Statistical Inference Of Type Ⅱ Progressive Censored Data Based On Weibull Distribution

With the rapid development of science and technology, and the accelerated pace of life. Human life science research are increasingly concerned about the production of the product life and reliability.Reliability of life and survival analysis is the core content areas of research needed a large number of scholars to explore in depth the long-term scientific research. Therefore, in order to analyze the life and reliability of a product, you need a lot of tests in life and reliability testing for different research purposes, you can get the progressively type I censored data and the progressively typeⅡ censored data. In General, the distribution of censored data is unknown, and probably is not continuous, but the complexity of discrete data is not conducive to effective research.Therefore, we study the problem of statistical inference for the progressively typeⅡ censored data of two parameters Weibull distribution. The basic contents of statistical inference including parameter estimator and hypothesis testing.Firstly, the censored data model and the joint density function for the progressively typeⅡ censored data of two parameters Weibull distribution is gave out.Secondly, the maximum likelihood estimator is solved that the unknown parameters for the censored data model. However, because of the complexity of the model so that the analytically expressions of maximum likelihood estimator can not be given for a parameter, but we can analyze the existence and uniqueness. Thirdly, we try to research the precise distribution, density function of parameter estimator and interval estimator(or confidence interval) of the parameter, and using Matlab draw the figures of the distribution function and density function, and construct the confidence interval by the methods of Monte Carlo simulation. Finally, the hypothesis testing of parameter for the censored data model,and gives the power function and coverage probability, and using Monte Carlo simulation compare the likelihood ratio testing and the simple hypothesis testing.