Admissibility of lifetime performance index with respect to weighted squared-error loss function in Pareto distribution under progressive type II right censored sample

In this paper، under the assumption of Pareto distribution، construct a maximum likelihood estimator، UMVUE and also، assuming the Exponential prior distribution and weighted squared-error loss function، this study construct Bayes and Empirical Bayes estimator of C_L based on the progressive type II right censored sample. An admissible estimator of C_L is given for Pareto distribution with respect to the weighted squared-error loss function. The MLE and Bayes estimator of C_L is then utilize to develop a confidence and credible interval. Moreover، we also propose a likelihood Ratio Tests and a Bayesian Test to assess the lifetime performance index. Finally، we give one example to illustrate the use of testing procedure under given significance level.