Tests For A Change Point Of Gamma Distribution And Its Analysis

Change point problems have been hot topics in statistics since the70’s. They have originally arisen in the context of meteorological and quality control. Also, they occur in many natural and social fields such as economic, finance, computer science and so on. In this thesis, we discuss mainly the statistical inference of change point problems in F distribution.Former research focused on change point problems in mean and variance mostly, where the mean and variance are independent parameters. However, the mean and variance of T distribution depend on common v and A simultaneously. In the second chapter, we discuss the moment of T and Tl, which are statistics we put forward to give preliminary analysis. Then the procedures about detection and estimation of v change point are proposed by maximum likelihood method. Critical values of Tl are displayed by table. At the same time, we present critical region and power function. In the third chapter, hypothesis test and estimation about parameter A are considered. When change point exists, point estimation and interval estimation are presented by local comparison method. Also, we discuss more than one change point condition and procedures are also presented. Lastly, simulations results point that sensitivity of model has a strong relationship about the choose of window and sample size.As a practical application of change point problem, in the fourth chapter we research the successive rises and falls of Shanghai stock returns by change point analysis methods in F distribution. Based on the example of Shanghai stock index returns, the following result is gained:The distributions of the successive rises and falls of returns are fitted with Gamma distribution well in period "T+0","T+I","rise and stop"," reduce state stake in listed companies".