我們提出了基於 copula 的馬可夫模型的估計問題，因為在實踐中，連續數據通常具有相關性結構。在這個項目中，我們研究了 survival-Gumbel copula，其邊際分佈是韋伯分佈。我們獲得似然函數以及最大似然估計量。另外，為了解決區間估計，我們用三個觀察 Fisher 信息矩陣估計標準誤差。在模擬研究中，通過覆蓋概率比較三種方法哪一種更適合所提出的模型。最後，在實證研究中，分析了從 2005/1/1 到 2017/1/1 的每日收盤價 VIX 及在西班牙醫院開展手術的結直腸癌患者進行說明。特別是，我們研究了 VIX 數據的兩個邊際分佈，即韋伯分佈和指數分佈。

We propose the estimation problem for a copula-based Markov model since in practice, serially data often has the dependent structure. In this project, we study the survival-Gumbel copula with the marginal distribution being the Weibull distribution. The likelihood function and the maximum likelihood estimators (MLEs) are obtained. In addition, in order to solve the interval estimation, we estimate the standard errors (SEs) with the three observed Fisher information matrices. The comparison of the three methods for investigating which one is more suitable for the proposed model in terms of the coverage probability through the simulation study. Finally, in the empirical study, the daily close VIX from 2005/1/1 to 2017/1/1 and the patients with colorectal cancer who have operations in a hospital in Spain are analyzed for illustration. In particular, we study two marginal distributions for the data, which are the Weibull distribution and the exponential distribution.

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