Multivariate Modeling with Copulas and Engineering Applications

Springer Handbooks

Volumn , Issue , 2006, Pages 973-990

  Yan, Jun ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Archimedean Copula; Clayton Copula; Control Chart; Multivariate Distribution; Multivariate Normal Distribution

Indexed keywords

EID: 85088289786     PISSN: 25228692     EISSN: 25228706     Source Type: Book Series    
DOI: 10.1007/978-1-84628-288-1_51     Document Type: Chapter

References (51)

1. 51.1 R. B. Nelsen: An Introduction to Copulas (Springer, Berlin Heidelberg New York 1999)
2. 51.2 H. Joe: Multivariate Models and Dependence Concepts (Chapman Hall, Norwell 1997)
3. 51.3 C. Genest, J. MacKay: The joy of copulas: Bivariate distributions with uniform marginals (Com: 87V41 P248), Am. Statist. 40, 280–283 (1986)
4. 51.4 N. I. Fisher: Copulas. In: Encyclopedia of Statistical Sciences, ed. by S. Kotz, C. B. Read, D. L. Banks (Wiley, New York 1997) pp. 159–163
5. 51.5 E. W. Frees, J. Carriere, E. A. Valdez: Annuity valuation with dependent mortality, J. Risk Insur. 63, 229–261 (1996)
6. 51.6 E. W. Frees, E. A. Valdez: Understanding relationships using copulas, North Am. Actuar. J. 2, 1–25 (1998)
7. 51.7 E. W. Frees, P. Wang: Credibility using copulas, North Am. Actuar. J. 9, 31–48 (2005)
8. 51.8 E. Bouyè, V. Durrleman, A. Bikeghbali, G. Riboulet, T. Roncalli: Copulas for Finance – A Reading Guide and Some Applications, Working Paper (Goupe de Recherche Opérationnelle, Crédit Lyonnais, Lyon 2000)
9. 51.9 P. Embrechts, F. Lindskog, A. McNeil: Modelling dependence with copulas and applications to risk management. In: Handbook of Heavy Tailed Distribution in Finance, ed. by S. Rachev (Elsevier, Amsterdam 2003) pp. 329–384
10. 51.10 U. Cherubini, E. Luciano, W. Vecchiato: Copula Methods in Finance (Wiley, New York 2004)
11. 51.11 W. Wang, M. T. Wells: Model selection and semiparametric inference for bivariate failure-time data (C/R: p73-76), J. Am. Statist. Assoc. 95, 62–72 (2000)
12. 51.12 G. Escarela, J. F. Carrière: Fitting competing risks with an assumed copula, Statist. Methods Med. Res. 12, 333–349 (2003)
13. 51.13 J. Yan: Copula: Multivariate Dependence with Copula, R package version 0.3-3 2005) CRAN, http://cran.r-project.org
14. 51.14 R Development Core Team: R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna 2005)
15. 51.15 A. W. Sklar: Fonctions de répartition à n dimension et leurs marges, Publ. Inst. Statist. Univ. Paris 8, 229–231 (1959)
16. 51.16 A. Sklar: Random variables, distribution functions, and copulas – A personal look backward and forward. In: Distributions with Fixed Marginals and Related Topics, IMS Lecture Notes Monogr. Ser., Vol. 28, ed. by L. Rüschendorf, B. Schweizer, M. D. Taylor (Institute of Mathematical Statistics, Bethesda 1996) pp. 1–14
17. 51.17 B. Schweizer: Thirty years of copulas. In: Advances in Probability Distributions with Given Margins: Beyond the Copulas, ed. by G. Dall’Aglio, S. Kotz, G. Salinetti (Kluwer Academic, Dordrecht 1991) pp. 13–50
18. 51.18 P. Embrechts, A. McNeil, D. Straumann: Correlation and dependence in risk management: Properties and pitfalls. In: Risk Management: Value at Risk and Beyond, ed. by M. Dempster (Cambridge Univ. Press, Cambridge 2002) pp. 176–223
19. 51.19 K.-T. Fang, S. Kotz, K. W. Ng: Symmetric Multivariate and Related Distributions (Chapman Hall, Norwell 1990)
20. 51.20 P. X.-K. Song: Multivariate dispersion models generated from Gaussian copula, Scandin. J. Statist. 27, 305–320 (2000)
21. 51.21 S. Demarta, A. J. McNeil: The t copula and related copulas, Int. Statist. Rev. 73, 111–129 (2005)
22. 51.22 A. Genz, F. Bretz, T. Hothorn: Mvtnorm: Multivariate Normal and T Distribution, R package version 0.7-2 2005) CRAN, http://cran.r-project.org
23. 51.23 A. W. Marshall, I. Olkin: Families of multivariate distributions, J. Am. Statist. Assoc. 83, 834–841 (1988)
