Research On Parameter Estimation Method Of Spatial Extreme Value Model Based On Dirichlet Process And Its Application In The Extreme Value Distribution

For the analysis of natural disasters in China,floods are one of several common natural disasters.At present,the occurrence of extreme weather and climate events has aroused great concern of the scientific community and society,which has an important impact on production and life.Has caused a serious loss to the economy,and it is particularly attractive because of its low frequency of loss,especially for actuaries,because the actuaries are most concerned with the tail of the loss of data accuracy.As a study of random phenomena,the extreme value theory can be traced back to the early 19th century,but until the last few decades,it began to really attract the attention of scholars,and began to model it.Extreme value theory is the first application in the field of engineering research,now has been widely used in insurance,finance and other fields.Based on the actual rainfall data of an insurance company in Beijing,the extremely rare event has the characteristics of low probability and high loss intensity.The accident will cause direct or indirect economic loss,which will seriously threaten the stable operation of the insurance company,Extreme climate has a very critical guiding role,so accurate prediction of extreme rare events is particularly important.At present,the method of forecasting extremely widely used methods is extreme value theory.However,the extreme value theory is extremely sensitive to the selection of thresholds,and is the subjective judgment used,and the previous estimates of the parameters are not related to the explicit theoretical support In this paper,we use the generalized Pareto distribution model("GPD")to establish the model by using the data of the data above the threshold,and use the maximum likelihood estimation parameters(MLE),MOM and other methods The parameters are estimated and the advantages and disadvantages are compared.Then the parameters are estimated by using the prior distribution of Bayesian theory and the posterior distribution of the Markov chain Monte Carlo(MCMC)method.The use of the Dirichlet process(The Dirichlet process referred to as:"DP")to establish the model after the test or use the mixed normal distribution model to test,the extreme value of the theoretical distribution of the method used are:super threshold peak(referred to as:POT),generalized Pareto distribution("GPD"),the paper also includes the selection of thresholds,thick tail Diagnosis,the use of GPD,MLE parameter estimation method,Bayesian prior distribution and MCMC posterior distribution,and finally through the actual example as an empirical analysis,draw conclusions.Finally,the results are for the national rainfall data,for the extreme probability theory of small probability prediction,found that the generalized Pareto distribution model more accurate and more effective.