Statistical Inference On Stress-Strength From Generalized Pareto Distribution

It was in 1975 that the Generalized Pareto distribution was first put forward by Pickends, which could be applied in many fields, including Research on Relia-bility, Financial Risk Measurement, Earthquake Prediction, etc. Not until in 2003 kotz provided a way to comprehensive treatment of stress strength model could the Theory of Stress Strength Model based on the concept of stress strength parameters proposed by Harris get extensive application in kinds of fields. The paper is about to study the statistical inference in Stress-Strength II Parameter and III Parameter of the Generalized Pareto distribution.In this paper, the stress intensity two-parameter of the generalized Pareto dis-tribution refers to the strength random variables X and the stress random variables Y are the generalized Pareto distribution parameters, where the position parameters are known, the scale parameters are same and the shapes parameters are different. Firstly, derive the stress intensity two-parameter expression of the generalized Pare-to distribution and estimate the strength parameters with the most commonly used maximum likelihood method from frequency angle. Since the maximum likelihood estimation is a rough mathematical expectation, which cannot reflect the accuracy of parameters estimation, this paper will further study several confidence interval-s of the stress strength parameters in the large and small sample test. Secondly, describe the estimation superiority of the stress intensity parameters from the dif-ferent perspective such as the consistency of the stress intensity two-parameter of the generalized Pareto distribution, the unbiased estimation and the uniformly min-imum variance unbiased estimator. Then, conclude the strength parameters Stress Bayesian estimation from the Bayesian research perspective. Finally, compare the results with Monte Carlo simulation and give analysis with different methods.In this paper, the stress intensity three-parameter of the generalized Pareto dis-tribution refers to the strength random variables X and the stress random variables Y are the generalized Pareto distribution parameters, where the position parameters are known, the scale parameters are same and the shapes parameters are different. We will use the similar method to research the statistical inference of the stress intensity two-parameter of the generalized Pareto distribution. Firstly, conclude the stress intensity parameters expressions, the improved maximum likelihood estima-tion, the asymptotic distributions and confidence intervals. Then, get the strength parameters Stress Bayesian estimation and finally compare the results with the Monte Carlo simulation and give analysis.