對於刪減區間及截斷資料下，一般對於參數的估計及截斷資料之被截斷的比例是未知的，我們有興趣的是，如何由得到的刪減區間及截斷資料來估計參數及被截斷數據的比例。在這篇論文中，我們以 Turnbull 的演算法為概念，提出一個相似的演算法來估計參數，並依此估計被截斷數據的比例。我們以模擬分析的方法比較我們提出的演算法和Turnbull 的演算法，我們提出的演算法有較佳的結果。

For interval-censored and truncated failure time data, the truncation ratio is unknown. In this paper, we propose an algorithm, similar to Turnbull's, to estimate the parameters. The truncation ratio for the interval-censored and truncated failure time data can also be estimated by the convergence result of the algorithm. A simulation study is proposed to compare with Turnbull (1976). Our algorithm seems to have better result.

Contents

1. Introduction…………………………………………………………….1
2.Turnbull's algorithm ……………………………………………………3
3. Lee's selection procedure ...……………………………………………7
4. Our proposed algorithm ……………………………………………...10
4.1 The estimation of p and q in Lee's procedure …………………....10
4.2 The estimation of truncation ratio ………………………………..17
5. Simulation study ……………………………………………………..18
6. Conclusion …………………………………………………………...23
7. Reference …………………………………………………………….24

[1] Turnbull, B.W. (1976). The empirical distribution function with arbitrarily grouped censored and truncated data. Journal of the Royal Statistical Society, Series B. Vol. 38, 290-295.

[2] Lee, Chinsan (1999). Urn model in the simulation of interval censored failure time data. Statistics & Probability Letters. Vol. 45, 131-139.

[3] Sen, Ching-Fu (2001): On the consistency of a simulation procedure and the construction of a non-parametric test for interval-censored data. Master Thesis. Department of Applied Mathematics, National Sun Yat-Sen University. Kaohsiung, Taiwan.