Mathematics of Computation

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



Computer methods for sampling from Student's $ t$ distribution

Authors: A. J. Kinderman, J. F. Monahan and J. G. Ramage
Journal: Math. Comp. 31 (1977), 1009-1018
MSC: Primary 65C10
MathSciNet review: 0443294
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Abstract: Several new algorithms for generating deviates from the t family for the degrees of freedom parameter $ \geqslant 1$ are presented. Both acceptance-rejection and probability mixing procedures are developed. The new algorithms outperform traditional methods for generating deviates from the t family. Recommendations are made concerning choosing an algorithm suited to its application.

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  • [1] J. H. Ahrens and U. Dieter, Computer methods for sampling from the exponential and normal distributions, Comm. ACM 15 (1972), 873–882. MR 0336955
  • [2] J. H. Ahrens and U. Dieter, Extensions of Forsythe’s method for random sampling from the normal distribution, Math. Comp. 27 (1973), 927–937. MR 0329190, 10.1090/S0025-5718-1973-0329190-8
  • [3] J. H. Ahrens and U. Dieter, Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing (Arch. Elektron. Rechnen) 12 (1974), no. 3, 223–246 (English, with German summary). MR 0395151
  • [4] D. F. ANDREWS ET AL., Robust Estimates of Location, Princeton Univ. Press, Princeton, N. J., 1972. MR 48 #9927.
  • [5] A. J. KINDERMAN & J. F. MONAHAN, "Computer generation of random variables using the ratio of uniform deviates," ACM Trans. Math. Software. (To appear.)
  • [6] A. J. KINDERMAN & J. G. RAMAGE, "Computer generation of normal random variables," J. Amer. Statist. Assoc., v. 71, 1976, pp. 893-896.
  • [7] Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969. MR 0286318
  • [8] P. A. W. LEWIS, A. S. GOODMAN & J. M. MILLER, "A pseudo-random number generator for the system/360," IBM Systems J., v. 8, 1969, pp. 136-146.
  • [9] George Marsaglia, Random variables and computers, Trans. Third Prague Conf. Information Theory, Statist. Decision Functions, Random Processes (Liblice, 1962) Publ. House Czech. Acad. Sci., Prague, 1964, pp. 499–512. MR 0164424
  • [10] G. Marsaglia, One-sided approximations by linear combinations of functions, Approximation Theory (Proc. Sympos., Lancaster, 1969) Academic Press, London, 1970, pp. 233–242. MR 0266401
  • [11] G. Marsaglia and T. A. Bray, A convenient method for generating normal variables, SIAM Rev. 6 (1964), 260–264. MR 0172441
  • [12] G. MARSAGLIA, M. D. MACLAREN & T. A. BRAY, "A fast procedure for generating normal random variables," Comm. ACM, v. 7, 1964, pp. 4-10.
  • [13] T. G. NEWMAN & P. L. ODELL, The Generation of Random Variables, Hafner, New York, 1971.
  • [14] "STUDENT", "The probable error of a mean," Biometrika, v. 6, 1908, pp. 1-25.

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Keywords: Random number generator, Student's t distribution
Article copyright: © Copyright 1977 American Mathematical Society