On Estimation of Burr Type III Model Using Improved Adaptive Progressive Censoring with Application to Engineering Data

ABSTRACT This article considers the estimation of the model parameters of the Burr III distribution (BIIID) when an improved adaptive progressive Type‐II censored sample is available. Based on the frequentist approach, the process of evaluating the model parameters is carried out using the maximum likelihood (ML) and the maximum product of spacing (MPOS) methods. The adequate condition for the existence and uniqueness (EaU) of the MLE is discussed. Moreover, the Metropolis–Hasting technique is provided to evaluate the Bayes estimates (BEs) since the joint posterior distribution has a difficult shape. The approximate confidence intervals (ACIs) and the Bayesian credible intervals (BCIs) are created using the Fisher matrix and Markov chain Monte Carlo (MCMC) method, respectively. Different proposed strategies are compared by Monte Carlo simulation. An engineering application of the acquired results is presented using the sewer invert trap (SIT) data.