This article aims to estimate the parameters and stress-strength reliability \(R = P(Y < X)\) based on the generalized progressive hybrid censored data when X and Y follow independent xgamma distributions with different scale parameters. The maximum likelihood estimators and asymptotic confidence intervals for parameters and stress-strength reliability R have been obtained based on both classical and Bayesian setups. The Bayes estimators for the model parameters and stress-strength reliability R are derived under the assumption of independent gamma prior using symmetric and asymmetric loss functions. The Markov chain Monte Carlo technique is employed for Bayesian computations due to the complexity of the posterior, which lacks a closed-form expression for Bayesian estimators. We have also computed the highest probability density credible intervals for the Bayes estimators. Additionally, a simulation study is conducted to study the effectiveness of Bayes and maximum likelihood estimators using mean squared errors. In the end, a real data set has been utilized for illustrative purposes.
