Objective Bayesian Estimators for the Right Censored Rayleigh Distribution

Evaluating the Al-Bayyati Loss Function

Abstract

The Rayleigh distribution, serving as a special case of the Weibull distribution, is known to have wide applications in survival analysis, reliability theory and communication engineering. In this paper, Bayesian estimators (including shrinkage estimators) of the unknown parameter of the censored Rayleigh distribution are derived using the Al-Bayyati loss function, whilst simultaneously considering different objective prior distributions. Comparisons are made between the proposed estimators by calculating the risk functions using simulation studies and an illustrative example.