Bayes Shrinkage Estimation of the Parameter of Rayleigh Distribution for Progressive Type-II Censored Data

Abstract

This paper derives Bayes shrinkage estimator of Rayleigh parameter and its associated risk based on conjugate prior under the assumption of general entropy loss function for progressive type-II censored data. Risk function of maximum likelihood estimate, Bayes estimate and Bayes shrinkage estimate have also been derived and compared. A procedure has been suggested to include a guess value in case of the Bayes shrinkage estimation. Risk function of empirical Bayes estimate and empirical Bayes shrinkage estimate have also been derived and compared. In conclusion, an illustrative example is presented to assess how the Rayleigh distribution fits a real data set.