Exact Likelihood Inference for the ExponentialDistribution base on two–stage sampling

• Main Authors: Jia-Bin Chang, 張家賓
• Other Authors: Jyh-Shyang Wu
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/41451284054409801661

碩士 === 淡江大學 === 數學學系碩士班 === 96 === In a life testing experiment, Type-I, Type-II, and Hybrid censored samples generally lead into some disadvantages, one is that it is inefficient to analyze because of the few number of failures, the other is that the cost becomes higher for a long observing time. In this paper, under the end time of sampling period censored, we propose two-stage sampling and set a criteria to determine whether to proceed to the second stage or not. Using this method, we can not only get an acceptable number of failures but also decrease the observing time to save the cost of the experiment. When the n units are put on test and the failure times are independent and identically distributed as exponential with parameter theta, we discuss the maximum likelihood estimator, the probability density function, the confidence interval of theta . We also present one sample to illustrate all the results finally.