Abstract
Rayleigh model is especially suitable for the life-testing of the products that age with time. In this paper, the Bayesian Predictive Intervals of the two component mixture of the Rayleigh distribution using some standard informative conjugate priors. The possible conjugate priors include the Inverted Chi, the Inverted Rayleigh and the Square Root Inverted Gamma priors. The Bayesian predictive intervals are evaluated for different choices of the values of the hyper-parameters. The motivation is to explore the most appropriate prior for the Rayleigh mixture among these. A mixture data is simulated and the censored sampling is assumed to be employed. The comparison of the capacity of the said conjugate priors is made to produce precise estimates. The trends for the changes in the lower limits, upper limits and the lengths of the predictive intervals of a future observation in terms of the hyper-parameters of each prior distributions are reported. The expressions for the Bayes estimates and their variances using the different informative conjugate priors are also given. A comparison of the Bayes estimates and their variances using the most suitable Informative prior (the Square Root Inverted Gamma distribution) and the Uninformative prior (the uniform distribution), is also presented. Adding objectivity to the subjective prior information is discussed in the light of the trend observed in the scatter of the predictive distribution in terms of corresponding hyper-parameters.