Block adaptive progressive type-II censored sampling for the inverted exponentiated Pareto distribution: parameter inference and reliability assessment

This article explores the estimation of unknown parameters and reliability characteristics under the assumption that the lifetimes of the testing units follow an Inverted Exponentiated Pareto (IEP) distribution. Here, both point and interval estimates are calculated by employing the classical maximum likelihood method, a pivotal estimation method and a hierarchical Bayesian estimation method. Also, existence and uniqueness of the maximum likelihood estimates are verified. Further, asymptotic confidence intervals are derived by using the asymptotic normality property of the maximum likelihood estimator. Moreover, generalized confidence intervals are obtained by utilizing the pivotal quantities. Also, the 95% highest posterior density (HPD) intervals are constructed based on a Markov chain Monte Carlo (MCMC) algorithm within the Bayesian estimation context. Additionally, some mathematical developments of the IEP distribution are discussed based on the concept of order statistics. Furthermore, all the estimations are performed on the basis of the block censoring procedure, where an adaptive progressive Type-II censoring is employed to every block. In this regard, the performances of the three estimation methods, namely, maximum likelihood estimation, pivotal estimation and the hierarchical Bayesian estimation are evaluated and compared through a simulation study. Finally, a real data is illustrated to demonstrate the flexibility of the proposed IEP model.