Inference of P(X > Y) for the Burr‐XII model under generalized progressive hybrid censored data with binomial removals

Abstract

SummaryIn this paper, we studied the estimation of based on the Burr‐XII distribution under the generalized progressive hybrid censoring scheme. This censoring scheme has become quite popular depending progressive hybrid censoring scheme cannot be applied when few failures occur before pre‐determined time . In this progressive censoring plan, amount of units withdrawn at each failure is assumed to be random and subject to the binomial distributions. Inferences of are obtained under equal shape parameters and different shape parameters, respectively. Maximum likelihood (MLE) and the Bayesian estimation methods are used. We obtain the MLEs of the parameters using Newton‐Raphson (NR) and expectation maximization (EM) methods, respectively. In the Bayesian section, Lindley's approximation and Markov Chain Monte Carlo (MCMC) method with Metropolis‐Hasting algorithm are used. Simulation studies are used to evaluate the performance of the proposed estimators and two real‐data examples are provided to exemplify the theoretical outcomes.