Initialization for NORTA: Generation of Random Vectors with Specified Marginals and Correlations

References

• Beasley J. D., Springer S. G. Algorithm AS 111. The percentage points of the normal distribution. Applied Statistics (1977) 26:118–121Crossref, Google Scholar
• Best D. J., Roberts D. E. Algorithm AS 91. The percentage points of the χ2 distribution. Applied Statistics (1975) 24:385–388Crossref, Google Scholar
• Broste N. A. Digital generation of random sequences. IEEE Transactions on Automatic Control (1971) AC-16:213–214Crossref, Google Scholar
• Cario M. C., Nelson B. L. Autoregressive to anything: time-series input processes for simulation. Operations Research Letters (1996) 19:51–58Crossref, Google Scholar
• Cario M. C., Nelson B. L.Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix (1997) (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL) . Technical ReportGoogle Scholar
• Cario M. C., Nelson B. L. Numerical methods for fitting and simulating autoregressive-to-anything processes. INFORMS Journal on Computing (1998) 10:72–81Link, Google Scholar
• Chen H.Stochastic Root Finding in System Design (1994) (School of Industrial Engineering, Purdue University, West Lafayette, IN) . Ph.D. DissertationGoogle Scholar
• Chen H., Jeng C. Generation of multivariate random vectors using retrospective approximation algorithms. Proceedings of the 1995 Chinese Industrial Engineering Conference (1995) (Taoyuan, Taiwan)839–846Google Scholar
• Chen H., Schmeiser B. W. Stochastic root finding: problem definition, examples, and algorithms. Proceedings of the Third Industrial Engineering Research Conference (1994a) (Institute of Industrial Engineers, Norcross, GA) 605–610Google Scholar
• Chen H., Schmeiser B. W. Retrospective approximation algorithms for stochastic root finding. Proceedings of the 1994 Winter Simulation Conference (1994b) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 255–261Google Scholar
• Chen H., Schmeiser B. W. Stochastic root finding via retrospective approximation. IIE Transactions (2001) 33:259–275Crossref, Google Scholar
• Clemen R. T., Fischer G. W., Winkler R. L. Assessing dependence: some experimental results. Management Science (2000) 46:1100–1115Link, Google Scholar
• Clemen R. T., Reilly T. Correlations and copulas for decision and risk analysis. Management Science (1999) 45:208–224Link, Google Scholar
• Conte S. D., de Boor C.Elementary Numerical Analysis: An Algorithmic Approach (1980) (McGraw-Hill, New York) Google Scholar
• Corner J. L., Kirkwood C. W. The magnitude of errors in proximal multiattribute decision analysis with probabilistically dependent attributes. Management Science (1996) 42:1033–1042Link, Google Scholar
• Devroye L.Non-Uniform Random Variate Generation (1986) (Springer Verlag, New York) Crossref, Google Scholar
• Gaver D. P., Lewis P. A. W. First-order autoregressive gamma sequences and point processes. Adv. Appl. Prob. (1980) 12:727–745Crossref, Google Scholar
• Ghosh S., Henderson S.Chessboard distributions and random vectors with specified marginals (2000) (Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI) . Technical ReportGoogle Scholar
• Gilks W. R., Wild P. Adaptive rejection sampling for Gibbs sampling. Applied Statistics (1992) 41:337–348Crossref, Google Scholar
• Gujar V. G., Kavanagh R. J. Generation of random signals with specified probability density functions and power density spectra. IEEE Transactions on Automatic Control (1968) AC-13:716–719Crossref, Google Scholar
• Hörmann W. A rejection technique for sampling from T-concave distributions. ACM Transactions on Math. Softw. (1995) 21:182–193Crossref, Google Scholar
• Huber P. J. Robust estimation of a location parameter. Annals of Mathematical Statistics (1964) 35:73–101Crossref, Google Scholar
• Hull J. C. Dealing with dependence in risk simulations. Operational Research Quarterly (1977) 28:201–213Crossref, Google Scholar
• Johnson M. E.Multivariate Statistical Simulation (1987) (John Wiley & Sons, New York) Crossref, Google Scholar
