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Bivariate survival models with Clayton aging functions. (English) Zbl 1075.62091

Summary: In some recent papers [see, e.g., J. Multivariate Anal. 93, No. 2, 313–339 (2005; Zbl 1070.60015)], the authors considered a function \(B\) that describes the level curves of an exchangeable bivariate survival function \(\overline F\). The function \(B\) permits the analysis of several “multivariate aging properties” of \(\overline F\). In this paper, the authors consider survival models characterized by the condition that \(B\) is a D. G. Clayton copula [Biometrika 65, 141–151 (1978; Zbl 0394.92021)] and analyze a related invariance property. This property concerns the family of level curves of the joint survival function of residual lifetimes, when “ages” are increasing.

MSC:

62N99 Survival analysis and censored data
62H99 Multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Aczél, J., Lectures on Functional Equations and Their Applications (1966), Academic Press · Zbl 0139.09301
[2] Bassan, B., Spizzichino, F., 2001. Dependence and multivariate aging: the role of level sets of the survival function. System and Bayesian Reliability, 229-242. Ser. Qual. Reliab. Eng. Stat., 5. World Scientific Publishing, River Edge, NJ.; Bassan, B., Spizzichino, F., 2001. Dependence and multivariate aging: the role of level sets of the survival function. System and Bayesian Reliability, 229-242. Ser. Qual. Reliab. Eng. Stat., 5. World Scientific Publishing, River Edge, NJ.
[3] Bassan, B.; Spizzichino, F., On some properties of dependence and aging for residual lifetimes in the exchangeable case, (Lindqvist, B. H.; Doksum, K. A., Mathematical and Statistical Methods in Reliability. Mathematical and Statistical Methods in Reliability, Series on Quality, Reliability and Engineering Statistics, vol. 7 (2003), World Scientific Publishing)
[4] Bassan, B.; Spizzichino, F., Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes, J. Multivariate Anal., 93, 313-339 (2005) · Zbl 1070.60015
[5] Charpentier, A., 2004. Tail Dependence for Archimedean Copulas. Preprint.; Charpentier, A., 2004. Tail Dependence for Archimedean Copulas. Preprint. · Zbl 1183.62086
[6] Charpentier, A., Juri, A., Wüthrich, M.V., 2003. Dependence in Tail Distributions. Preprint.; Charpentier, A., Juri, A., Wüthrich, M.V., 2003. Dependence in Tail Distributions. Preprint.
[7] Clayton, D. G., A model for association in bivariate life tables and its application in epidemiologic studies of familial tendency in chronic disease incidence, Biometrika, 65, 141-151 (1978) · Zbl 0394.92021
[8] Durante, F., Sempi, C. Semi-copulae. Kybernetika, in press.; Durante, F., Sempi, C. Semi-copulae. Kybernetika, in press.
[9] Marshall, A. W.; Olkin, I., Inequalities: Theory of Majorization and its Applications (1979), Academic Press: Academic Press New York · Zbl 0437.26007
[10] Nelsen, R. B., An Introduction to Copulas (1999), Springer: Springer New York · Zbl 0909.62052
[11] Oakes, D., A model for association in bivariate survival data, J. Am. Stat. Assoc., 84, 487-493 (1989) · Zbl 0677.62094
[12] Oakes, D. On the preservation of copula structure under truncation. Can. J. Stat., 33, in press.; Oakes, D. On the preservation of copula structure under truncation. Can. J. Stat., 33, in press. · Zbl 1101.62040
[13] Spizzichino, F., Subjective Probability Models for Lifetimes (2001), Chapman and Hall/CRC: Chapman and Hall/CRC Boca Raton, FL · Zbl 1078.62530
[14] Sungur, E. A., Truncation invariant dependence structures., Commun. Stat. Theor. Methods, 28, 2553-2568 (1999) · Zbl 0973.62044
[15] Sungur, E. A., Some results on truncation dependence invariant class of copulas, Commun. Stat. Theor. Methods, 31, 1399-1422 (2002) · Zbl 1075.62561
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