| Summary: | 碩士 === 國立中央大學 === 統計研究所 === 107 === Copulas and frailty models are two major tools for modeling dependence among multiple failure time distributions. The objective of this thesis is to introduce a general class of multivariate survival models that includes copula models and frailty models as special cases. The resultant model accommodates both frailty (for heterogeneity) and a copula (for dependence), unlike the existing models that accommodate only one of them. We derive properties of the models, including Kendall’s tau, quantile, and some other useful measures for statistical inference. As an application to reliability theory, we develop likelihood-based inference methods based on competing risks data arising from industrial life tests, where multiple types of failure determine the total lifespan of a unit. We also develop a model-diagnostic procedure and an accelerated failure time (AFT) model. We conduct simulations to examine the performance of the proposed methods. We analyze a real dataset for illustration.
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