An extension of weighted generalized cumulative past measure of information

In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative function. Our results include linear transformations, stochastic ordering, bounds and aging classes properties and some relationships with other survival concepts. We also define the conditional weighted generalized cumulative entropy and weighted generalized cumulative Kerridge inaccuracy measure. For these concepts, we obtain some properties and characterization results under suitable assumptions. Finally, we propose an estimator of this shift-dependent measure using empirical approach. In addition, we study large sample properties of this estimator.