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Polar generation of random variates with the $ t$-distribution


Author: Ralph W. Bailey
Journal: Math. Comp. 62 (1994), 779-781
MSC: Primary 65C10; Secondary 62E15
MathSciNet review: 1219702
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Abstract: The "polar" method of Box and Muller uses two independent uniform variates in order to generate two independent normal variates. It can be adapted so that two variates from Student's t-distribution with parameter $ \nu $ are generated, though the two variates are now not independent. An algorithm based on the polar method is exact, inexpensive, and valid for all $ \nu > 0$.


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

  • [1] G. E. P. Box and M. E. Muller, A note on the generation of random normal deviates, Ann. Math. Statist. 29 (1958), 610-611..
  • [2] Luc Devroye, Nonuniform random variate generation, Springer-Verlag, New York, 1986. MR 836973
  • [3] E. R. Golder and J. G. Settle, The Box-Müller method for generating pseudo-random normal deviates, J. Roy. Statist. Soc. Ser. C Appl. Statist. 25 (1976), no. 1, 12–20. MR 0428682
  • [4] G. Marsaglia and T. A. Bray, A convenient method for generating normal variables, SIAM Rev. 6 (1964), 260–264. MR 0172441
  • [5] A. M. Mathai and G. Pederzoli, Characterizations of the normal probability law, Halsted Press [John Wiley & Sons], New York-London-Sydney, 1977. MR 0471135
  • [6] H. R. Neave, On using the Box-Muller transformation with multiplicative congruential pseudo-random number generators, Appl. Statist. 22 (1973), 92-97.

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DOI: http://dx.doi.org/10.1090/S0025-5718-1994-1219702-8
Article copyright: © Copyright 1994 American Mathematical Society