On the computation of a bivariate distribution
Authors:
D. E. Amos and W. G. Bulgren
Journal:
Math. Comp. 23 (1969), 319333
MSC:
Primary 65.25; Secondary 62.00
MathSciNet review:
0242348
Fulltext PDF Free Access
Abstract 
References 
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Abstract: The cumulative bivariate distribution associated with random variables , is considered where , are bivariate normal with correlation coefficient and is an independent random variable with degrees of freedom. Representations in terms of series and simple, onedimensional quadratures are presented together with efficient computational procedures for the special functions used in numerical evaluation.
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 C. W. Dunnett, ``A multiple comparison procedure for comparing several treatments with a control,'' J. Amer. Statist. Assoc., v. 50, 1955, pp. 10961121.
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 C. W. Dunnett & M. Sobel, ``A bivariate generalization of Student's distribution, with tables for certain special cases,'' Biometrika, v. 41, 1954, pp. 153169. MR 15, 885. MR 0061793 (15:885f)
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 A. Erdélyi, et al., Higher Transcendental Functions, Vol. 1, McGrawHill, New York, 1953. MR 15, 419.
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 A. Erdélyi, et al., Higher Transcendental Functions, Vol. 2, McGrawHill, New York, 1953. MR 15, 419.
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 A. Erdélyi, et al., Tables of Integral Transforms, Vol. 1, McGrawHill, New York, 1954. MR 15, 868.
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 W. Gautschi, ``Computational aspects of threeterm recurrence relations,'' SIAM Rev., v. 9, 1967, pp. 2482. MR 35 #3927. MR 0213062 (35:3927)
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 S. S. Gupta & M. Sobel, ``On a statistic which arises in selection and ranking problems,'' Ann. Math. Statist., v. 28, 1957, pp. 957967. MR 20 #366. MR 0093846 (20:366)
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 S. S. Gupta, ``Probability integrals of multivariate normal and multivariate ,'' Ann. Math. Statist., v. 34, 1963, pp. 792828. MR 27 #2048.
 [10]
 S. John, ``On the evaluation of the probability integral of the multivariate distribution,'' Biometrika, v. 48, 1961, pp. 409417. MR 26 #1951. MR 0144406 (26:1951)
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 S. John, ``Methods for the evaluation of probabilities of polygonal and angular regions when the distribution is bivariate ,'' Sankhyā, Ser. A, v. 26, 1964, pp. 4754. MR 33 #6736. MR 0198581 (33:6736)
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 P. R. Krishnaiah & J. V. Armitage, Percentage Points of the Multivariate Distribution, ARL 65199, Aerospace Research Laboratories, WrightPatterson Air Force Base, Ohio, 1965.
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 N. N. Lebedev, Special Functions and Their Applications, Fizmatgiz, Moscow, 1963; English transl., PrenticeHall, Englewood Cliffs, N. J., 1965. MR 30 #4987; MR 30 #4988. MR 0174795 (30:4988)
 [14]
 D. B. Owen, ``A special case of a bivariate noncentral distribution,'' Biometrika, v. 52, 1965, pp. 437147. MR 34 #5190. MR 0205361 (34:5190)
 [15]
 K. C. S. Pillai & K. V. Ramachandran, ``On the distribution of the ratio of the th observation in an ordered sample from a normal population to an independent estimate of the standard deviation,'' Ann. Math. Statist., v. 25, 1954, pp. 565572. MR 16, 270. MR 0064356 (16:270d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196902423480
PII:
S 00255718(1969)02423480
Article copyright:
© Copyright 1969
American Mathematical Society
