Analysis of progressive type-II censored gamma distribution

The aim of this study is to describe the both frequentist and Bayesian parametric estimation methods for the gamma distribution using progressive Type II censoring data. We first take into account, maximum likelihood method and its competitive method, known as the maximum product of spacing method for estimation of parameters of the model. In addition, approximate confidence intervals based on asymptotic theory have been considered for both the methods. Further, based on flexible gamma priors for the shape and scale parameters, Bayes estimators under the assumption of squared error loss function are obtained using likelihood and maximum product of spacing functions, and also the associated highest posterior density credible intervals of the parameters are obtained. Monte-Carlo simulations are carried out to examine the performance of the proposed estimates using various criteria. We further present an optimal progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, to show the applicability of the proposed methodologies in a real-life situation, one engineering data set and a clinical data set are investigated. The numerical results confirm that our proposed methods work satisfactorily.