Comprehensive Investigation of Statistical Inference and Predictive Analysis for Joint Type-II Censored Data From Two Poisson-Exponential Populations

This paper presents a comprehensive investigation of statistical inference and predictive analysis for two Poisson-exponential distributions using a joint type-II censored sample. The Poisson-exponential distribution is widely used in reliability and survival analysis where failure times follow an exponential distribution within each groups. Parameter estimation is performed using the expectation-maximization algorithm, with approximate confidence intervals derived from the observed Fisher information matrix. Bayesian estimators are obtained via importance sampling under squared error, linear-exponential, and generalized entropy loss functions, along with corresponding credible intervals. A shrinkage pretest estimator combining Bayesian and maximum likelihood approaches is also proposed. The paper provides the best unbiased and Bayesian predictors for future failure times based on the observed joint type-II censored data, including point and interval predictions. Extensive simulations across various sample sizes evaluate the proposed methods, and their practical application is illustrated using two real datasets.