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Generation of random bivariate normal deviates and computation of related integrals

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Abstract

A method which transforms two random variables having rectangular distributions into a pair of bivariate normal deviates with prescribed covariance matrix is described. The same transformation is used for integrating the bivariate normal distribution over areas which are the intersection of the domain outside an equiprobability ellipse and a sector determined by two lines through the point of gravity of the normal distribution.

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References

  1. G. E. P. Box and Mervin E. Muller,A Note on the Generation of Random Normal Deviates, Annals Math. Stat. 29 (1958), pp. 610–611.

    Google Scholar 

  2. Birger Jansson,Autocorrelations between pseudo-random numbers, BIT no. 1, 1964.

  3. Harald Cramér,Mathematical Methods of Statistics, Princeton 1946.

  4. J. C. Butcher,Random sampling from the normal distribution, Comp. J. 3 (1961), pp. 251–253.

    Google Scholar 

  5. G. Marsaglia,Expressing a random variable in terms of uniform random variables, Annals Math. Stat. 32 (1961), pp. 894–898.

    Google Scholar 

  6. G. Marsaglia,Generating exponential random variables, Annals Math. Stat. 32 (1961), pp. 899–900.

    Google Scholar 

  7. G. Marsaglia,Generating a variable from the tail of the normal distribution, Technometrics Vol. 6, no. 1, February 1964, pp. 101–102.

    Google Scholar 

  8. G. Marsaglia, M. D. MacLaren, T. A. Bray,A fast procedure for generating normal random variables, Comm. ACM, Vol. 7, no. 1, Jan. 1964, pp. 4–10.

    Google Scholar 

  9. M. D. MacLaren, G. Marsaglia, T. A. Bray,A fast procedure for generating exponential random variables, Comm. ACM, Vol. 7, no. 5, May 1964, pp. 298–300.

    Google Scholar 

  10. M. E. Muller,A comparison of methods for generating normal deviates on digital computers, J. Assoc. Comp. Mach. 6 (1959), pp. 376–383.

    Google Scholar 

  11. Masaki Sibuya,On exponential and other random variable generators, Annals of the Institute of Stat. Math., Tokyo, Vol. 13 (1961/62): 3, pp. 231–237.

    Google Scholar 

  12. S. S. Gupta,Probability integrals of multivariate normal and multivariate t, Annals Math. Stat. 34 (1963), pp. 792–828.

    Google Scholar 

  13. S. S. Gupta,Bibliography on the multivariate normal integrals and related topics, Annals Math. Stat. 34 (1963), pp. 829–838.

    Google Scholar 

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Authors and Affiliations

  1. Research Institute of National Defence, Stockholm, Sweden

    Birger Jansson

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  1. Birger Jansson
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Jansson, B. Generation of random bivariate normal deviates and computation of related integrals. BIT 4, 205–212 (1964). https://doi.org/10.1007/BF01939512

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  • DOI: https://doi.org/10.1007/BF01939512

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