Quantile-based cumulative inaccuracy measures

Numerous statistical models do not have explicitly known distribution functions. Because of this, the study of properties of the cumulative residual (past) inaccuracy measures using distribution function-based approach are difficult. Further, it is well-known that in modeling and analyzing statistical data, an equivalent alternative to distribution function is quantile function. The objective of this paper is to introduce and study quantile versions of the cumulative residual (past) inaccuracy measures and their dynamic forms. We obtain some bounds, relations with other quantile-based reliability measures, monotonicity results and characterizations. Various examples are provided to show the importance of the proposed quantile-based measures and the associated results.