Bayesian Estimation for three components mixture of some lifetime distributions

Abstract

The efforts for the current study have explored the heterogeneous population under Bayesian analysis of three components mixture of some lifetime distributions using Type I right censored data. Various types of prior distributions and loss functions have been utilized to select the suitable prior and loss function for three components of the mixture distribution. Extensive simulation studies have been conducted to highlight the properties of Bayes estimates under different loss functions. The inverse transformation method has been adopted for the simulation study. The comparison of Bayes estimates has been made on the basis of sample size, censoring rate, mixing proportions and different combinations of the parameters of the mixture distributions. For maximum likelihood estimates, the system of non-linear equations and information matrices have been evaluated through the numerical iteration process. Method of elicitation has been used in order to find the most precise values of the hyperparameters of the informative priors. Akaike information criterion and the Bayesian information criterion have also employed the for comparison of three components mixture distributions with the simple and two components mixture distributions on the basis of different lifetime data sets. The main purpose of the model selection criteria is to get more evidence for using the three components mixture. Bayesian Shrinkage estimates have also compared with the Bayesian and maximum likelihood estimates. For statistical computation R language, Mathematica, SAS and Maple Packages have been utilized. In the end, the conclusion and recommendation have been provided on the basis of the entire study.