References
- Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In: Petrov, B. N., and Csáki, F. Second International Symposium on Information Theory, 267–81. Budapest: Akadémiai Kiadó.
- Andersen, P. K., J. P. Klein, K. M. Knudsen, and R. T. Palacios. 1997. Estimation of variance in Cox’s regression model with shared gamma frailties. Biometrics 53 (4):1475–84. doi:https://doi.org/10.2307/2533513.
- Andersen, P. K., C. T. Ekstrøm, J. P. Klein, Y. Shu, and M.-J. Zhang. 2005. A class of goodness of fit tests for a copula based on bivariate right-censored data. Biometrical Journal 47 (6):815–24. doi:https://doi.org/10.1002/bimj.200410163.
- Bairamov, I., and S. Kotz. 2002. Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions. Metrika 56 (1):55–72. doi:https://doi.org/10.1007/s001840100158.
- Bertholon, H. 2001. Une modélisation du vieillissement. Ph.D. thesis., Université Joseph Fourier, Grenoble, France.
- Bousquet, N., H. Bertholon, and G. Celeux. 2006. An alternative competing risk model to the Weibull distribution for modelling aging in lifetime data analysis. Lifetime Data Analysis 12 (4):481–504. doi:https://doi.org/10.1007/s10985-006-9019-8.
- Bouzebda, S., and A. Keziou. 2009. A new test procedure of independence in copula models via χ2-divergence. Communications in Statistics—Theory and Methods 39 (1):1–20. doi:https://doi.org/10.1080/03610920802645379.
- Bouzebda, S., and A. Keziou. 2010. New estimates and tests of independence in semiparametric copula models. Kybernetika 46 (1):178–201.
- Breslow, N., and J. Crowley. 1974. A large sample study of the life table and product limit estimates under random censorship. The Annals of Statistics 2 (3):437–53. doi:https://doi.org/10.1214/aos/1176342705.
- Broniatowski, M., and A. Keziou. 2006. Minimization of φ-divergences on sets of signed measures. Studia Scientiarum Mathematicarum Hungarica 43 (4):403–42. doi:https://doi.org/10.1556/SScMath.43.2006.4.2.
- Clayton, D. G. 1978. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65 (1):141–51. doi:https://doi.org/10.1093/biomet/65.1.141.
- Duffy, D. L., N. G. Martin, and J. D. Mathews. 1990. Appendectomy in Australian twins. American Journal of Human Genetics 47 (3):590–2.
- Farlie, D. J. 1960. The performance of some correlation coefficients for a general bivariate distribution. Biometrika 47 (3-4):307–23. doi:https://doi.org/10.1093/biomet/47.3-4.307.
- Fermanian, J.-D., D. Radulovic, and M. Wegkamp. 2004. Weak convergence of empirical copula processes. Bernoulli 10 (5):847–60. doi:https://doi.org/10.3150/bj/1099579158.
- Frees, E. W., J. Carriere, and E. Valdez. 1996. Annuity valuation with dependent mortality. The Journal of Risk and Insurance 63 (2):229–61. doi:https://doi.org/10.2307/253744.
- Galambos, J. 1975. Order statistics of samples from multivariate distributions. Journal of the American Statistical Association 70 (351a):674–80. doi:https://doi.org/10.1080/01621459.1975.10482493.
- Genest, C., K. Ghoudi, and L.-P. Rivest. 1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 (3):543–52. doi:https://doi.org/10.1093/biomet/82.3.543.
- Gribkova, S., and O. Lopez. 2015. Non-parametric Copula estimation under bivariate censoring. Scandinavian Journal of Statistics 42 (4):925–46. doi:https://doi.org/10.1111/sjos.12144.
- Gribkova, S., O. Lopez, and P. Saint-Pierre. 2013. A simplified model for studying bivariate mortality under right-censoring. Journal of Multivariate Analysis 115:181–92. doi:https://doi.org/10.1016/j.jmva.2012.10.005.
- Gumbel, E. J. 1958. Distributions à plusieurs variables dont les marges sont données. Comptes Rendus de L’Académie Des Sciences, Paris 246 (19):2717–9.
