Statistical analysis for the truncated unit exponentiated Ailamujia distribution under progressive Type–Ⅱ censoring

This study introduces and investigates the truncated unit exponentiated Ailamujia (TUEA) distribution within the framework of a progressive Type–Ⅱ censoring scheme. By incorporating truncation on the unit interval, the proposed model extends the unit exponentiated Ailamujia distribution, significantly enhancing its flexibility for modeling bounded lifetime data. We derive the fundamental mathematical properties of the TUEA model, including the probability density function, the cumulative distribution function, reliability measures, and hazard rate functions. Statistical inference for the model parameters is developed within both frequentist and Bayesian frameworks using progressive Type–Ⅱ censored data. The maximum likelihood estimates are computed through the Newton–Raphson iterative algorithm, whereas Bayesian inference is carried out under symmetric squared error and asymmetric LINEX loss functions. Point estimates and highest posterior density credible intervals are obtained via Markov chain Monte Carlo (MCMC) sampling procedures. In addition, a comprehensive Monte Carlo simulation study is conducted to investigate the finite sample performance of the new estimators in terms of bias, mean square error, and confidence interval coverage probability. In addition, the practical usefulness of the TUEA distribution is shown via an analysis of a real-life data sets, where the new model exhibits a better fit than competing models.