Bayesian inference on parameters and reliability characteristics for inverse Xgamma distribution under adaptive-general progressive Type-II censoring

In this article, we focus on estimating an unknown parameter in the context of the inverse Xgamma distibution (IXGD), particularly when dealing with an adaptive-general progressive Type-II censoring scheme. Our approach encompasses both point and interval estimates. For point estimation, we employ two distinct methods: the maximum likelihood method and Bayesian estimation. In the Bayesian estimation method, we leverage the Markov Chain Monte Carlo (MCMC) technique to derive estimates, considering both symmetric and asymmetric loss functions. In terms of interval estimation, we provide two types of intervals, namely, asymptotic confidence intervals (ACIs) and credible intervals. ACIs are calculated based on the observed Fisher Information, while taking into account the asymptotic normality properties of the maximum likelihood estimator (MLE) and the logtransformed MLE. To evaluate the performance of our proposed estimation techniques, we conduct an extensive simulation study. Additionally, we put the IXGD model to practical use by applying it to real-life data, thus assessing its applicability in real-world scenarios.