- Gumbel, E. J. 1960. Bivariate exponential distributions. Journal of the American Statistical Association 55 (292):698–707. doi:https://doi.org/10.1080/01621459.1960.10483368.
- Habib, M., and D. Thomas. 1986. Chi-square goodness-of-fit tests for randomly censored data. The Annals of Statistics 14 (2):759–65. doi:https://doi.org/10.1214/aos/1176349953.
- Hougaard, P. 1986. Survival models for heterogeneous populations derived from stable distributions. Biometrika 73 (2):387–96. doi:https://doi.org/10.1093/biomet/73.2.387.
- Hougaard, P., B. Harvald, and N. V. Holm. 1992. Measuring the similarities between the lifetimes of adult Danish twins born between 1881–1930. Journal of the American Statistical Association 87 (417):17–24. doi:https://doi.org/10.2307/2290447.
- Huang, J. S., and S. Kotz. 1999. Modifications of the Farlie-Gumbel-Morgenstern distributions. A tough hill to climb. Metrika 49 (2):135–45. doi:https://doi.org/10.1007/s001840050030.
- Huster, W. J., R. Brookmeyer, and S. G. Self. 1989. Modelling paired survival data with covariates. Biometrics 45 (1):145–56. doi:https://doi.org/10.2307/2532041.
- Joe, H. 1993. Parametric families of multivariate distributions with given margins. Journal of Multivariate Analysis 46 (2):262–82. doi:https://doi.org/10.1006/jmva.1993.1061.
- Klein, J. P., M. Moeschberger, Y. H. Li, and S. T. Wang. 1992. Estimating random effects in the Framingham heart study. In Survival analysis: State of the art, 99–120. Dordrecht: Springer.
- Liang, K.-Y., S. G. Self, and Y.-C. Chang. 1993. Modelling marginal hazards in multivariate failure time data. Journal of the Royal Statistical Society: Series B (Methodological) 55 (2):441–53. doi:https://doi.org/10.1111/j.2517-6161.1993.tb01914.x.
- Lopez, O., and P. Saint-Pierre. 2012. Bivariate censored regression relying on a new estimator of the joint distribution function. Journal of Statistical Planning and Inference 142 (8):2440–53. doi:https://doi.org/10.1016/j.jspi.2012.02.046.
- Morgenstern, D. 1956. Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt Fur Mathematische Statistik 8:234–5.
- Neuhaus, G. 1971. On weak convergence of stochastic processes with multidimensional time parameter. The Annals of Mathematical Statistics 42 (4):1285–95. doi:https://doi.org/10.1214/aoms/1177693241.
- Oakes, D. 1994. Multivariate survival distributions. Journal of Nonparametric Statistics 3 (3–4):343–54. doi:https://doi.org/10.1080/10485259408832593.
- Pollard, D. 1984. Convergence of stochastic processes. New York: Springer-Verlag.
- Romeo, J. S., N. I. Tanaka, and A. C. Pedroso-de-Lima. 2006. Bivariate survival modeling: A Bayesian approach based on copulas. Lifetime Data Analysis 12 (2):205–22. doi:https://doi.org/10.1007/s10985-006-9001-5.
- Romeo, J. S., R. Meyer, and D. I. Gallardo. 2018. Bayesian bivariate survival analysis using the power variance function copula. Lifetime Data Analysis 24 (2):355–83. doi:https://doi.org/10.1007/s10985-017-9396-1.
- Shih, J. H., and T. A. Louis. 1995. Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51 (4):1384–99. doi:https://doi.org/10.2307/2533269.
- Stute, W. 1993. Consistent estimation under random censorship when covariables are present. Journal of Multivariate Analysis 45 (1):89–103. doi:https://doi.org/10.1006/jmva.1993.1028.
- Tsukahara, H. 2005. Semiparametric estimation in copula models. Canadian Journal of Statistics 33 (3):357–75. doi:https://doi.org/10.1002/cjs.5540330304.
- van der Vaart, A. W., and J. A. Wellner. 1996. Weak convergence and empirical processes with applications to statistics. New York: Springer.
- Wang, W., and M. T. Wells. 1997. Nonparametric estimators of the bivariate survival function under simplified censoring conditions. Biometrika 84 (4):863–80. doi:https://doi.org/10.1093/biomet/84.4.863.