Abstract
This work addresses the estimation issues of the XLindley distribution using an adaptive Type-II progressive hybrid censoring scheme. Maximum likelihood and Bayesian approaches are used to estimate the unknown parameter, reliability, and hazard rate functions. Bayesian estimators are explored under the assumption of independent gamma priors and a symmetric loss function. The approximate confidence intervals and the highest posterior density credible intervals are also computed. An extensive simulation study that takes into account various sample sizes and censoring schemes is implemented to evaluate the various estimating methods. Finally, for an explanation, two real data sets from the chemical engineering field are provided to show that the XLindley distribution is the best model compared to some competitive models for the same real data. The Bayesian paradigm utilizing the Metropolis-Hastings algorithm to generate samples from the posterior distribution is recommended to estimate any parameter of life of the XLindley distribution when data are obtained from adaptive Type-II progressively hybrid censored sample.