Statistical Inference Of Generalized Pareto Distribution Under Random Censorship

Censorship often occurs in reliability analysis and life test.The most common Censorship occasion is random censorship.The Generalized Pareto distribution model is a very common model.GPD has a wide range of applications in the fields of finance,insurance and meteorology.This paper mainly study the maximum likelihood estimation,Bayes estimation and empirical Bayes estimation of the generalized Pareto distribution parameters under random censorship.Firstly,under random censorship,the value of expected test time for data to obey generalized Pareto distribution in life test is calculated.The reliability function,the risk function and maximum likelihood estimation of the model is studied.It is found that the exact expression of the parameter estimation is not easy to be obtained.So Newton-Raphson calculation is used.The approximate solution of the parameter is obtained by Newton-Raphson algorithm,and the related properties of the MLE are proved.The ideal numerical simulation results are obtained.Secondly,under random censorship,the Bayesian estimation of the generalized Pareto distribution is discussed.Because the result is a complex integral form and it can not be solved directly,the approximate solution of the estimation is obtained by the Lindley approximation,and compared with the maximum likelihood estimation.The result shows that the estimation are close.The Bayesian estimation is better,Since Bayesian estimation are more stable.Finally,in the case of the unknown censored distribution and the prior distribution,the empirical Bayesian estimation of the generalized Pareto distribution under random censorship is obtained by constructing the product limit estimation and the kernel density estimation.The asymptotic normality of the estimation is proved under certain conditions by the control convergence theorem.