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On the preservation of copula structure under truncation. (English) Zbl 1101.62040
Summary: The author characterizes the copula associated with the bivariate survival model of D. G. Clayton [Biometrika 65, 141–151 (1978; Zbl 0394.92021)] as the only absolutely continuous copula that is preserved under bivariate truncation.

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62N99 Survival analysis and censored data
62H20 Measures of association (correlation, canonical correlation, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] A. Charpentier (2003). Conditional Copula and Tail Dependence. Mimeo report.
[2] Clayton, A model for association in bivariate life tables and its application in epidemiologic studies of familial tendency in chronic disease incidence, Biometrika 65 pp 141– (1978) · Zbl 0394.92021
[3] Cook, A family of distributions for modelling non-elliptically symmetric multivariate data, Journal of the Royal Statistical Society Series B 43 pp 210– (1981) · Zbl 0471.62046
[4] Genest, Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données, The Canadian Journal of Statistics 14 pp 145– (1986) · Zbl 0605.62049
[5] Kimeldorf, Uniform representations of bivariate distributions, Communications in Statistics-Theory and Methods 4 pp 617– (1975) · Zbl 0312.62008
[6] Manatunga, A measure of association for bivariate survival distributions, Journal of Multivariate Analysis 56 pp 60– (1996) · Zbl 0864.62039
[7] Nelsen, An Introduction to Copulas (1999) · Zbl 0909.62052
[8] Oakes, A model for association in bivariate survival data, Journal of the Royal Statistical Society Series B 44 pp 414– (1982) · Zbl 0503.62035
[9] Oakes, Bivariate survival models induced by frailties, Journal of the American Statistical Association 84 pp 487– (1989) · Zbl 0677.62094
[10] Prentice, Covariance and survivor function estimation using censored multivariate failure time data, Biometrika 79 pp 495– (1992) · Zbl 0764.62095
[11] Sungur, Truncation invariant dependence structures, Communications in Statistics-Theory and Methods 28 pp 2553– (1999) · Zbl 0973.62044
[12] Sungur, Some results on truncation dependence invariant class of copulas, Communications in Statistics-Theory and Methods 31 pp 1399– (2002) · Zbl 1075.62561
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