Evaluation of two inverted Nadarajah–Haghighi production lines via joint progressive type-II censoring with two physical applications

This study enables the simultaneous estimations of the unknown parameters of two inverted Nadarajah–Haghighi populations. The estimations are conducted using data collected from joint progressively type-II censored samples from the populations of interest. The estimations are based on the assumption that the parameters of the two populations are unknown and unequal. To achieve this, we use classical and Bayesian estimation methods to obtain point and interval estimates for the various unknown parameters. The maximum likelihood and approximate interval estimates are derived from the classical perspective. From the Bayesian perspective, both Bayes estimates and credible intervals are acquired using gamma prior distributions. The Bayes estimates are calculated using squared error loss and by sampling from the posterior distribution through the Markov chain Monte Carlo procedure. All point and interval estimates are validated through a simulation study. In addition, two physical applications are provided to demonstrate the practical significance of the methodologies employed.