Statistical Inference Of Generalized Pareto Distribution And Its Application

Extreme value theory is an important tool for extreme event analysis and prediction,which mainly includes block maxima model and peaks over threshold model.In the study of extreme events,at first,only the maximum data is considered and the block maxima model is used for analysis,but this data selection method may cause a lot of losses.In order to make full use of the extreme information in the data,scholars turn to the modeling and statistical inference of peaks over threshold data.Under certain conditions,the peaks over threshold data approximately follows the generalized Pareto distribution,which is the research focus of extreme value theory nowadays.In recent years,the generalized Pareto distribution has been widely used in traffic accident prediction,insurance compensation prediction,financial risk management and other fields.Since Pickands introduced the generalized Pareto distribution in 1975,many scholars have done a lot of research on it and achieved results.In this thesis,based on the peaks over threshold theory,we study the statistical inference of the two-parameter generalized Pareto distribution,including parameter estimation,extreme quantile estimation,threshold selection and practical application.In this thesis,we first introduce the research background and current situation of extreme value theory and the generalized Pareto distribution,and then describe the definition and properties of the generalized Pareto distribution.Then,five existing parameter estimation methods of the generalized Pareto distribution are introduced,and a new parameter estimation method-partial probability weighted moments method is proposed on the basis of probability weighted moments,which uses the proportion of data less than or equal to threshold,makes full use of data information and is more suitable for peaks over threshold model.Finally,numerical simulation and practical application are carried out to compare the estimation effects of different methods.The data used in the empirical study are observations of the daily return of the Dow Jones Industrial Average from 2019 to 2021.The simulation and application results show that the partial probability weighted moments method proposed in this thesis has high estimation accuracy in parameter estimation and extreme quantile estimation.