Statistical Inference For Generating Generalized Pareto Distribution

The Generalized Pareto Distribution(GPD)is a generalization of the Pareto Distribution(PD).It describes the actual data effectively because it is a skewed distribution.For example,modelling for rainfall depths and estimation of the size of the maximum inclusion in clean steels,so it plays an important role in economics,socialogy,environmental science and actuaries.The statistical inferences of GPD are studied by domestic and foreign scholars.However,the GPD doesn't fit some actual data well sometimes,so we get the Generating Generalized Pareto Distribution(GGPD)by adding two shape parameters,and study the properties and statistical inference of the GGPD.This thesis constructs the GGPD by the quantile function of GPD.Making use of the relationship of the GGPD and Beta Distribution and properties of Beta Function,we caculate the cumulative distribution function,probability density function,expectation,variance,skewness and kurtosis of GGPD.Specially,when a = 2,we estimate the parameters by Method of Moment(MOM),Probability Weighted Moment(PWM),L-Moment(LM)and Maximum Likelihood Estimation(MLE).And the Monte Carlo simulation results show that for different b,the effects of the parameter estimation methods for ?,? and k are different,but for b,MLE is much better than other methods.Totally,while the sample number increases,the effects of all parameter estimation methods are better.