The Statistical Inference Of Generating Generalized Extreme Value Distribution

Generalized Extreme Value Distribution has a wide range of applications,including e-conomics,finance,environmental science,and engineering mechanics.Although the research results on GEVD have been perfected,the various estimation effects of the three-parameter GEVD are generally limited by the shape parameter k of the distribution(actually should be the tail finger),and the estimation effect is not satisfactory.In this paper,we generalize the GEVD by introducing two shape parameters,a and b,to describe the characteristics of the left and right tail of the distribution respectively.The generalized distribution can obtain a larger range of applications.This generalized five-parameter distribution is called Generating Generalized Extreme Value Distribution(GGEVD).In this thesis we mainly studied the properties of GGEVD and parameter estimation prob-lems.The thesis mainly consists of four parts.The first part introduces the research background,significance and research status of GGEVD.The second part:It gives the definition of GGEVD,probability density function,etc.,as well as the basic properties of the distribution,expectation,variance,kurtosis coefficient and skewness coefficient,etc.The third part estimates the param-eters of GGEVD for b = 1,? = 0,gives the moment estimation and proves the asymptotic normality of the estimation;Maximum Likelihood Estimation and Proof of Asymptotic Nor-mality of the Estimates.Several estimation methods such as probabilistic weighted moments,L moments,and quantile estimations are given.The fourth part carries on the numerical simulation to the estimation method and makes the comparative analysis to the simulation result.