Extensions of von Neumann's method for generating random variables
Author:
John F. Monahan
Journal:
Math. Comp. 33 (1979), 10651069
MSC:
Primary 65C10
MathSciNet review:
528058
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Abstract: Von Neumann's method of generating random variables with the exponential distribution and Forsythe's method for obtaining distributions with densities of the form are generalized to apply to certain power series representations. The flexibility of the power series methods is illustrated by algorithms for the Cauchy and geometric distributions.
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J. VON NEUMANN, "Various techniques used in connection with random digits," in Monte Carlo Method, Nat. Bur. Standards Appl. Math. Series, v. 12, 1951, pp. 3638.
 [1]
 J. H. AHRENS & U. DIETER, "Extensions of Forsythe's method for random sampling from the normal distribution," Math. Comp., v. 27, 1973, pp. 927937. MR 0329190 (48:7532)
 [2]
 A. C. ATKINSON & M. C. PIERCE, "The computer generation of beta, gamma and normal random variables," J. Roy. Statist. Soc. Ser. A, v. 139, 1976, pp. 431448. MR 0433803 (55:6774)
 [3]
 R. P. BRENT, "Algorithm 488: A Gaussian pseudorandom number generator," Comm. ACM, v. 17, 1974, pp. 704706.
 [4]
 U. DIETER & J. H. AHRENS, "A combinatorial method for the generation of normally distributed random numbers," Computing, v. 11, 1973, pp. 137146. MR 0388727 (52:9561)
 [5]
 G. FORSYTHE, "Von Neumann's comparison method for random sampling from the normal and other distributions," Math. Comp., v. 26, 1972, pp. 817826. MR 0315863 (47:4412)
 [6]
 A. J. KINDERMAN, J. F. MONAHAN & J. G. RAMAGE, "Computer methods for sampling from Student's t distribution," Math. Comp., v. 31, 1977, pp. 10091018. MR 0443294 (56:1664)
 [7]
 J. VON NEUMANN, "Various techniques used in connection with random digits," in Monte Carlo Method, Nat. Bur. Standards Appl. Math. Series, v. 12, 1951, pp. 3638.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905280587
PII:
S 00255718(1979)05280587
Keywords:
Random number generation,
von Neumann's comparison method
Article copyright:
© Copyright 1979
American Mathematical Society
