An inverse method for the generation of random normal deviates on large-scale computers

Author:
Mervin E. Muller

Journal:
Math. Comp. **12** (1958), 167-174

MSC:
Primary 65.00; Secondary 68.00

DOI:
https://doi.org/10.1090/S0025-5718-1958-0102905-1

MathSciNet review:
0102905

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References | Similar Articles | Additional Information

**[1]**G. E. P. Box & M. E. Muller, ``A note on the generation of normal deviates,''*Ann. Math. Stat.*, to be published.**[2]**George E. Forsythe, ``Generation and testing of random digits at the National Bureau of Standards, Los Angeles,''*Monte Carlo Method*, NBS, Applied Mathematics Series 12, U. S. Government Printing Office, Washington, D. C., 1951, p. 34-35. [*MTAC*, Rev.**42**, v. XI, 1957, p. 43-44.]**[3]**Joseph O. Harrison Jr.,*Piecewise polynomial approximation for large-scale digital calculators*, Math. Tables and Other Aids to Computation**3**(1949), 400–407. MR**0032202**, https://doi.org/10.1090/S0025-5718-1949-0032202-9**[4]**F. B. Hildebrand,*Introduction to numerical analysis*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR**0075670****[5]**D. L. Johnson,*Generating and testing pseudo random numbers on the IBM Type 701*, Math. Tables Aids Comput.**10**(1956), 8–13. MR**0076467**, https://doi.org/10.1090/S0025-5718-1956-0076467-X**[6]**M. L. Juncosa,*Random number generation on the BRL high-speed computing machines*, Rep. No. 855, Ballistic Research Laboratories, Aberdeen Proving Ground, Md., 1953. MR**0059617****[7]**Herman Kahn, ``Applications of Monte Carlo,'' RAND Project Report, 1954, Revised 1956, RAND Project Report RM-1237-AEC.**[8]**C. Lanczos, ``Trigonometric interpolation of empirical and analytical functions,''*Jn. Math. Phys.*, v. 17, 1938, p. 123-199.**[9]**Cornelius Lanczos,*Chebyshev polynomials in the solution of large-scale linear systems*, Proceedings of the Association for Computing Machinery, Toronto, 1952, Sauls Lithograph Co. (for the Association for Computing Machinery), Washington, D. C., 1953, pp. 124–133. MR**0067580****[10]**D. H. Lehmer,*Mathematical methods in large-scale computing units*, Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery, 1949, Harvard University Press, Cambridge, Mass., 1951, pp. 141–146. MR**0044899****[11]**D. H. Lehmer, Description of ``Random number generation of the BRL high-speed computing machines,''*Mathematical Reviews*, v. 15, 1954, p. 559.**[12]**NBS, Applied Mathematics Series 12, Monte Carlo Methods, 1951, p. 34-35.**[13]**Jack Moshman,*The generation of pseudo-random numbers on a decimal calculator*, J. Assoc. Computing Mach.**1**(1954), 88–91. MR**0061882****[14]**Mervin E. Muller,*Some continuous Monte Carlo methods for the Dirichlet problem*, Ann. Math. Statist.**27**(1956), 569–589. MR**0088786**, https://doi.org/10.1214/aoms/1177728169**[15]**M. E. Muller, ``A comparison of methods for generating normal deviates,'' Technical Report No. 9, Statistical Techniques Research Group, Department of Mathematics, Princeton University, to be published.**[16]**N. E. Norlund,*Vorlesungen Uber Differenzenrechnung*, Springer, Berlin, 1924.**[17]**Herbert A. Meyer, Editor,*Symposium on Monte Corlo Methods*, held at the University of Florida, 1954, John Wiley and Sons, Inc., New York, 1956. [*MTAC*, Rev.**43**, v. XI, 1957, p. 44-46.]**[18]**The Rand Corporation,*One Million Random Digits and 100,000 Normal Deviates*, The Free Press, Glencoe, Illinois, 1955. [*MTAC*, Rev.**11**, v. X, 1956, p. 39-43.]**[19]**NBS, Applied Mathematics Series 23,*Tables of Normal Probability Functions*, U. S. Government Printing Office, Washington, D. C., 1953.**[20]**Olga Taussky and John Todd,*Generation and testing of pseudo-random numbers*, Symposium on Monte Carlo methods, University of Florida, 1954, John Wiley and Sons, Inc., New York; Chapman and Hall, Limited, London, 1956, pp. 15–28. MR**0080382****[21]**D. Teichroew,*Distribution Sampling with High-Speed Computers*, Ph.D. Thesis, University of North Carolina, 1953.**[22]**D. F. Votaw Jr. and J. A. Rafferty,*High speed sampling*, Math. Tables and Other Aids to Computation**5**(1951), 1–8. MR**0039181**, https://doi.org/10.1090/S0025-5718-1951-0039181-8**[23]**Herman Wold,*Random Normal Deviates. 25,000 Items Compiled from Tract No. XXIV (M. G. Kendall and B. Babington Smith’s Tables of Random Sampling Numbers)*, Cambridge University Press, 1948. MR**0029132**

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DOI:
https://doi.org/10.1090/S0025-5718-1958-0102905-1

Article copyright:
© Copyright 1958
American Mathematical Society