Bayesian estimation of the parameter and reliability of a Rayleigh distribution using records

Abstract

In this paper we obtain Bayes estimators for the unknown parameter of a Rayleigh distribution based on upper record values. Bayes estimators are obtained under symmetric and asymmetric loss functions using a conjugate family of priors. The performance of the estimators is assessed on the basis of their relative risk under the two loss functions. A numerical study illustrates the results. We also estimate the reliability function using an asymmetric loss function and compare its performance to the symmetric loss function based on a Monte Carlo simulation study. A real life data set is used for illustrative purposes.