On a generation of normal pseudo-random numbers

  • Hirotaka Sakasegawa


Generation Speed Principal Part Normal Random Variable Fortran Program Uniform Random Number 


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  1. [1]
    Ahrens, J. H. and Dieter, U. (1972). Computer methods for sampling from the exponential and normal distributions,Comm. ACM,15, 873–882.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Ahrens, J. H. and Dieter, U. (1973). Extension of Forsythe's method for random sampling from the normal distributions,Math. Comp.,27, 927–937.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Ahrens, J. H. and Dieter, U. (1974). Computer methods for sampling from gamma, beta, Poisson and binomial distributions,Computing,12, 223–246.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Atkinson, A. C. and Pearce, M. C. (1976). The computer generation of beta, gamma and normal random variables.J. R. Statist. Soc. A139, 431–461.MathSciNetGoogle Scholar
  5. [5]
    Box, G. E. P. and Muller, M. E. (1958). A note on the generation of normal random deviates.Ann. Math. Statist.,29, 610–611.CrossRefGoogle Scholar
  6. [6]
    Brent, R. P. (1974). A Gaussian pseudo-random number generator,Comm. ACM,17, 704–706.CrossRefGoogle Scholar
  7. [7]
    Forsythe, G. E. (1972). Von Neumann's comparison method for random sampling from the normal and other distributions,Math. Comp.,26, 817–826.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Kinderman, A. J. and Ramage, J. G. (1976). Computer generation of normal random variables,J. Amer. Statist. Ass.,71, 893–896.CrossRefGoogle Scholar
  9. [9]
    Marsaglia, G. (1962). Improving the poler method for generating a pair of random variables, Boeing Sci. Res. Lab. D1-82-0203.Google Scholar
  10. [10]
    Marsaglia, G. (1964). Generating a variable from the tail of the normal distribution,Technometrics,6, 101–102.Google Scholar
  11. [11]
    Marsaglia, G. and Bray, T. A. (1964). A convenient method for generating normal variables,SIAM Rev.,6, 260–264.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Marsaglia, G., MacLaren, M. D. and Bray, T. A. (1964). A fast procedure for generating normal random variables,Comm. ACM,7, 4–10.CrossRefGoogle Scholar
  13. [13]
    Muller, M. E. (1961). A comparison of method for generating normal deviates on digital computers.J. ACM,6, 376–383.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Newman, T. G. and Odell, P. L. (1971).The Generation of Random Variates, Charles Griffin, 22–26.Google Scholar
  15. [15]
    Shimizu, R. (1976).Central Limit Theorem (in Japanese), Kyoiku Shuppan, 232–243.Google Scholar

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© The Institute of Statistical Mathematics, Tokyo 1978

Authors and Affiliations

  • Hirotaka Sakasegawa

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