An application of copulas to accident precursor analysis

Management Science

Volumn 44, Issue 12 PART 2, 1998, Pages

  Yi, Woojune ^a   Bier, Vicki M ^a  

^a NONE

Author keywords

Accident Precursors; Bayesian Analysis; Copulas; Dependencies; Risk Analysis

Indexed keywords

ACCIDENTS; DATA REDUCTION; STATISTICAL METHODS;

ACCIDENT PRECURSOR ANALYSIS; BAYESIAN ANALYSIS; COPULAS;

RISK ASSESSMENT;

EID: 0032295954     PISSN: 00251909     EISSN: None     Source Type: Journal    
DOI: 10.1287/mnsc.44.12.s257     Document Type: Article

References (40)

1. Abrahams, J., J. B. Thomas, 1984, A note on the characterization of bivariate densities by conditional densities. Comm. Statist. Theory Methods 13 395-400.
2. Abramson, L. R. 1994. A unified statistical approach to estimating core damage frequency based on accident sequence precursor conditional core damage probabilities. PSAM-II, San Diego, CA. March.
3. Apostolakis, G., A. Mosleh. 1979. Expert opinion and statistical evidence: an application to reactor core melt frequency. Nuclear Sci. Engrg. 70 133-149.
4. Bier, V. M. 1993. Statistical methods for the use of accident precursor data in estimating the frequency of rare events. Reliability Engrg. System Safety 41 267-280.
5. _, A. Mosleh. 1990. The analysis of accident precursors and near misses: implications for risk assessment. Reliability Engrg. System Safety 27 91-101.
6. _, _. 1991. An approach to the analysis of accident precursors. B. J. Garrick and W. C. Gekler, eds. The Analysis, Communication, and Perception of Risk, Plenum Press, New York.
7. _, W. Yi. 1995. A Bayesian method for analyzing dependencies in precursor data. Internat. J. Forecasting 11 25-41.
8. Chow, T. C., R. M. Oliver. 1988. Predicting nuclear incidents. J. Forecasting 7 49-61.
9. _, _, G. A. Vignaux. 1990. A Bayesian escalation model to predict nuclear accidents and risk. Oper. Res. 36 265-277.
10. Clemen, R. T., T. Reilly. 1998. Correlations and copulas for decision and risk analysis. To appear in Man. Sci.
11. Cook, R. D., M. E. Johnson. 1981. A family of distributions for modeling non-elliptically symmetric multivariate data. J. Royal Statist. Society - B 43 210-218.
12. Cooke, R., L. Goossens. 1990. The accident sequence precursor methodology for the European Post-Seveso era. Reliability Engrg. System Safety 27 117-130.
13. _, _, A. R. Hale, J. Van Der Horst. 1987. Accident sequence precursor methodology: a feasibility study for the chemical process industries. Technische Universiteit Delft, The Netherlands.
14. Cuadras, C. M., J. Augé. 1981. A continuous general multivariate distribution and its properties. Comm. Statist. Theory Methods A10 339-353.
15. Frank, M. J. 1979. On the simultaneous associativity of F(x, y) and x + y - F(x, y). Aequations Math. 19 194-226.
16. Genest, C. 1987. Frank's family of bivariate distributions. Biometrika 74 549-555.
17. _, J. MacKay. 1986. The joy of copulas: bivariate distributions with uniform marginals. Amer. Statistician 40 280-283.
18. _, L. Rivest. 1993. Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc. Theory Methods 88 1034-1043.
19. Gumbel, E. J. 1961. Bivariate logistic distributions. J. Amer. Statist. Assoc. 56 335-349.
20. Hutchinson, T. P., C. D. Lai. 1990. Continuous Bivariate Distributions, Emphasizing Applications. Rumsby Scientific Publishing, Adelaide, Australia.
21. Johnson, N. L., S. Kotz. 1972. Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
22. Johnson, J. W., D. M. Rasmuson. 1996. The US NRC's accident sequence precursor program: an overview and development of a Bayesian approach to estimate core damage frequency using precursor information. Reliability Engrg. System Safety 53 205-216.
23. Jouini, M. N., R. T. Clemen. 1996. Copula models for aggregating expert opinions. Oper. Res. 44 444-457.
24. Kaplan, S. 1992. "Expert information" versus "expert opinions." Another approach to the problem of eliciting/combining/using expert knowledge in PRA. Reliability Engrg. System Safety 35 61-72.
25. Kapur, J. N. 1994. Measures of Information and Their Applications. Wiley, New Delhi, India.
26. Kimeldorf, G., A. Sampson. 1975. One-parameter family of bivariate distributions with fixed marginals. Comm. Statist. 4 293-301.
27. MacKenzie, G. R. 1994. Approximately maximum-entropy multivariate distributions with specified marginals and pairwise correlations. Ph.D. Thesis, University of Oregon, Eugene, OR.
28. Mardia, K. V. 1970. A translation family of bivariate distributions and Fréchet's bounds. Sankhyā, Ser. A 32 119-122.
29. Martin, J. J. 1967. Bayesian Decision Problems and Markov Chains. Wiley, New York.
30. McCormick, N. J. 1981. Reliability and Risk Analysis: Methods and Nuclear Power Applications. Academic Press, New York.
31. Meeuwissen, A. M. 1991. Dependent random variables in uncertainty analysis. Ph.D. Thesis, Technische Universiteit Delft, The Netherlands.
32. Minarick, J. W., C. A. Kukielka. 1982. Precursors to potential severe core damage accidents: 1969-1979, a status report. NUREG /CR-2497, U.S. Nuclear Regulatory Commission, Washington, DC.
33. Mosleh, A., V. M. Bier, G. Apostolakis. 1987. Methods for the elicitation and use of expert opinion in risk assessment: phase 1 - a critical evaluation and directions for future research. NUREG/CR-4962, U.S. Nuclear Regulatory Commission, Washington, DC.
34. Oliver, R. M., H. J. Yang. 1990. Bayesian updating of event tree parameters to predict high risk incidents. R. M. Oliver and J. Q. Smith, Eds. Influence Diagrams, Belief Nets and Decision Analysis. Wiley, Chichester, UK, 1990.
35. Schweizer, B., E. F. Wolff. 1981. On nonparametric measures of dependence for random variables. Ann. Statist. 9 879-885.
36. _, A. Sklar. 1983. Probabilistic Metric Spaces. North-Holland, New York.
37. Sklar, A. 1959. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. l'Université de Paris 8 229-231.
38. _. 1973. Random variables, joint distribution functions, and copulas." Kybernetica 9 463-501.
39. Smith, W. 1983. Inequalities for bivariate distributions with X ≤ Y and marginals given. Comm. Statist. Theory Methods 12 1371-1379.
40. Yi, W. 1997. Bayesian precursor methods for modeling intersystem dependencies in event trees. Ph.D. Thesis, University of Wisconsin-Madison, Madison, WI.