Residual Inaccuracy Extropy and its properties

Abstract In this paper, we introduce a novel concept of a dynamic residual inaccuracy measure based on extropy. We extend the traditional residual inaccuracy measure to its dynamic version, which allows us to measure the discrepancy between two residual life distributions. We study the properties of the proposed measure, including its discrimination principle and the proportional hazard rate model. We also investigate a characterization problem related to the extropy inaccuracy measure and propose some alternative expressions of the dynamic residual measure of inaccuracy. Furthermore, we establish upper and lower bounds and some inequalities concerning dynamic residual inaccuracy measures based on extropy. We demonstrate that the defined measure of inaccuracy is invariant under scale but not under location transformation. The given findings have important implications for statistical inference, estimation, and modeling. The proposed extropy-based dynamic residual inaccuracy measure provides a powerful tool for quantifying the discrepancy between two residual life distributions over time. At the end of the paper, we provide two non-parametric estimators for the proposed extropy measure of inaccuracy for both the non-censored (complete sample) and the right-censored scheme. The performances of these estimators are compared numerically based on their bias and MSE.