Statistical Inference And Application Of Generalized Pareto Distribution

Extreme value theory is a powerful tool to deal with extreme events.As an important branch of extreme value theory,generalized Pareto distribution has an important application in the research field of extreme event early warning.Initially,scholars focused on the asymptotic property of the maximum value of random variables,the block maxima model was often used to deal with the data,but this practice will lose a lot of data,resulting in a waste of information.Therefore,in order to make more reasonable and full use of the data,scholars began to use the peaks over threshold model to deal with the data.Since the introduction of generalized Pareto distribution by Pickands,it has been widely used in economics,environmental science,meteorology and other fields,domestic and foreign scholars have made fruitful achievements in their research on it.Based on peaks-over-threshold（POT）framework,this thesis makes an in-depth study on the statistical inference of the generalized Pareto distribution,including parameter estimation,threshold selection,extreme quantile estimation,expectile estimation and practical application.In this thesis,based on the concept of least square and the existing parameter estimation methods of generalized Pareto distribution,a new parameter estimation method is proposed,which can estimate the shape parameter and scale parameter of the generalized Pareto distribution at the same time.For the data,the new method estimates the parameters by minimizing the sum of squared deviations between the theoretical distribution function and its expectation.Finally,simulation and practical application illustrate the superiority of the proposed method.The simulation results show that the proposed method has good effects on extreme quantile estimation and expectile estimation.In terms of practical application,we select the PM2.5 observations of the air pollution index in Beijing from 2017 to 2020 as the sample data,and use the proposed parameter estimation method to model and predict the data.