- Andel, J. (1974),
On evaluation of some two-dimensional normal probabilities,
Aplikace Matematiky 19, pp. 28-35.
- Cornish, E.A. (1954),
The Multivariate t-Distribution Associated with a Set of Normal Sample Deviates
Australian Journal of Physics 7, pp. 531-542.
- Cox, D.R. and Wermuth, N. (1991),
A Simple Approximation for Bivariate and Trivariate Normal Integrals,
International Statistics Review 59, pp. 263-269.
- Davis, P.J. and Rabinowitz, P. (1984).
Methods of Numerical Integration, Academic Press, New York.
- Drezner, Z. (1978),
Computation of the Bivariate Normal Integral,
Mathematics of Computation 32, pp. 277-279.
- Drezner, Z. and Wesolowsky G.O., (1989),
On the Computation of the Bivariate Normal Integral,
Journal of Statist. Comput. Simul. 35, pp. 101-107
- Drezner, Z. (1992),
Computation of the Multivariate Normal Integral,
ACM Transactions on Mathematics Software 18, pp. 450-460.
- Drezner, Z. (1994),
Computation of the Trivariate Normal Integral,
Mathematics of Computation 62, pp. 289-294.
- Donnelly, T.G. (1963),
Algorithm 462: Bivariate Normal Distribution,
Communications of the ACM 16, pp. 638.
- Dunnett, C.W. and Sobel, M. (1954), A Bivariate Generalization of
Student's t-Distribution, with Tables for Certain Special Cases,
Biometrika 41, pp. 153-169.
- Gassmann, H.I. (2000),
Rectangle Probabilities of Trivariate Normal Distributions,
technical report available at
http://www.mgmt.dal.ca/sba/profs/hgassmann/.
- Gassmann, H.I., Deák, I. and Szántai, T. (2002),
Computing multivariate normal probabilities: A new look.
Journal of Computational and Graphical Statistics 11, pp. 920-949.
- Genz, A. (1993),
Comparison of Methods for the Computation of Multivariate Normal Probabilities,
Computing Science and Statistics 25, pp. 400-405.
- Genz, A. and Bretz, F. (2002),
Comparison of Methods for the Computation of Multivariate
Probabilities,
J. Comp. Graph. Stat. 11, pp. 950-971.
- Genz, A., Bretz, F. and Hochberg, Y. (2003),
Approximations to Multivariate
Probabilities with Application to Multiple
Comparison Procedures,
technical report available at http://www.math.wsu.edu/faculty/genz.
- Mee, R.W. and Owen, D.B. (1983),
A Simple Approximation for Bivariate Normal Probability,
Journal of Quality Technology 15, pp. 72-75.
- Owen, D.B., (1956),
Tables for Computing Bivariate Normal Probability,
Annals of Mathematical Statistics 27, pp. 1075-1090.
- Patefield, M. and Tandy, D. (2000),
Fast and Accurate Computation of Owen's T-Function,
Journal of Statistical Software 5, No. 5,
http://www.jstatsoft.org.
- Plackett, R.L. (1954),
A Reduction Formula for Normal Multivariate Probabilities,
Biometrika 41, pp. 351-360.
- Piessens, R., deDoncker E., Uberhuber, C. and Kahaner, D. (1983),
QUADPACK: A Subroutine Package for Automatic Integration,
Springer-Verlag, New York.
- Schervish, M. (1984)
Multivariate Normal Probabilities with Error Bound,
Applied Statistics 33, pp. 81-87.
- Sheppard, W.F. (1900),
On the Computation of the Double Integral Expressing Normal Correlation,
Transactions of the Cambridge Philosophical Society 19,
pp. 23-69.
- Steen, N.M., Byrne, G.O. and Gelhard, E.M. (1969)
Gaussian Quadratures,
Mathematics of Computation 23, pp. 661-671.
- Terza, J.V. and Welland, U. (1988)
A Comparison of Bivariate Normal Algorithms,
Journal of Statist. Comput. Simul. 19, pp. 115-127.
- Tong, Y.L. (1990),
The Multivariate Normal Distribution,
Springer-Verlag, New York.
- Wang, M. and Kennedy, W.J. (1992),
A Numerical Method for Accurately Approximating Multivariate Normal
Probability,
Computational Statistics and Data Analysis 13, pp. 197-210.
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