Bayesian Analysis of a 3-Component Mixture of Rayleigh Distributions under Type-I Right Censoring Scheme

Abstract

Since the last few decades, constructing flexible parametric classes of probability distributions has been the most popular approach in the Bayesian analysis. As compared to simple probability models, a mixture model of some suitable lifetime distributions may be more capable of capturing the heterogeneity of the nature. In this study, a 3- component mixture of Rayleigh distributions is investigated by considering type-I right censoring scheme to obtain data from a heterogeneous population. The closed form expressions for the Bayes estimators and posterior risks assuming the non-informative (uniform and Jeffreys’) priors under squared error loss function, precautionary loss function and DeGroot loss function are derived. The performance of the Bayes estimators for different sample sizes, test termination times and parametric values under different loss functions is investigated. The posterior predictive distribution for a future observation and the Bayesian predictive interval are constructed. In addition, the limiting expressions for the Bayes estimators and posterior risks are derived. Simulated data sets are used for the different comparisons and the model is finally illustrated using the real data.

Keywords

• 3-Component mixture model; Loss function; Posterior risk; Predictive interval; Test termination time.