Bayesian inference for two populations of Lomax distribution under joint progressive Type-II censoring schemes with engineering applications

The joint progressive Type-II censoring scheme is an advantageous cost-saving strategy. In this paper, investigated classical and Bayesian methodologies for estimating the combined parameters of two distinct Lomax distributions employing the joint progressive Type-II censoring scheme. Maximum likelihood estimators have been derived, and asymptotic confidence intervals are presented. Bayesian estimates and their corresponding credible intervals are calculated, incorporating both symmetry and asymmetry loss functions through the utilization of the Markov Chain Monte Carlo (MCMC) method. The simulation aspect has employed the MCMC approximation method. Furthermore, discussed the practical application of these methods, providing illustration through the analysis of a real dataset.