Analysis Of Parameter Change Point In The Generalized Exponential Distribution And Its Application

In the field of statistics, more and more statists pay attention to the research of change point. The change point refers to a position or time, in which the observed values or data follow two different models. Now change point has been widely applied in many fields such as economy, finance, medicine, hydrology and meteorology, quality control and so on. Generalized exponential distribution is a kind of life distribution, and it has great significance in the research of reliability statistics. In this paper, we study the parameter change point test, online monitoring and estimation of generalized exponential distribution, and the method proposed is applied to the practical example.Chapter one introduces the concept of change point and generalized exponential distribution, at the same time, the research results about the change point test, monitoring and estimation are given. Chapter two introduces the likelihood ratio method and CUSUM method to test the parameter change point, and the Bootstrap method is proposed for the critical value of the statistics. The results show that the method is effective and feasible. In chapter three, the CUSUM method and the square CUSUM method are proposed to monitor the shape parameter and the scale parameter change points. The null distributions of the monitoring statistics are obtained, and some critical values are tabulated. Under the alternative hypothesis, the consistency of the procedures is also proved. Simulations indicate that online monitoring has higher power than change point test. At last, the conclusion is verified by monitoring the voltage data. In chapter four, the CUSUM type estimators of the parameter change point are given, moreover, the consistency is proved and the convergence rate is derived. The results show that the larger the jump degree is, the more accurate the estimate is. Chapter five presents the conclusion and the prospect of further research.