Estimation of parameters of the 3-component mixture of Pareto distributions using type-I right censoring under Bayesian paradigm

As compared to simple probability models, a mixture model of some suitable lifetime distributions may be more capable of capturing the heterogeneity of nature. In this study, a 3-component mixture of Pareto distributions was investigated by considering the type-I right censoring scheme to obtain data from a heterogeneous population. First, considering a Bayesian structure, some mathematical properties of the 3-component mixture of Pareto distributions are discussed. These mathematical properties include Bayes estimators and posterior risks for the unknown component and proportion parameters using the uninformative (uniform and Jeffreys') and informative (gamma) priors under squared error loss and DeGroot loss functions. Then, the performance of the Bayes estimators for different sample sizes and test termination times under different loss functions were examined. In addition, limiting expressions of Bayes estimators and posterior risks are derived. Finally, the superiority of the Bayes estimators was established through a simulation study and a real life example.