Monte Carlo Simulation for Correlated Variables with Marginal Distributions
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 120, Issue 3
Abstract
As computation speed increases, Monte Carlo simulation is becoming a viable tool for engineering design and analysis. However, restrictions are often imposed on multivariate cases in which the involved stochastic parameters are correlated. In multivariate Monte Carlo simulation, a joint probability distribution is required that can only be derived for some limited cases. This paper proposes a practical multivariate Monte Carlo simulation that preserves the marginal distributions of random variables and their correlation structure without requiring the complete joint distribution. For illustration, the procedure is applied to the reliability analysis of a bridge pier against scouring.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ang, A. H‐S., and Tang, W. H. (1984). Probability concepts in engineering planning and design, Vol. II: Decision, risk, and reliability. John Wiley and Sons, Inc., New York, N.Y.
2.
Box, G. E. P., and Muller, M. E. (1958). “A note on generation of random normal deviates.” Ann. Math. Stat., 29, 610–611.
3.
Dagpunar, J. (1988). Principles of random variates generation. Oxford University Press, New York, N.Y.
4.
Der Kiureghian, A., and Liu, P. L. (1985). “Structural reliability under incomplete probability information.” J. Engrg. Mech., ASCE, 112(1), 85–104.
5.
Johnson, P. A. (1992). “Reliability‐based pier scour engineering.” J. Hydr. Engrg., ASCE, 118(10), 1344–1358.
6.
Li, S. T., and Hammond, J. L. (1975). “Generation of pseudo‐random numbers with specified univariate distributions and covariance matrix.” IEEE Trans. on Systems, Man. and Cybernetics, Sep., 557–561.
7.
Liu, P. L., and Der Kiureghian, A. (1986). “Multivariate distribution models with prescribed marginals and covariances.” Probabilistic Engrg. Mech., 1(2), 105–112.
8.
Parrish, R. S. (1990). “Generating random deviates from multivariate Pearson distributions.” Computational Statistics and Data Analysis, 9, 283–296.
9.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1989). Numerical recipes. Cambridge University Press, New York, N.Y.
10.
Ronning, G. (1977). “A simple scheme for generating multivariate gamma distributions with nonnegative covariance matrix.” Technometrics, 19(2), 179–183.
11.
Thoft‐Christensen, P., and Baker, M. J. (1982). Structural reliability theory and its applications. Springer‐Verlag, New York, N.Y.
12.
Tung, Y. K., and Mays, L. W. (1980). “Risk analysis for hydraulic design.” J. Hydraul. Div., ASCE, 106(5), 893–913.
13.
Yeh, K. C., and Tung, Y. K. (1993). “Uncertainty and sensitivity of a pit migration model.” J. Hydr. Engrg., ASCE, 119(2), 262–281.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: May 6, 1993
Published online: Mar 1, 1994
Published in print: Mar 1994
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.