Bayes Statistical Inference Of The Generalized Pareto Distribution

The generalized pareto distribution is extensively used in the field of finance、insurance etc. Statistical inference for this distribution has become a hot topic of many scholars. Currently Bayesian statistical inference theory is research tool of every discipline. Bayes statistical inference for two parameter generalized pareto distribution is studied in this paper.This paper is divided into three parts. The differences and connections of classical statistical methods and Bayes statistical methods in theory and practice are introduced in the first part, and introduced Bayes statistical methods and parameter estimation methods, give with some common definition and inequality of the article.The main parts of the paper are second parts and third parts. Under MLinex loss function, the two parameters generalized pareto distribution is discussed in the second part about the following content.1. Application of Bayes theory to obtain the posterior distribution of parameter, when prior distribution is inverted Gamma distribution, the two parameters generalized pareto distribution. And then Bayes estimated is obtained by using the posterior distribution of parameter, and this Bayes estimate proved Admissibility.2. According to Bayes estimation of the parameter, Bayes confidence interval lover and maximum a posteriori estimation can be obtained in the confidence level of-1?.And to verify Jeffers no prior distribution for the prior distribution, Bayes estimation of the parameter also its Minimax estimation.The purpose of the third part is study the empirical Bayes one-side test problem for the parameter of Generalized Pareto distribution, it based on the independent and identically distributed samples. The empirical Bayes one-side test rule for the parameter of Generalized Pareto distribution are constructed by using the kernel estimation in this paper. The asymptotically optimal property for the propose EB and convergence rate for the propose EB test rule are obtained under certain conditions.