Extensions of von Neumann's method for generating random variables

Author:
John F. Monahan

Journal:
Math. Comp. **33** (1979), 1065-1069

MSC:
Primary 65C10

MathSciNet review:
528058

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**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**0329190**, 10.1090/S0025-5718-1973-0329190-8**[2]**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**0433803****[3]**R. P. BRENT, "Algorithm 488: A Gaussian pseudo-random number generator,"*Comm. ACM*, v. 17, 1974, pp. 704-706.**[4]**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**0388727****[5]**George E. Forsythe,*von Neumann’s comparison method for random sampling from the normal and other distributions*, Math. Comp.**26**(1972), 817–826. MR**0315863**, 10.1090/S0025-5718-1972-0315863-9**[6]**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**0443294**, 10.1090/S0025-5718-1977-0443294-4**[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. 36-38.

Retrieve articles in *Mathematics of Computation*
with MSC:
65C10

Retrieve articles in all journals with MSC: 65C10

Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1979-0528058-7

Keywords:
Random number generation,
von Neumann's comparison method

Article copyright:
© Copyright 1979
American Mathematical Society