Random Number Generators

Abstract

Previous article Next article Random Number GeneratorsT. E. Hull and A. R. DobellT. E. Hull and A. R. Dobellhttps://doi.org/10.1137/1004061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. D. Barnett, The behavior of pseudo-random sequences generated on computers by the multiplicative congruential method, Math. Comp., 16 (1962), 63–69 MR0136046 (24:B2085) 0108.13701 N. P. Buslenko and , Ju. A. Sreider, The Monte-Carlo method and how it is carried out on digital computers, Gosudarsty. Izdat. Fiz-Mat. Lit., Moscow, 1961, (Russian) CrossrefGoogle Scholar[2] J. Bass and , J. Guilloud, Méthode de Monte-Carlo et suites uniformément denses, Chiffres, 1 (1958), 149–155 MR0100338 (20:6771) 0089.11502 G. Miller Clark, Corrections to [86], Math. Comp., 16 (1962), 261– CrossrefGoogle Scholar[3] N. W. Bazley and , P. J. Davis, Accuracy of Monte Carlo methods in computing finite Markov chains, J. Res. Nat. Bur. Standards Sect. B, 64B (1960), 211–215 MR0129107 (23:B2144) 0102.12105 Joel N. Franklin, Deterministic simulation of random processes, Technical Report, 118, Computing Center, California Institute of Technology, 1962 CrossrefGoogle Scholar[4] W. F. Bauer, The Monte Carlo method, J. Soc. Indust. Appl. Math., 6 (1958), 438–451 10.1137/0106028 MR0098455 (20:4913) 0084.34601 Masatugu Isida and , Hiroji Ikeda, Random number generator, Ann. Inst. Statist. Math., Tokyo, 8 (1956), 119–126 MR0086369 (19,174c) 0075.28903 LinkISIGoogle Scholar[5] Eve, Bofinger and , V. J. Bofinger, On a periodic property of pseudo-random sequences, J. Assoc. Comput. Mach., 5 (1958), 261–265 MR0131949 (24:A1796) 0091.14503 R. K. Pathria, A statistical study of randomness among the first $10,000$ digits of $\pi$, Math. Comp., 16 (1962), 188–197 MR0144443 (26:1988) 0106.13402 CrossrefISIGoogle Scholar[6] Eve Bofinger and , V. J. Bofinger, The gap test for random sequences, Ann. Math. Statist., 32 (1961), 524–534 MR0126909 (23:A4203) 0109.37302 CrossrefISIGoogle Scholar[7] Eve Bofinger and , V. J. Bofinger, A note on the paper by W. E. Thomson on "ERNIE—a mathematical and statistical analysis", J. Roy. Stat. Soc., A124 (1961), 240–243 CrossrefGoogle Scholar[8] G. E. P. Box and , Muller E. Mervin, A Note on the generation of random normal deviates, Annals Math. Stat., 29 (1958), 610–611 0085.13720 CrossrefISIGoogle Scholar[9] George W. Brown, History of RAND's random digits—summary, Monte Carlo Method, Appl. Math. Series 12, Nat. Bur. Stand., 1951, 31–32 Google Scholar[10] J. C. Butcher, A partition test for pseudo-random numbers, Math. Comp., 15 (1961), 198–199 MR0130089 (23:B3121) 0111.14702 CrossrefGoogle Scholar[11] J. C. Butcher, Random sampling from the normal distribution, Comput. J., 3 (1960/1961), 251–253 10.1093/comjnl/3.4.251 MR0127512 (23:B558) 0094.13503 CrossrefISIGoogle Scholar[12] James W. Butler, Herbert A. Meyer, Machine sampling from given probability distributions, Symposium on Monte Carlo methods, University of Florida, 1954, John Wiley and Sons, Inc., New York, 1956, 249–264 MR0079823 (18,152b) Google Scholar[13] J. M. Cameron, Monte Carlo experiments on SEAC, Working Paper SEL-52-5, Nat. Bur. Stand., 1951, (Oct. 27) Google Scholar[14] J. M. Cameron, Results of some tests of randomness on pseudo-random numbers (preliminary report), Annals Math. Stat., 23 (1952), 138–, Abstract ISIGoogle Scholar[15] E. D. Cashwell and , C. J. Everett, A practical manual on the Monte Carlo method for random walk problems., International Tracts in Computer Science and Technology and their Application, Vol. 1, Pergamon Press, New York, 1959ix+153 MR0106538 (21:5269) Google Scholar[16] J. Certaine, On sequences of pseudo-random numbers of maximal length, J. Assoc. Comput. Mach., 5 (1958), 353–356 MR0127511 (23:B557) 0091.14504 CrossrefISIGoogle Scholar[17] Charles E. Clark, The utility of statistics of random numbers, Operations Res., 8 (1960), 185–195 MR0115262 (22:6064) 0090.11102 CrossrefISIGoogle Scholar[18] Charles E. Clark and , Betty Weber Holz, Exponentially distributed random numbers, Published for Operations Research Office, The Johns Hopkins University by The Johns Hopkins Press, Baltimore, Md., 1960vii+249 MR0115263 (22:6065) 0101.11703 Google Scholar[19] R. R. Coveyou, Serial correlation in the generation of pseudo-random numbers, J. Assoc. Comput. Mach., 7 (1960), 72–74 MR0117869 (22:8643) 0096.33903 CrossrefISIGoogle Scholar[20] J. H. Curtiss, "Monte Carlo" methods for the iteration of linear operators, J. Math. Physics, 32 (1954), 209–232 MR0059622 (15,560b) 0055.11301 CrossrefISIGoogle Scholar[21] P. Davis and , P. Rabinowitz, Some Monte Carlo experiments in computing multiple integrals, Math. Tables Aids Comput., 10 (1956), 1–8 MR0076451 (17,901c) 0072.14403 CrossrefGoogle Scholar[22] Edward L. Dodd, Certain tests for randomness applied to data grouped into small sets, Econometrica, 10 (1942), 249–257 MR0007239 (4,108a) 0063.01126 CrossrefGoogle Scholar[23] H. J. A. Duparc, , C. G. Le