• Johnson M. E., Ramberg J. S.Transformation of the multivariate normal distribution with applications to simulation (1978) (Los Alamos Sci. Lab., Los Alamos, NM) . Technical Report LA-UR-77-2595Google Scholar
• Kendall M. G., Stuart A.The Advanced Theory of Statistics (1967) 13rd ed.(Griffin, London, U.K) Google Scholar
• Lancaster H. O. Some properties of the bivariate normal distribution considered in the form of a contingency table. Biometrika (1957) 44:289–292Crossref, Google Scholar
• Law A. M., Kelton W. D.Simulation Modeling and Analysis (2000) 3rd ed.(McGraw-Hill, New York) Google Scholar
• Lehmann E. L.Theory of Point Estimation (1983) (John Wiley & Sons, New York) Crossref, Google Scholar
• Lenth R. V. Algorithm AS 243. Cumulative distribution function of the noncentral t distribution. Applied Statistics (1989) 38:185–189Crossref, Google Scholar
• Lewis P. A. W. Generating negatively correlated gamma variates using the beta-gamma transformation. Proceedings of the 1983 Winter Simulation Conference (1983) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 175–176Google Scholar
• Leydold J. A rejection technique for sampling from log-concave multivariate distributions. ACM Transactions on Modeling and Computer Simulation (1998) 8:254–280Crossref, Google Scholar
• Li S. T., Hammond J. L. Generation of pseudorandom numbers with specified univariate distributions and correlation coefficients. IEEE Transactions on System, Man, and Cybernetics (1975) 5:557–561Crossref, Google Scholar
• Lurie P. M., Goldberg M. S. An approximate method for sampling correlated random variables from partially specified distributions. Management Science (1998) 44:203–218Link, Google Scholar
• Mardia K. V.Families of Bivariate Distributions (1970) (Griffin, London, U.K) Google Scholar
• Moonan W. J. Linear transformation to a set of stochastically dependent normal variables. Journal of American Statistical Association (1957) 52:247–252Crossref, Google Scholar
• Nelson B. L., Yamnitsky M. Input modeling tools for complex problems. Proceedings of the 1998 Winter Simulation Conference (1998) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 105–112Crossref, Google Scholar
• Parrish R. S. Generating random deviates from multivariate Pearson distributions. Computational Statistics … Data Analysis (1990) 9:283–295Crossref, Google Scholar
• Ripley B. D.Stochastic Simulation (1987) (John Wiley … Sons, New York) Crossref, Google Scholar
• Ronning G. A simple scheme for generating multivariate gamma distributions with nonnegative covariance matrix. Technometrics (1977) 19:179–183Crossref, Google Scholar
• Scheuer E. M., Stoller D. S. On the generation of normal random vectors. Technometrics (1962) 4:278–281Crossref, Google Scholar
• Schmeiser B. W., Heyman D. P., Sobel M. J. Simulation experiments. Handbooks in Operations Research and Management Science (1990) 2(North-Holland, New York)295–330Google Scholar
• Schmeiser B. W. Advanced input modeling for simulation experimentation. iProceedings of the 1999 Winter Simulation Conference (1999) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 110–115Crossref, Google Scholar
• Schmeiser B. W., Lal R. Bivariate gamma random vectors. Operations Research (1982) 30:355–374Link, Google Scholar
• Song W. T., Hsiao L. Generation of autocorrelated random variables with a specified marginal distribution. Proceedings of the 1993 Winter Simulation Conference (1993) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 374–377Crossref, Google Scholar
• Song W. T., Hsiao L., Chen Y. Generating pseudo-random time series with specified marginal distributions. European Journal of Operational Research (1996) 94:194–202Crossref, Google Scholar
• Stanfield P. M., Wilson J. R., Mirka G. A., Glasscock N. F., Psihogios J. P., Davis J. R. Multivariate input modeling with Johnson distributions. Proceedings of the 1996 Winter Simulation Conference (1996) (Institute of Electrical and Electronics Engineers, Piscataway, NJ) 1457–1464Crossref, Google Scholar