Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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
MathSciNet review: 0102905
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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, 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, 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
  • [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, 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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.00, 68.00

Retrieve articles in all journals with MSC: 65.00, 68.00


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1958-0102905-1
Article copyright: © Copyright 1958 American Mathematical Society