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Abstract
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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.
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