This article investigates the concept of a past inaccuracy measure and its dynamic version. The properties of this measure are studied and the discrimination principle is applied to obtain the proportional reversed hazard rate (PRHR) model. Under the assumption that the reference distribution and true distribution satisfy the PRHR model, it has been shown that the proposed measure determines the lifetime distribution uniquely. Furthermore, the provided measure of inaccuracy is demonstrated to be invariant on scale transformation but not on location transformation. We propose some alternative expressions of the dynamic past measure of inaccuracy. A study is conducted on a characterization problem for the suggested extropy inaccuracy measure. Additionally, several inequalities and upper and lower bounds for the extropy-based dynamic past inaccuracy measure are established. Moreover, a simulation study is used to evaluate the performance of kernel-based non parametric estimators for the suggested measure. Finally, an application for model selection based on the proposed measure is provided.
