Semi-parametric Analysis And Statistics Simulation Of Extreme Rainfall Data

Density ratio model is a kind of important semi-parametric model,which is a hot spot of statistics.The principle is that one of the sample sequences is selected as the reference sequence,and there is an exponential link between the rest of each sequence and the density of the reference sequence.All the sample sequences are linked together,and the newly generated full samples are fitted and analyzed.This method has the advantage of enlarging the sample size and increasing the precision of fitting.The traditional method of studying the differentiation of rainfall extreme value belongs to the parameter statistical method,which may not achieve good discriminant effect under the complicated real data.Therefore,this paper proposes a multi-sample semi-parametric function density ratio model based on logistic regression model,which can analyze more complex real data.The results of statistical simulation show that the estimation accuracy of the semi-parametric method is better than that of the parametric method when the population distribution is known,so the multi-dimensional semiparametric density ratio model can be used in a wider range than the traditional parameter estimation method,and the fitting effect is better.In this paper,the maximum likelihood estimation method is used to estimate the parameters of the semi-parametric density ratio model in the differentiation and fitting problem of rainfall extremum data by.Based on the daily precipitation observation data of 10 meteorological stations in Jiangsu,Zhejiang and Shanghai during 1951-2018,the annual maximum daily rainfall series was fitted and the goodness of fit was compared by K-S method.The results show that the Density Ratio Model is suitable for the fitting of rainfall extreme differentiation at different stations,and is superior to the methods commonly used in the fitting of rainfall extreme differentiation.The research results are of great significance for the analysis of the characteristics of rainfall extreme differentiation.The first chapter is the introduction,which introduces the topic of this paper,the semi-parametric density function ratio model and the research status of the statistical distribution of extreme rainfall.In the second chapter,the model is established.Under the two-sample semi-parametric density function ratio model,the multi-copy semiparametric density function ratio model is established,and the parameter estimation and goodness of fit test are carried out on the model.The third chapter is the statistical simulation,which verifies the basic hypothesis of gamma distribution,beta distribution,normal distribution,lognormal distribution and weibull distribution respectively.The fourth chapter is an example analysis.When the overall distribution is unknown,the semi-parameter density ratio model proposed in the paper and the commonly used statistical fitting model for rainfall extreme data are used to carry out statistical fitting for the real sample data.The fifth chapter is a summary of the semi-parametric density function ratio model proposed in the paper and its research prospects,and summarizes several advantages of the new method.