The Research On Change-point Problem For Generalized Pareto Distribution And Its Application

The generalized Pareto distribution(GPD) has been widely applied in the areas of the hydrometeorology, traffic accident analysis and reliability study, and has been a hot point in analysis of extremum problem.Considering the possible change of GPD parameters after one or some points, this dissertation explores the change-point problem of GPD, which has not only theoretical importance, but also extremely important practical significance.The primary work of this thesis includes the hypothesis test problem of GPD change-point, the limit theory after parameter transformation, power simulation of the test, the application of change-point method in GPD.The main work is organized as follows:Firstly, the hypothesis test problem with change-point and maximization log-likelihood ratio test statistic are presented under the two different cases for the change-point problem in GPD.Secondly, a series of limit properties is derived out and the test power simulation of maximization log-likelihood ratio test statistic is made.Considering the different situation of the shape parameter, the thesis takes advantage of appropriate parameter transformation for GPD to study the characters of the first and second order partial derivations of log-likelihood function in discontinuity point, and deduce the convergence condition of the reparameterized GPD moments in discontinuity point.In addition, the method of Taylor expansion, and other methods, are used to prove a series of limit properties of likelihood function and its estimate, and then the asymptotic distribution of the test statistic is obtained and its critical value is got by simulating.The simulation results of test power turn out that the change-point problem in GPD can be well solved by the statistic.Finally, the thesis further concerned the application problems of change-point method in GPD.We take nearly 50 years of rainfall data in Shenzhen city and the roadway occupancy rate data in Guiyang Grand Cross Lane as the research examples to analyze based on the change-point model of GPD.With regard to the former example, the 1980 s was detected that it is a node of Shenzhen climate change,before this point, the estimate of the extreme value index is negative, after this point,it is positive.Meanwhile, the degree of rainstorm disaster which below 100-year return period is much less than before, the disaster degree of above 100-year return period is more serious than before and the extreme weather phenomena is more frequent than before.According to the latter example, the study shows that the occurrence ratio of traffic congestion and other incidents in central Guiyang city are indeed decreasing since the actions of the special license-plate lottery, the limit number and the limit line are taken in 2011, theoretically support of the positive effect from these measures is gained.The above empirical results indicate that the model which bases on the method of GPD change-point is able to do many things such as acquiring the inherent law from practical problems, evaluating and analysing reasonably for the effect from the relevant policies, while conventional GPD model cannot, and then the former has more practical interest.