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 
References 
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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.
 [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
(49 #1728)
 [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
(48 #7532), http://dx.doi.org/10.1090/S00255718197303291908
 [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 (52 #15949)
 [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. 893896.
 [7]
Donald
E. Knuth, The art of computer programming. Vol. 2: Seminumerical
algorithms, AddisonWesley Publishing Co., Reading, Mass.LondonDon
Mills, Ont, 1969. 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.
 [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
(29 #1721)
 [10]
G.
Marsaglia, Onesided approximations by linear combinations of
functions, Approximation Theory (Proc. Sympos., Lancaster, 1969)
Academic Press, London, 1970, pp. 233–242. MR 0266401
(42 #1307)
 [11]
G.
Marsaglia and T.
A. Bray, A convenient method for generating normal variables,
SIAM Rev. 6 (1964), 260–264. MR 0172441
(30 #2660)
 [12]
G. MARSAGLIA, M. D. MACLAREN & T. A. BRAY, "A fast procedure for generating normal random variables," Comm. ACM, v. 7, 1964, pp. 410.
 [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. 125.
 [1]
 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)
 [3]
 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.
 [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. 893896.
 [7]
 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.
 [9]
 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)
 [10]
 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)
 [11]
 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)
 [12]
 G. MARSAGLIA, M. D. MACLAREN & T. A. BRAY, "A fast procedure for generating normal random variables," Comm. ACM, v. 7, 1964, pp. 410.
 [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. 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
