Computer methods for sampling from Student's distribution
Authors:
A. J. Kinderman, J. F. Monahan and J. G. Ramage
Journal:
Math. Comp. 31 (1977), 10091018
MSC:
Primary 65C10
MathSciNet review:
0443294
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Abstract 
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Abstract: Several new algorithms for generating deviates from the t family for the degrees of freedom parameter are presented. Both acceptancerejection 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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 J. H. AHRENS & U. DIETER, "Computer methods for sampling from the exponential and normal distributions," Comm. ACM, v. 15, 1972, pp. 873881. MR 49 #1728. MR 0336955 (49:1728)
 [2]
 J. H. AHRENS & U. DIETER, "Extensions of Forsythe's method for random sampling from the normal distribution," Math. Comp., v. 27, 1973, pp. 927937. MR 48 #7532. MR 0329190 (48:7532)
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 J. H. AHRENS & U. DIETER, "Computer methods for sampling from gamma, beta, Poisson, and binomial distributions," Computing (Arch. Electron. Rechnen.), v. 12, 1974, pp. 223246. MR 52 #15949. MR 0395151 (52:15949)
 [4]
 D. F. ANDREWS ET AL., Robust Estimates of Location, Princeton Univ. Press, Princeton, N. J., 1972. MR 48 #9927.
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 A. J. KINDERMAN & J. F. MONAHAN, "Computer generation of random variables using the ratio of uniform deviates," ACM Trans. Math. Software. (To appear.)
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 A. J. KINDERMAN & J. G. RAMAGE, "Computer generation of normal random variables," J. Amer. Statist. Assoc., v. 71, 1976, pp. 893896.
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 D. E. KNUTH, The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, AddisonWesley, Reading, Mass., 1969. MR 44 #3531. MR 0286318 (44:3531)
 [8]
 P. A. W. LEWIS, A. S. GOODMAN & J. M. MILLER, "A pseudorandom number generator for the system/360," IBM Systems J., v. 8, 1969, pp. 136146.
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 G. MARSAGLIA, "Random variables and computers," Trans. Third Prague Conf. on Information Theory, Statistics, Decision Functions, and Random Processes, Publ. House Czech. Acad. Sci., Prague, 1964, pp. 499512. MR 29 #1721. MR 0164424 (29:1721)
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 G. MARSAGLIA, "Onesided approximations by linear combinations of functions," Approximation Theory (A. Talbot, Editor), Academic Press, New York, 1970, pp. 233242. MR 42 #1307. MR 0266401 (42:1307)
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 G. MARSAGLIA & T. A. BRAY, "A convenient method for generating normal variables," SIAM Rev., v. 6, 1964, pp. 260264. MR 30 #2660. MR 0172441 (30:2660)
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 G. MARSAGLIA, M. D. MACLAREN & T. A. BRAY, "A fast procedure for generating normal random variables," Comm. ACM, v. 7, 1964, pp. 410.
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 T. G. NEWMAN & P. L. ODELL, The Generation of Random Variables, Hafner, New York, 1971.
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 "STUDENT", "The probable error of a mean," Biometrika, v. 6, 1908, pp. 125.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704432944
PII:
S 00255718(1977)04432944
Keywords:
Random number generator,
Student's t distribution
Article copyright:
© Copyright 1977 American Mathematical Society
