A residual inaccuracy measure based on the relevation transform

Inaccuracy and information measures based on the cumulative residual entropy are useful in various fields, and are attracting increasing attention in Probability Theory and Statistics. In this paper, we introduce and study an inaccuracy measure concerning the relevation transform of two nonnegative continuous random variables. We investigate various distributional properties and characterization results that are based on the mean residual lifetime and involve the generalized Pareto distribution. A connection with the proportional hazards model is also provided. We obtain comparison results involving the proposed inaccuracy measure and some existing inaccuracy measures. Some illustrative examples are finally given.