Statistical Inference on the CR Extropy and DCR Extropy of Equilibrium distribution of order r

This study develops estimators for Cumulative Residual Extropy (CR Extropy) and Dynamic Cumulative Residual Extropy (DCR Extropy) of the equilibrium distribution of order $r$ of Lomax distribution under progressively Type-II censored data. Maximum likelihood and Bayesian estimators are obtained. The Bayesian estimators are evaluated based on LINEX loss functions. Non-informative and informative priors are considered for unknown parameters. By using Lindley's approximation and the Importance Sampling Methods, it is possible to approximate the closed-form expressions of the Bayesian estimators. The confidence intervals for the estimators are calculated using the normal approximation method and bootstrap algorithms. We have conducted simulation studies to evaluate how well the proposed estimators perform. Additionally, we have tested the practical utility of these estimators using a real data.