A general class of multivariate survival models derived from frailty and copula models: application to reliability theory

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王尹辰(Yin-Chen Wang) 查詢紙本館藏

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統計研究所

論文名稱

(A general class of multivariate survival models derived from frailty and copula models: application to reliability theory)

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摘要(中)

Copula和frailty模型是在多個故障時間分佈之間建模依賴關係的兩個主要工具。本文的目的是介紹一類多變量生存模型，其中包括copula模型和frailty模型作為兩種特例。與僅容納其中一個的現有模型不同，我們所提出的模型既適用於frailty模型（描述異質性）也適用copula模型（描述相關性）。我們推導出模型的性質，包括Kendall’s tau，
分位數(quantile)和一些其他有用的統計推斷度量。作為可靠性理論的應用，我們透過工業實驗中壽命檢測(life tests)所產生的競爭風險資料(competing risks data)開發基於可能性的推理方法，其中單個元件的總壽命由多種類的故障方式決定。我們還開發了模型診斷程序。我們進行模擬以檢查所提出方法的性能。最後包含分析一個真實的數據並進行說明。

摘要(英)

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.

關鍵字(中)

★ 競爭風險
★ Copula模型
★ 脆弱模型
★ 可靠度
★ 存活分析
★ 韋伯分布

關鍵字(英)

★ Competing Risk
★ Copula
★ Frailty
★ Reliability
★ Survival Analysis
★ Weibull distribution

論文目次

摘要 i
Abstract ii
致謝詞 iii
Chapter 1: Introduction 1
Chapter 2: Review 4
2.1 Review of copulas 4
2.2 Review of frailty model 7
Chapter 3: Frailty-copula model 9
3.1 Frailty-copula model 9
3.2 The frailty-Clayton model 12
Example 1 (The gamma-Clayton model): 12
Example 2 (The lognormal-Clayton model): 15
3.3 The frailty-Gumbel model 17
Example 3 (The gamma-Gumbel model): 18
Example 4 (The lognormal-Gumbel model): 21
Example 5 (The truncated-lognormal-Gumbel model): 24
Example 6 (The folded-normal-Gumbel model): 27
3.4 The frailty-FGM model: 30
Example 7 (The gamma- FGM model): 31
Chapter 4: Competing risks in reliability theory 35
4.1 Competing risks data 36
4.2 Proposed model 36
4.3 Properties of the proposed model 37
4.4 Likelihood-based inference 39
4.5 Goodness-of-fit 45
4.6 Simulations 46
4.7 Real data analysis 50
4.7.1 The ARC-1 VHF radio data 50
4.7.2 The results of data analysis 51
4.8 AFT model 54
4.9 Likelihood inference under the AFT model 56
4.10 Simulations of the AFT model 62
4.11 Link function 64
4.11.1 The gamma-Gumbel copula model (4-2) with the link 64
4.11.2 The gamma-Gumbel copula model (4-2) with the link 66
4.11.3 The AFT model with the link 67
4.11.4 The AFT model with the link 69
4.12 Simulations of the proposed model (4-2) with link functions 71
4.13 Simulations of the AFT model with link functions 72

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指導教授

江村剛志(Takeshi Emura)

審核日期

2019-7-10

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