Bayesian inference using record values from Rayleigh model with application

Abstract

In this article, based on a set of upper record values from a Rayleigh distribution, Bayesian and non-Bayesian approaches have been used to obtain the estimators of the parameter, and some lifetime parameters such as the reliability and hazard functions. Bayes estimators have been developed under symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. These estimators are derived using the informative and non-informative prior distributions for σ. We compare the performance of the presented Bayes estimators with known, non-Bayesian, estimators such as the maximum likelihood (ML) and the best linear unbiased (BLU) estimators. We show that Bayes estimators under the asymmetric loss functions are superior to both the ML and BLU estimators. The highest posterior density (HPD) intervals for the Rayleigh parameter and its reliability and hazard functions are presented. Also, Bayesian prediction intervals of the future record values are obtained and discussed. Finally, practical examples using real record values are given to illustrate the application of the results.