Rayleigh Distribution Revisited Via Extension of Jeffreys Prior Information and a New Loss Function

Abstract

In this paper we present Bayes estimators of the parameter of the Rayleigh distribution, that stems from an extension of Jeffreys prior (Al-Kutubi (2005)) with a new loss function (Al-Bayyati (2002)). The performance of the proposed estimators has been compared in terms of bias and the mean squared error of the estimates based on Monte Carlo simulation study. We also derive the credible and the highest posterior density intervals for the Rayleigh parameter. We present an illustrative example to test how the Rayleigh distribution fits to a real data set.