COMPARISON OF ESTIMATORS OF SURVIVOR FUNCTION FOR THE EXPONENTIAL DISTRIBUTION UNDER PROGRESSIVE TYPE Ⅱ CENSORING

• Main Authors: Kuo Hui Fang, 郭惠芳
• Other Authors: 黃文典
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/79455194016098800526

碩士 === 國立成功大學 === 數學系 === 89 === Let the life times of random variables are assumed to be identically distributed and have an one-parameter exponential distribution. When the experiment is in the Type Ⅱ censoring , the survivor function can be estimated by the maximum likelihood estimator (M.L.E.) and the Bayes estimator under the conjugate prior distribution. In this study, we extend it to the progressive Type Ⅱ censoring in k-stage and find the M.L.E. and the Bayes estimator of the survivor function for non-changing failure rate and changing failure rate cases. The approximate bias, variance and mean square error (MSE) of the M.L.E. and the Bayes estimator are derived. The comparisons of the M.L.E. and the Bayes estimator are investigated based on the MSE criterion. Finally, some properties will be discussed in the article. 2.Estimators of the Survivor Function……………………………… 6 2.1 The TypeⅡ Censoring………………………………………… 6 2.2 The Progressive TypeⅡ Censoring…………………………7 2.2.1 The Two-stage Case……………………………………………7 2.2.2 The k-stage Case………………………………………………12 3.Comparison of Estimators of Survivor Function for Progressive TypeⅡ Censoring in k-stage Case………………………………………18 3.1 Non-changing failure rate…………………………………18 3.2 Changing failure rate………………………………………28 4.Discussion...……………………………………………………………36 5.Reference…………………………………………………………………38