Classical and Bayesian Analyses of a Mixture of Exponential and Lomax Distributions

The exponential and the Lomax distributions are widely used in life testing experiments in mixture models. A mixture model of exponential distribution and Lomax distribution is proposed. Parameters of the proposed model are estimated using classical and Bayesian procedures under type-I right censoring. Expressions for Bayes estimators are derived assuming noninformative (uniform and Jeffreys) priors under symmetric and asymmetric loss functions. Posterior predictive distributions of a future observation are derived and predictive estimates are obtained. Extensive Monte Carlo simulations are carried out to investigate performance of the estimators in terms of sample sizes, censoring times and mixing proportions. The analysis of mixture model is carried out using a data set of lifetime of transmitter receivers. Interesting properties of estimators are observed and discussed.