Generalized cumulative residual entropy has been shown an alternative uncertainty measure to cumulative residual entropy in the literature. We find its applications in the theory of communication, actuarial and computer science. In this chapter, we consider a shift-dependent version of the generalized cumulative residual entropy for the k-th upper record and its dynamic version. The advantage of the proposed measure over the existing measure is discussed. Various results including some useful properties, effect of affine transformations, bounds, stochastic ordering and aging properties are obtained. In addition, inequalities based on the proportional hazard rate model are derived. Further, we obtain some characterization results for various probability models based on the proposed information measure. A nonparametric estimator of the proposed measure is provided and then, its asymptotic normality is established. © 2019, Springer International Publishing AG, part of Springer Nature.