Statistical Analysis of the Lifetime Mixture Models Under Bayesian Approach

Abstract

This thesis deals with statistical analysis of the lifetime mixture models under Bayesian approach. Type-I right censored sampling scheme is used. Choice of distribution is made keeping in view the originality and applicability. These contain Inverse Rayleigh, Gunmbel Type-II, Frechet, Inverse Weibull and Inverted Exponential distributions. These mixtures distribution have not been explored so far in Bayesian setup. Bayes estimators for the parameters of the mixture models are derived in closed form using type-I right censoring. To conduct Bayesian analysis, informative and noninformative priors are considered while three different loss functions, Squared error loss function, Precautionary loss function and DeGroot loss function are employed. A thorough simulation study is made to scrutinize the properties of proposed Bayes estimators. For the Inverse Weibull model, when all the parameters are unknown, Bayes estimators can not be gained in closed form, thus importance sampling technique is used to get the Bayes estimate in this case. For the elicitation of hyperparametrs , we used prior predictive and prior mean method. Limiting expressions of the Bayes estimators and their corresponding posterior risks are also derived. For the Inverse Weibull distribution, Bayes estimators and the posterior risks for reliability function are also discussed. Graphical representation of the simulation analysis results are also presented for each mixture model. Applications of these mixture models are also offered by applying a real data set in each case.