Mixture of two generalized inverted exponential distributions with censored sample: properties and estimation

Abstract

Mixture models have significantly been used in survival analysis. This study considers Bayesian analysis of the two-component mixture distribution of generalized inverted exponential distributions. Also its reliability characteristics and important
distributional properties are presented. We have considered this particular distribution because it is skewed and is considered appropriate in engineering processes, when an engineer suspects a high failure rate in the beginning, but after continuous inspection, the failures go down. The Bayesian estimation of unknown parameters of the mixture of generalized inverted exponentialdistributions under type-I censoring, assuming two priors is investigated using different loss functions.It is seen that the closed-form expressions for the Bayes estimators cannot be obtained for scale parameter. The efficiencies of the proposed set of estimates of the mixture model parameters are studied through simulation. Posterior risks
are evaluated and compared to explore the effect of prior beliefs and loss functions. Simulated results and an example based on a real-life data are also given to interpret the study.