Bayes Estimation Of Exponential Distribution With Change Points For Left Truncated And Right Censored Data

In recent decades, the changing point problem has become a hot spot in the research of the statistic direction, theoretical researches and practical applications have developed rapidly. There have been a lot of research achievements about theoretical researches and practical applications of changing point problem both at home and abroad. Many researchers’ studies of change point problems have a great influence, such as Csorgo, Horvath, Haccon, Daniel and George e.p.box, Zhang Piyuan, li-hua xiong,etc.As statisticians made more effort and paid more attention to the problem, the statistical methods got constant innovation and development. There have been some better methods to deal with change point problem, such as, least squares method, partial comparison method, nonparameters method, Bayes method, maximum likelihood method, etc. Bayes method means inferring basing on the over all sample and a priori information, and then the posterior distribution is derived through the priori information.The Bayes statistics is developing very fast. More and more professional meetings about Bayes statistics appear. The Bayes statistics school has gradually become a very influential one. The Bayes method permeates various fields of mathematical statistics,influences everyone learning statistics to make everybody know of the Bayes method.Therefore the Bayes method obtained increasingly extensive application in practice. In addition, Markov Chain Monte Carlo(MCMC) method of the Bayes simplified the operational process and made the complex experiment of changing point problem convenient and feasible.This main research contents of this paper:Firstly, the status quo of changing point problem is analyzed, three common research methods of changing point problem and related knowledge about Bayes statistics are introduced in detail; Secondly, left truncated and right censored model is established and the left truncated and right censored data is deduced under the exponential distribution of the likelihood function. And then a method of completion data is adopted to make the incomplete data convert to complete data. Fisher information matrix is used to determine the parameters of have no a priori information,and the theory of Bayes is adopted to estimate derived left truncated and right censoreddata under exponential distribution change some parameters of the conditional distribution. Finally, with the help of R software, the author undertook simulation analysis of single point and diverse parameters respectively and verified the effectiveness of using MCMC method combined with the Metropolis-Hastings algorithm to deal with the truncated data.