Optimal plan and statistical inference for the inverse Nakagami-m distribution based on unified progressive hybrid censored data

The present paper studies parametric inference for the inverse Nakagami-m distribution under a unified progressive hybrid censored sample. Maximum likelihood estimates of the unknown parameters are obtained using the Newton-Raphson method and the expectation-maximization algorithm. Approximate confidence intervals for the parameters are constructed via the variance-covariance matrix. Furthermore, Bayes estimates are investigated under the squared error and LINEX loss functions using gamma prior distributions for the unknown parameters. The Markov chain Monte Carlo approximation approach is employed to obtain the Bayes estimates and derive the highest posterior density credible intervals. The issue of hyperparameter selection is also discussed. In addition to Bayes estimates, maximum a posteriori estimates of the unknown parameters are computed using the Newton-Raphson method. The efficacy of the proposed approach is assessed through a Monte Carlo simulation study. The convergence of the MCMC sample is evaluated using various diagnostic plots. Three optimality criteria are presented to select the most suitable progressive scheme from different sampling plans. Two real-world applications that involve the fracture toughness of silicon nitride ($\text{Si}_3\text{N}_4$) and the active repair times (in hours) for an airborne communication transceiver are used to illustrate the practical utility of the proposed methodology.