Extensions of von Neumann’s method for generating random variables

Monahan, John F.

doi:10.1090/S0025-5718-1979-0528058-7

Extensions of von Neumann’s method for generating random variables
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by John F. Monahan PDF

Math. Comp. 33 (1979), 1065-1069 Request permission

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 ${e^{ - G(x)}}$ 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.

References

J. H. Ahrens and U. Dieter, Extensions of Forsythe’s method for random sampling from the normal distribution, Math. Comp. 27 (1973), 927–937. MR 329190, DOI 10.1090/S0025-5718-1973-0329190-8
A. C. Atkinson and M. C. Pearce, The computer generation of beta, gamma and normal random variables, J. Roy. Statist. Soc. Ser. A 139 (1976), no. 4, 431–461. With a discussion and a reply by the authors. MR 433803, DOI 10.2307/2344349

Comm. ACM

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, DOI 10.1007/bf02252903
George E. Forsythe, von Neumann’s comparison method for random sampling from the normal and other distributions, Math. Comp. 26 (1972), 817–826. MR 315863, DOI 10.1090/S0025-5718-1972-0315863-9
A. J. Kinderman, J. F. Monahan, and J. G. Ramage, Computer methods for sampling from Student’s $t$ distribution, Math. Comp. 31 (1977), no. 140, 1009–1018. MR 443294, DOI 10.1090/S0025-5718-1977-0443294-4

Monte Carlo Method