Bayesian and non-Bayesian analysis of the novel unit inverse exponentiated Lomax distribution using progressive censoring schemes with optimal scheme and data application

This article presents a novel unit distribution called the unit inverse exponentiated Lomax distribution. Some of its key characteristics are carefully examined. The distribution parameters are estimated using both traditional and Bayesian approaches, taking into account the progressive Type II censoring schemes. Using the symmetric loss function and the Markov chain Monte Carlo technique, the Bayesian methodology is investigated to determine the point and credible interval estimates of parameters. In order to select the best progressive censoring scheme, a number of optimization criteria are taken into consideration. According to the selected criteria measures, the simulations showed that the Bayesian estimates outperform the maximum likelihood estimates in terms of accuracy, indicating better parameter estimation precision. Additionally, most coverage probabilities were high, at about 95%. The novel unit distribution flexibility is validated using a three-real data set from different domains.