An Application of Copulas to Accident Precursor Analysis

References

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