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Deak, Istvan

Three digit accurate multiple normal probabilities. (English) Zbl 0453.65007

Numer. Math. 35, 369-380 (1980).
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Cited in 20 Documents

MSC:

65D20 Computation of special functions and constants, construction of tables
33B20 Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
65C05 Monte Carlo methods
65C99 Probabilistic methods, stochastic differential equations
65-04 Software, source code, etc. for problems pertaining to numerical analysis
90C15 Stochastic programming
62H99 Multivariate analysis

Keywords:

multidimensional normal distribution function; numerical examples
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Full Text: DOI EuDML

References:

[1] Ahrens, J.H., Dieter, U.: Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing12, 223-246 (1974) · Zbl 0285.65009 · doi:10.1007/BF02293108
[2] Davis, P.J., Rabinowitz, P.: Methods of numerical integration. New York: Academic Press (1975) · Zbl 0304.65016
[3] Deák, I.: Computing the probabilities of sets in higher dimensional spaces in case of normal distribution. Alkalmaz. Mat. Lapok2, 17-26 (1976) (in Hungarian)
[4] Deák, I.: Monte Carlo methods for computing probabilities of sets in higher dimensional spaces in case of normal distribution. Alkalmaz. Mat. Lapok4, 35-94 (1978) (in Hungarian) · Zbl 0429.65002
[5] Deák, I.: Fast procedures for generating stationary normal vectors, J. Statist. Comp. and Simulation10, 225-242 (1980) · Zbl 0432.65007 · doi:10.1080/00949658008810371
[6] Deák, I.: Computation of multiple normal probabilities. Symposium on Stochastic Programming. Lecture Notes in Mathematics. (P. Kall, ed.) Berlin Heidelberg New York: Springer (in press, 1980)
[7] Donelly, T.G.: Bivariate normal distribution. Comm. ACM16, 638 (1973) · doi:10.1145/362375.362414
[8] Dutt, J.E.: A representation of multivariate normal probability integrals by integral transforms. Biometrika60, 637-645 (1973) · Zbl 0269.60011 · doi:10.1093/biomet/60.3.637
[9] Gupta, S.S.: Probability integrals of multivariate normal and multivariate. Ann. Math. Stat.34, 792-828 (1963). · Zbl 0124.35505 · doi:10.1214/aoms/1177704004
[10] Hill, I.D., Pike, M.C.: Chi-squared integral. Comm. ACM10, 243-244 (1967) · doi:10.1145/363242.363274
[11] Johnson, N.L., Kotz, S.: Distributions in statistics. IV. Vol. New York: John Wiley 1972 · Zbl 0248.62021
[12] Knuth, D.E.: The art of computer programming. II. Vol. Reading Mass.: Addison Wesley 1969 · Zbl 0191.18001
[13] Milton, R.C.: Computer evaluation of the multivariate normal integral. Technometrics14, 881-889 (1972) · Zbl 0243.62015 · doi:10.2307/1267136
[14] Prékopa, A.: Contributions to the theory of stochastic programming. Math. Programming4, 202-221 (1973) · Zbl 0273.90045 · doi:10.1007/BF01584661
[15] Prékopa, A., Ganczer, S., Deák, I., Patyi, K.: The STABIL stochastic programming model and its experimental application to the electrical energy sector of the Hungarian economy. In: Proceedings of the Internat. Symposium on Stochastic Programming (M. Dempster, ed.) Oxford: Academic Press. 1974
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