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 approximations for large-scale digital calculations.'' [*MTAC*, v. III, 1949, p. 400-407.] MR**0032202 (11:264i)****[4]**F. B. Hildebrand,*Introduction to Numerical Analysis*, McGraw-Hill Book Co., Inc., New York, 1956. MR**0075670 (17:788d)****[5]**D. L. Johnson, ``Generating and testing pseudo random numbers on the IBM type 701,''*MTAC*, v. X, 1956, p. 8-13. MR**0076467 (17:902k)****[6]**M. L. Juncosa, ``Random number generation on the BRL High-Speed computing machines,'' Report 855, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, 1953. MR**0059617 (15:559c)****[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]**C. Lanczos,*Tables of Chebyshev Polynomials*and , NBS, Applied Mathematics Series 9, U. S. Government Printing Office, Washington, D. C., 1952. [*MTAC*, Rev.**1103**, v. 7, 1953, p. 174.] MR**0067580 (16:751e)****[10]**D. H. Lehmer, ``Mathematical methods in large scale computing units,''*Proceedings Second Symposium on Large-Scale Digital Calculating Machinery*, 1949, p. 141-146. Harvard University Press, Cambridge, Mass., 1951. MR**0044899 (13:495f)****[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]**J. Moshman, ``The generation of pseudo-random numbers on a decimal calculator,''*Jn.*, Assoc. for Computing Machinery, v. 1, 1954, p. 88-91. MR**0061882 (15:900c)****[14]**M. E. Muller, ``Some continuous Monte Carlo methods for the Dirichlet problem,''*Ann. Math. Stat.*, v. 27, p. 569-589. MR**0088786 (19:580b)****[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]**O. Taussky & J. Todd, ``Generation and testing of pseudo-random numbers,''*Symposium on Monte Carlo Methods*, University of Florida, 1954, John Wiley and Sons, Inc., 1956, p. 15-28. MR**0080382 (18:239b)****[21]**D. Teichroew,*Distribution Sampling with High-Speed Computers*, Ph.D. Thesis, University of North Carolina, 1953.**[22]**D. F. Votaw, Jr. & J. A. Rafferty, ``High speed sampling,''*MTAC*, v. 5, 1951, p. 1-8. MR**0039181 (12:509d)****[23]**H. Wold, ``Random normal deviates,''*Tracts for Computers*, No. XXV, Cambridge University Press, New York, 1948. MR**0029132 (10:553c)**

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

Article copyright:
© Copyright 1958
American Mathematical Society