Abstract:
Known methods are described for evaluating the multivariate normal distribution function in general and in a number of special cases. Methods are presented for evaluation of the one-dimensional normal distribution function and its inverse.
Citation:
G. V. Martynov, “Evaluation of the normal distribution function”, Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern., 17, VINITI, Moscow, 1979, 57–84; J. Soviet Math., 17:3 (1981), 1857–1875
\Bibitem{Mar79}
\by G.~V.~Martynov
\paper Evaluation of the normal distribution function
\serial Itogi Nauki i Tekhniki. Ser. Teor. Veroyatn. Mat. Stat. Teor. Kibern.
\yr 1979
\vol 17
\pages 57--84
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intv43}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=578763}
\zmath{https://zbmath.org/?q=an:0449.60014|0463.60025}
\transl
\jour J. Soviet Math.
\yr 1981
\vol 17
\issue 3
\pages 1857--1875
\crossref{https://doi.org/10.1007/BF01085187}
Linking options:
https://www.mathnet.ru/eng/intv43
https://www.mathnet.ru/eng/intv/v17/p57
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Yosef Rinott, Vladimir Rotar, “A remark on quadrant normal probabilities in high dimensions”, Statistics & Probability Letters, 51:1 (2001), 47
R. Kannan, Guangxing Li, Proceedings of 37th Conference on Foundations of Computer Science, 1996, 204
Simon Ku, Eugene Seneta, “THE NUMBER OF PEAKS IN A STATIONARY SAMPLE AND ORTHANT PROBABILITIES”, Journal Time Series Analysis, 15:4 (1994), 385
Dror Rom, Sanat K. Sarkar, “Approximating probability integrals of multivariate normal using association models”, Journal of Statistical Computation and Simulation, 35:1-2 (1990), 109
Satish Iyengar, “Evaluation of Normal Probabilities of Symmetric Regions”, SIAM J. Sci. and Stat. Comput., 9:3 (1988), 418
P. A. P. Moran, “CALCULATION OF MULTIVARIATE NORMAL PROBABILITIES—ANOTHER SPECIAL CASE”, Australian Journal of Statistics, 27:1 (1985), 60
P. A. P. Moran, “THE MONTE CARLO EVALUATION OF ORTHANT PROBABILITIES FOR MULTIVARIATE NORMAL DISTRIBUTIONS”, Australian Journal of Statistics, 26:1 (1984), 39
P. A. P. Moran, “A NEW EXPANSION FOR THE MULTIVARIATE NORMAL DISTRIBUTION1”, Australian Journal of Statistics, 25:2 (1983), 339
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