An inverse method for the generation of random normal deviates on largescale computers
Author:
Mervin E. Muller
Journal:
Math. Comp. 12 (1958), 167174
MSC:
Primary 65.00; Secondary 68.00
MathSciNet review:
0102905
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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G. E. P. Box & M. E. Muller, ``A note on the generation of normal deviates,'' Ann. Math. Stat., to be published.
 [2]
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D. H. Lehmer, Description of ``Random number generation of the BRL highspeed computing machines,'' Mathematical Reviews, v. 15, 1954, p. 559.
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E. Muller, Some continuous Monte Carlo methods for the Dirichlet
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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.
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Sampling Numbers), Cambridge University Press, 1948. MR 0029132
(10,553c)
 [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. 3435. [MTAC, Rev. 42, v. XI, 1957, p. 4344.]
 [3]
 Joseph O. Harrison, Jr., ``Piecewise polynomial approximations for largescale digital calculations.'' [MTAC, v. III, 1949, p. 400407.] MR 0032202 (11:264i)
 [4]
 F. B. Hildebrand, Introduction to Numerical Analysis, McGrawHill 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. 813. MR 0076467 (17:902k)
 [6]
 M. L. Juncosa, ``Random number generation on the BRL HighSpeed 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 RM1237AEC.
 [8]
 C. Lanczos, ``Trigonometric interpolation of empirical and analytical functions,'' Jn. Math. Phys., v. 17, 1938, p. 123199.
 [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 LargeScale Digital Calculating Machinery, 1949, p. 141146. Harvard University Press, Cambridge, Mass., 1951. MR 0044899 (13:495f)
 [11]
 D. H. Lehmer, Description of ``Random number generation of the BRL highspeed computing machines,'' Mathematical Reviews, v. 15, 1954, p. 559.
 [12]
 NBS, Applied Mathematics Series 12, Monte Carlo Methods, 1951, p. 3435.
 [13]
 J. Moshman, ``The generation of pseudorandom numbers on a decimal calculator,'' Jn., Assoc. for Computing Machinery, v. 1, 1954, p. 8891. MR 0061882 (15:900c)
 [14]
 M. E. Muller, ``Some continuous Monte Carlo methods for the Dirichlet problem,'' Ann. Math. Stat., v. 27, p. 569589. 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. 4446.]
 [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. 3943.]
 [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 pseudorandom numbers,'' Symposium on Monte Carlo Methods, University of Florida, 1954, John Wiley and Sons, Inc., 1956, p. 1528. MR 0080382 (18:239b)
 [21]
 D. Teichroew, Distribution Sampling with HighSpeed 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. 18. 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718195801029051
PII:
S 00255718(1958)01029051
Article copyright:
© Copyright 1958
American Mathematical Society
