Residual and past varinaccuracy measures.

The article focuses on the introduction and study of dynamic measures of varinaccuracy—specifically residual varinaccuracy and past varinaccuracy—based on the Kerridge inaccuracy measure for absolutely continuous, non-negative random variables. These measures quantify the variability (dispersion) of inaccuracy in modeling residual and past lifetimes, extending the concept of varentropy (variance of entropy) to inaccuracy measures under truncated conditions common in reliability and life-testing experiments. The paper develops theoretical properties, including expressions for derivatives, bounds, and behavior under affine and monotone transformations, and explores their relationships under proportional hazard and proportional reversed hazard models. Applications include asymptotic distributions of residual information content and model selection in reliability analysis, illustrated with real data on bladder cancer remission times, where residual varinaccuracy aids in distinguishing models with similar residual inaccuracy but different variability.