Bayesian estimation of the parameter and the reliability characteristics of xgamma distribution using Type-II hybrid censored data

Abstract

In this article, the estimation of the parameter and reliability characteristics have been considered using hybrid Type-II censored observations where the experimental units are assumed to follow xgamma distribution, a special mixture of exponential and gamma distributions. The maximum likelihood estimate (MLE) of the parameter has been obtained using Newton–Raphson method, and the estimate of the reliability characteristics has been evaluated using invariance property of MLEs. The Bayes estimate for the same has been examined using informative prior and non-informative prior under squared error loss function. As the Bayes estimates do not assume explicit form, the Markov Chain Monte Carlo technique has been implemented to get the estimates. Further, $$95\%$$ asymptotic confidence intervals and the highest posterior density credible intervals have been constructed for the parameter. Finally, a real data set is analyzed to illustrate the proposed study.