Probabilities of simple n-dimensional sets for the normal distribution

IIE Transactions (Institute of Industrial Engineers)

Volumn 35, Issue 3, 2003, Pages 285-293

  Deák, Istvan ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; FORTRAN (PROGRAMMING LANGUAGE); INTEGRATION; MONTE CARLO METHODS; NORMAL DISTRIBUTION; PROBABILITY;

N-DIMENSIONAL SETS; SOFTWARE PACKAGE NORSET;

OPERATIONS RESEARCH;

EID: 0037337090     PISSN: 0740817X     EISSN: None     Source Type: Journal    
DOI: 10.1080/07408170304362     Document Type: Article

References (24)

1. Bjerager, P. (1990) On computation methods for structural reliability analysis. Structural Safety, 9, 79-96.
2. Breslaw, J.A. (1994) Evaluation of multivariate normal probability integrals using low variance simulator. Review of Economic Statistics, 76, 673-682.
3. Dantzig, G. and Glynn, P.W. (1990) Parallel processors for planning under uncertainty. Annals of Operations Research, 22, 1-21.
4. Deák, I. (1979) Computation of multiple normal probabilities, in Proceedings of the Symposium on Stochastic Programming Oberwolfach, Kall, P. (ed), Springer, Berlin, Heidelberg, New York, pp. 107-120.
5. Deák, I. (1980) Three digit accurate multiple normal probabilities. Numerische Mathematik., 35, 369-380.
6. Deák, I. (1986) Computing probabilities of rectangles in case of multidimensional normal distribution. Journal of Statistical Computations and Simulation, 26, 101-114.
7. Deák, I. (1988) Multidimensional integration and stochastic programming, in Numerical Techniques for Stochastic Optimization, (Ermoliev, Y. and Wets, R.), (eds), Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, pp. 187-200.
8. Deák, I. (1990) Random number generators and simulation. in Mathematical Methods of Operations Research, Prékopa, A. (ed), Akadémiai Kiadó, Budapest, p. 342.
9. Deák, I. (1998a) Normal probabilities - computer experiences and program description. Manuskripte der Institut fur Operations Research, Universitat Zurich.
10. Deák, I. (1998b) Regression estimators for multinormal distributions: computer experiences in root finding, in Lecture Notes in Economics and Mathematical Systems, Vol. 458, Marti, K. and Kall, P. (eds), Springer, pp. 279-293.
11. Deák, I. (2000) Subroutines for computing normal probabilities of sets - computer experiences, in Proceedings of the 7th International Conference on Stochastic Programming. Annals of Operations Research, 100, 103-122.
12. Ditlevsen, O.J. and Bjerager, P. (1989) Plastic reliability analysis by directional simulation. Journal of Engineering Mechanics, 115, 1347-1362.
13. Ducrocq, V. and Colleau, J.J. (1986) Interest in quantitative genetics of Dutt's and Deák's methods for numerical computation of multivariate normal probability integrals. Genetique, Selection et Evolution, 18, 447, 474.
14. Feenberg, D. and Skinner, J. (1994) The risk and durations of catastrophic health care expenditure. Review of Economical Statistics 76, 633-647.
15. Finster, M.P. (1987) An analysis of 5 simulation methods for determining the number of replications in a complex Monte Carlo study. Statistics and Probability Letters, 5, 353-360.
16. Gassmann, H. (1988) Conditional probability and conditional expectation of a random vector, in Numerical Techniques for Stochastic Optimization, Ermoliev, Y. and Wets, R. (eds), Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, pp. 237-254.
17. Johnson, N.L. and Kotz, S. (1972) Distributions in Statistics, Vols. I-IV, John Wiley, New York, NY.
18. Kall, P. and Mayer, J. (1996) An interactive model management system for stochastic linear programs. Mathematical Programming, 75, 221-240.
19. Lohr, S.L. (1993) Multivariate normal probabilities of star shaped regions. Applied Statistics, 42, 576-582.
20. Mayer, J. (1992) Computational techniques for probabilistic constrained optimization problems, in Lecture Notes on Economics and Mathematical Systems, 379, Springer, pp. 141-164.
21. Prékopa, A. (1995) Stochastic Programming in Mathematics and its Applications, 324, Kluwer, Dordrecht.
22. Prékopa, A., Ganczer, S., Deák, I. and Patyi, K. (1980) STABIL stochastic programming model and its experimental application to the electrical energy sector of the Hungarian economy. in Proceedings of the International Symposium on Stochastic Programming, Dempster, M. (ed), Academic press, pp. 369-385.
23. Szántai, T. (1986) Evaluation of a special multivariate gamma distribution function. Mathematical Programming Study, 27, 1-16.
24. Watanabe, T. (1993) Stochastic programming models for air-quality management. Computers and Operations Research, 20, 651-663.