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Life Expectancy Estimate with Bivariate Weibull Distribution using Archimedean Copula
Eun-Joo Lee, Chang-Hyun Kim, Seung-Hwan Lee
Pages - 149 - 161     |    Revised - 01-07-2011     |    Published - 05-08-2011
Volume - 5   Issue - 3    |    Publication Date - July / August 2011  Table of Contents
Archimedean Copula, Dependence, Weibull Distribution, Value at Risk
Archimedean copulas are used to construct bivariate Weibull distributions. Co-movement structures of variables are analyzed through the copulas, where the tail dependence between the variables is explored with more flexibility. Based on the distance between the copula distribution and its empirical version, a copula that may best fit data is selected. With extra computing costs, the adequacy of the copula chosen is then assessed. When multiple myeloma data are considered, it is found that relationship between survival time of a patient and the hemoglobin level is well described by the Clayton copula. The bivariate Weibull distribution constructed by the copula is used to estimate value at risk from which we investigate the anticipated longest life expectancy of a patient with the disease over the treatment period.
CITED BY (4)  
1 Zhang Zhen Ning, Cao Limei , & Ke Bingqing . ( 2014 ) . Bivariate Weibull statistics manifold structure and instability even geometry. Beijing University of Technology , 3, 013.
2 Verrill, S. P., Evans, J. W., Kretschmann, D. E., & Hatfield, C. A. (2014). Asymptotically Efficient Estimation of a Bivariate Gaussian–Weibull Distribution and an Introduction to the Associated Pseudo-truncated Weibull. Communications in Statistics-Theory and Methods, (just-accepted), 00-00.
3 Verrill, S. P., Evans, J. W., Kretschmann, D. E., & Hatfield, C. A. (2014). Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull. Series: Journal Articles.
4 Zhang Zhen Ning, Cao Limei, & Kebing Qing. (2014). Bivariate Weibull statistics manifold structure and instability even geometry. Beijing University of Technology, 3, 013.
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1 D.G. Clayton, “A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence”. Biometrika, 65:141-151, 1978
2 D. Collect, “Modelling Survival Data in Medical Research”. Chapman, 1999
3 R.D. Cook and M.E. Johnson, “A family of distributions for modeling non-elliptically symmetric multivariate data”. Journal of the Royal Statistical Society, Series B, 43, 210-218, 1981
4 M. Crouhy, D. Galai, and R. Mark, “Risk Management”. McGraw-Hill, 2001
5 B.G. Durie and S.E. Salmon, “A clinical staging system for multiple myeloma. Correlation of measured myeloma cell mass with presenting clinical features, response to treatment, and survival”. Cancer, 36(3), 842-854, 1975
6 V. Durrleman, A. Nikeghbail and T. Roncalli, “Which copula is the right one?”. Credit Lyonnais, Available at SSRN: http://ssm.com/abstract=1032545, 2000
7 P. Embrechts, A. McNeil and D. Straumann, “Correlation: Pitfall and Alternative”. Risk, 12, 69-71, 1999
8 M.J. Frank, “On the simultaneous associativity of and ”. Aequationes Mathematicae, 19, 194-226, 1979
9 M.J. Frees and E. Valdez, “Understanding relationships using copulas”. North American Actuarial Journal, 2, 1-25, 1998
10 C. Genest and R.J. MacKay, “Copules Archimediennes et Failles de Lois Bidimensionnelles Don’t les Marges Sont Donnees”, The Canadian Journal of Statistics, 14, 145-159, 1986a
11 C. Genest and R.J. MacKay, “The joy of copulas: Bivariate distributions with uniform marginals”. American Statistician, 40, 280-283, 1986b
12 C. Genest, and L. Rivest, “Statistical inference procedures for bivariate Archimedean copulas”. Journal of American Statistical Association, 88, 1034-1043, 1993
13 P.R. Greipp, J. San Miguel, B.G. Durie, J.J. Crowley, B. Barlogie, J. Bladé, M. Boccadoro, J.A. Child, H. Avet-Loiseau, R.A. Kyle, J.J. Lahuerta, H. Ludwig, G. Morgan, R. Powles, K. Shimizu, C. Shustik, P. Sonneveld, P. Tosi, I. Turesson, and J. Westin, “International staging system for multiple myeloma”. Journal of Clinical Oncology, 23, 3412-3420, 2005
14 E.J. Gumbel, “Bivariate exponential distributions”. Journal of American Statistical Association, 55, 698-707, 1960
15 P. Hougaard, “A class of multivariate failure time distributions”. Biometrika, 73, 671-678, 1986
16 H. Joe, “Multivariate Models and Dependence Concepts”. Chapman & Hall, London, 1997
17 P. Jorion, “Value at Risk: The New Benchmark for Managing Financial Risk”. McGraw-Hill Publication, 2007
18 J.M. Krall, V.A. Uthoff and J.B. Harley, “A step-up procedure for selecting variables associated with survival”. Biometrics, 31, 49-51, 1975
19 P. Kumar and M.M. Shoukri, “Evaluating Aortic Stenosis using the Archimedean copula methodology”. Journal of Data Science, 6, 173-187, 2008
20 R.A. Kyle and S.V. Rajkumar, Multiple myeloma. Blood, 111(6), 2962-2972, 2008
21 S. Lee, E.-J. Lee and B.O. Omolo, “Using integrated weighted survival difference for the two-sample censored data problem”. Computational Statistics and Data Analysis, 52, 4410-4416, 2008
22 S. Lee and S. Yang, “Checking the censored two-sample accelerated life model using integrated cumulative hazard difference”. Lifetime Data Analysis, 13, 371-380, 2007
23 D.Y. Lin, L.J. Wei and Z. Ying, “Checking the cox model with cumulative sums of martingale-based residuals”. Biometrika, 80, 557-72, 1993
24 A. McNeil, R. Frey and P. Embrechts, “Quantitative Risk Management: Concepts, Techniques and Tools”. Princeton University Press, 2005
25 M.R. Melchiori, “Which Archimedean copula is the right one?”. Yield Curve, 37, 1-20, 2003
26 R.B. Nelsen, “An introduction to copulas”. Springer, 1999
27 L. Rivest and M. Wells, “A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring”. Journal of Multivariate Analysis, 79, 138-155, 2001
28 A. Sklar, “Functions de repartition a n dimensions et leurs merges”. Publication of the Institute of Statistics, University of Paris, 8, 229-231, 1959
29 G. Venter, “Tails of copulas”. Proceedings of the Astin Colloquium, 2001.
30 M. Zheng and J. Klein, “Estimates of marginal survival for dependent competing risks based on an assumed copula”. Biometrika, 82, 127-138, 1995
Mr. Eun-Joo Lee
- United States of America
Mr. Chang-Hyun Kim
- United States of America
Associate Professor Seung-Hwan Lee
Illinois Wesleyan University - United States of America