An approximate method for sampling correlated random variables from partially-specified distributions

Management Science

Volumn 44, Issue 2, 1998, Pages 203-218

  Lurie, Philip M ^a   Goldberg, Matthew S ^a  

^a INSTITUTE FOR DEFENSE ANALYSES   (United States)

Author keywords

Correlation; Gauss Newton Method; Random Number Generation; Simulation

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; CORRELATION METHODS; COST ACCOUNTING; DATA REDUCTION; ITERATIVE METHODS; MATRIX ALGEBRA; RANDOM NUMBER GENERATION; VECTORS;

CHOLESKY DECOMPOSITION; COST ANALYSIS; GAUSS NEWTON METHODS;

PERT;

EID: 0032002017     PISSN: 00251909     EISSN: None     Source Type: Journal    
DOI: 10.1287/mnsc.44.2.203     Document Type: Article

References (25)

1. Buck, R. Creighton, Advanced Calculus, McGraw-Hill, New York, 1978.
2. Cheng, R. C. H., "Generation of Multivariate Normal Samples with Given Sample Mean and Covariance Matrix," J. Statistical Computation and Simulation, 21 (1985), 39-49.
3. Davenport, James M. and Ronald L. Iman, An Iterative Algorithm to Produce a Positive Definite Correlation Matrix from an Approximate Correlation Matrix, Report SAND-81-1376, Sandia National Laboratories, Albuquerque, NM, 1981.
4. Dennis, John E. and J. J. More, "Quasi-Newton Methods, Motivation and Theory," SIAM Rev., 19, 1 (1977), 46-89.
5. _ and Robert B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983.
6. Devroye, Luc, Non-Uniform Random Variate Generation, SpringerVerlag, New York, 1986.
7. Eyraud, H., "Les Principes de la Mesure des Correlations," Annales Universite Lyons, Series A, Sciences Mathematiques et Astronomie, 1 (1938), 30-47.
8. Farlie, D. J., "The Performance of Some Correlation Coefficients for a General Bivariate Distribution," Biometrika, 47 (1960), 307-323.
9. Feller, William, An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley, New York, 1971.
10. Fleishman, Allen I., "A Method for Simulating Non-Normal Distributions," Psychometrika, 43, 4 (1978), 521-532.
11. Gill, Philip E., Walter Murray, and Margaret H. Wright, Practical Optimization, Academic Press, London, England, 1981.
12. Gumbel, E. J., "Distribution àPlusieurs Variables dont les Marges sont Données," Comptes Rendus, 246 (1958), 2717-2719.
13. Henrici, Peter, Elements of Numerical Analysis, John Wiley, New York, 1964.
14. Johnson, Mark E., Multivariate Statistical Simulation, John Wiley, New York, 1987.
15. Johnson, Norman L. and Samuel Kotz, Distributions in Statistics: Continuous Multivariate Distributions, John Wiley, New York, 1972.
16. Lee, Mei-Ling Ting, A Family of Multivariate Density Functions with Given Marginals, Harvard Medical School, Cambridge, MA, May 25, 1993.
17. Li, Shing Ted and Joseph L. Hammond, "Generation of PseudoRandom Numbers with Specified Univariate Distributions and Correlation Coefficients," IEEE Trans, on Systems, Man, and Cybernetics, 5 (1975), 557-561.
18. Marsaglia, G. and I. Olkin, "Generating Correlation Matrices," SIAM. J. Scientific and Statistical Computing, 5 (1984), 470-475.
19. Morgenstern, D., "Einfache Beispiele Zweidimensionaler Verteilungen," Mitteilingsblatt für Mathematische Statistik, 8 (1956), 234-235.
20. Parrish, Rudolph S., "Generating Random Deviates from Multivariate Pearson Distributions," Computational Statistics and Data Analysis, 9 (1990), 283-295.
21. Pullin, D. I., "Generation of Normal Variates with Given Sample Mean and Variance," J. Statistical Computation and Simulation, 9 (1979), 303-309.
22. Seber, G. A. F. and C. J. Wild, Nonlinear Regression, John Wiley, New York, 1989.
23. Taylor, Angus E. and W. Robert Mann, Advanced Calculus, Xerox College Publishing, Lexington, MA, 1972.
24. Vale, C. David and Vincent A. Maurelli, "Simulating Multivariate Non-Normal Distributions," Psychometrika, 48, 3 (1983), 465-471.
25. Wilks, Samuel S., Mathematical Statistics, John Wiley, New York, 1962.