Statistical Inference On The Change Point Of Poisson Process

Due to the change point theory is widely used in various fields,the research of the problem has become a hot branch of statistical research.As an important st ochastic process,the Poisson process is discussed by the research methods of chan ging point.It will be a method of depth study of the Poisson process.So I make a study for parameter's changing point of the process.This article is divided into four chapters.The first chapter mainly introduced academic background of the change point problem.In this part,I also summarized the domestic and foreign literature and introduced the process.The second chapter mainly studied the application of CUSUM statistics in Poi sson process parameter change point problem,I proved the following conclusions:(1)When the ?2 is known,I constructed the test statistics named Tk in this section by CUSUM statistic.On that basis,I studied the statistics inference proble m of the Poisson process parameters changing point.I get the refusal to domain.More then and,the rationality of the change point estimation is justified.(2).When the ?2 is unknown,I found out the estimates.So then,the test st atistics is set up.As the result,the rejection region is given and variably point loc ation point estimation is given.The third chapter structured the test statistic Uk that adapted to the process by the test statistic U.Under the condition,I discussed the process parameter chan ging point hypothesis testing problem.Finally,changing point position is given.