Statistical inference of the Birnbaum-Saunders model using adaptive progressively hybrid censored data and its applications

Lately, the Birnbaum-Saunders distribution has gained a lot of attention, mainly due to its different density shapes and the non-monotonicity property of its failure rates. This work considered some estimation issues for the Birnbaum-Saunders distribution using adaptive progressive Type-Ⅱ hybrid censoring. Point and interval estimations were performed employing both conventional and Bayesian methodologies. In addition to estimating the model parameters, we obtained point and interval estimates for the reliability and hazard rate functions. We looked at the method of maximum likelihood as a classical approach, and its asymptotic traits were employed to obtain approximate confidence ranges. From a Bayesian point of perspective, we considered the squared error loss function to obtain the point estimates of the various parameters. The Bayes and highest posterior density credible intervals were additionally determined. For the complex form of the posterior distribution, Bayes estimates and credible intervals were computed by sampling from the posterior distribution through the Markov chain Monte Carlo procedure. For assessing the performance of all of these estimators, a Monte Carlo simulation was employed. Several statistical standards were applied to check the effectiveness of various estimates for multiple levels of censoring with small, moderate, and large sample sizes. Finally, two scenarios for applications were given in order to highlight the usefulness of the supplied approaches.