Bayesian Estimation of Power Transmuted Inverse Rayleigh Distribution

Abstract

In this article, Bayesian estimators of the population parameters of the power transmuted inverse Rayleigh (PTIR) distribution are discussed. The posteriors distribution of the PTIR distribution based on informative and non-informative priors represented by gamma and Jeffery’s priors, respectively, are derived. Four loss functions, namely minimum expected, squared error, precautionary and linear exponential are considered. The highest posterior density credible interval is constructed by using the Markov Chain Monte Carlo (MCMC) method. Simulation study is performed to examine and compare the Bayes estimates using MCMC method based on Random Walk Metropolis-Hastings (RWMH) sampling algorithms. The results of the study show that the Bayes estimates under minimum expected loss function in case of non-informative prior are preferable than the other estimates in approximately most of the situations. While, the Bayes estimates under squared error loss function in case of informative prior are superior to the other estimates in approximately most of the situations.