ahrens, A combinatorial method for the generation of normally distributed random numbers, Computing (Arch. Elektron. Rechnen) 11 (1973), no. 2, 137–146 (English, with German summary). MR 388727,
  • [3] John von Neumann, ``Various techniques used in connection with random digits, in Monte Carlo Method, Appl. Math. Series, vol. 12, U. S. Nat. Bureau of Standards, 1951, pp. 36-38 (Summary written by George E. Forsythe); reprinted in John von Neumann, Collected Works. Vol. 5, Pergamon Press; Macmillan, New York, 1963, pp. 768-770. MR 28 #1104.

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Keywords: Random variables, random deviates, normal, sample, von Neumann, comparison, center, tail, Gaussian, distribution
Article copyright: © Copyright 1972 American Mathematical Society