Computer methods for sampling from Student's distribution

Authors:
A. J. Kinderman, J. F. Monahan and J. G. Ramage

Journal:
Math. Comp. **31** (1977), 1009-1018

MSC:
Primary 65C10

DOI:
https://doi.org/10.1090/S0025-5718-1977-0443294-4

MathSciNet review:
0443294

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Abstract | References | Similar Articles | Additional Information

Abstract: Several new algorithms for generating deviates from the *t* family for the degrees of freedom parameter 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.

**[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**, https://doi.org/10.1145/355604.361593**[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**, https://doi.org/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**, https://doi.org/10.1137/1006063**[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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0443294-4

Keywords:
Random number generator,
Student's *t* distribution

Article copyright:
© Copyright 1977
American Mathematical Society