E-Bayesian Estimation of Rayleigh Distribution and Its Evaluation Standards: E-posterior Risks and E-MSEs under Progressive Type-II Censoring

Abstract

The present study considers the problem of estimating the scale parameter, reliability function, and hazard function of Rayleigh distribution using the E-Bayesian estimation approach when progressively Type-II censored data are available. The evaluation standards of these estimates are accessed through the definition of E-posterior risk (expected posterior risk) and E-MSE (expected mean square error). These estimations are carried out using conjugate prior distributions of the unknown parameters under four different loss functions i.e. quadratic, weighted squared error, Degroot, and entropy loss functions. Further, we perform Monte Carlo simulations to compare the performances of these proposed methods and use a real dataset for illustration purposes.