24. 51.24 D. G. Clayton: A model for association in bivariate life tables and its application in epi-demiological studies of familial tendency in chronic disease incidence, Biometrika 65, 141–152 (1978)
25. 51.25 M. J. Frank: On the simultaneous associativity of F(x‚y) and x + y − F(x‚y), Aequ. Math. 19, 194–226 (1979)
26. 51.26 E. J. Gumbel: Bivariate exponential distributions, J. Am. Statist. Assoc. 55, 698–707 (1960)
27. 51.27 P. Hougaard: A class of multivariate failure time distributions (Corr: V75 p395), Biometrika 73, 671– 678 (1986)
28. 51.28 J. M. Chambers, C. L. Mallows, B. W. Stuck: A method for simulating stable random variables (Corr: V82 P704; V83 P581), J. Am. Statist. Assoc. 71, 340–344 (1976)
29. 51.29 A. W. Kemp: Efficient generation of logarithmi-cally distributed pseudo-random variables, Appl. Statist. 30, 249–253 (1981)
30. 51.30 H. Joe, J. Xu: The Estimation Method of Inference Functions for Margins for Multivariate Models, Tech. Rep. 166 (Department of Statistics, University of British Columbia, Vancouver 1996)
31. 51.31 J. H. Shih, T. A. Louis: Inferences on the association parameter in copula models for bivariate survival data, Biometrics 51, 1384–1399 (1995)
32. 51.32 V. P. Godambe: An optimum property of regular maximum likelihood estimation (Ack: V32 p1343), Annal. Math. Statist. 31, 1208–1212 (1960)
33. 51.33 C. Genest, K. Ghoudi, L.-P. Rivest: A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82, 543–552 (1995)
34. 51.34 C. A. Lowry, D. C. Montgomery: A review of multivariate control charts, IIE Trans. 27, 800–810 (1995)
35. 51.35 H. Hotelling: Multivariate quality control – Illustrated by the air testing of sample bombsights. In: Techniques of Statistical Analysis, ed. by C. Eisenhart, M. W. Hastay, W. A. Wallis (McGraw–Hill, New York 1947) pp. 111–184
36. 51.36 R. L. Mason, J. C. Young: Multivariate Statistical Process Control with Industrial Applications, ed. by ASA-SIAM Ser. Statist. Appl. Probab. (SIAM, Philadelphia 2001) p. 263
37. 51.37 R. Y. Liu, J. Tang: Control charts for dependent and independent measurements based on boot- strap methods, J. Am. Statist. Assoc. 91, 1694–1700 (1996)
38. 51.38 M.-W. Lu, R. J. Rudy: Multivariate control chart. In: Recent Advances in Reliability and Quality Engineering, ed. by H. Pham (World Scientific, Singapore 2001) pp. 61–74
39. 51.39 Q. H. Vuong: Likelihood ratio tests for model selection and non-nested hypotheses (STMA V31 0456), Econometrica 57, 307–333 (1989)
40. 51.40 W. Q. Meeker, L. A. Escobar: Statistical Methods for Reliability Data (Wiley, New York 1998)
41. 51.41 C. S. Davis: Statistical Methods for the Analysis of Repeated Measurements (Springer, Berlin Heidelberg New York 2002)
42. 51.42 R. C. Littell, G. A. Milliken, W. W. Stroup, R. D. Wolfinger: SAS System for Mixed Models (SAS Institute, Cary 1996)
43. 51.43 J. C. Pinheiro, D. M. Bates: Mixed-Effects Models in S and S-PLUS (Springer, Berlin, New York 2000)
44. 51.44 W. P. Murray: Archival life expectancy of 3M mag-neto-optic media, J. Magn. Soc. Jpn. 17, 309–314 (1993)
45. 51.45 P. Lambert, F. Vandenhende: A copula-based model for multivariate non-normal longitudinal data: Analysis of a dose titration safety study on a new antidepressant, Statist. Med. 21, 3197–3217 (2002)
46. 51.46 P. Georges, A.-G. Lamy, E. Nicolas, G. Quibel, T. Roncalli: Multivariate survival modelling: A Unified Approach with Copulas, Working Paper (Goupe de Recherche Opérationnelle, Crédit Lyonnais, Lyon 2001)
47. 51.47 J.-D. Fermanian: Goodness-of-fit tests for copulas, J. Multivariate Anal. 95, 119–152 (2005)
48. 51.48 Insightful Corp.: S + Finmetrics Reference Manual (Insightful, Seattle 2002)
49. 51.49 Insightful Corp.: S-PLUS (Version 7.0) (Insightful, Seattle 2005)
50. 51.50 R Development Core Team: Writing R Extensions (R Foundation for Statistical Computing, Vienna 2005)
51. 51.51 J. M. Chambers: Programming with Data: A Guide to the S Language (Springer, Berlin, New York 1998)