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On Weighted Measures of Cumulative Entropy
Motivated by the work of Di Crescenzo and Longobardi (2006), in this paper, we consider a shift-dependent information measure. We call it weighted cumulative entropy. Few basic properties including the effect of linear transformations, stochastic orders, bounds and inequalities are studied. Normalized version is proposed. Some connections of the measure under study to reliability theory are obtained. Bivariate version of the proposed measure is introduced. To include the effect of the current age to the weighted cumulative entropy, we consider a dynamic version and study similar results. Further, to enhance the study, we propose a non-parametric class based on the monotonicity property of the dynamic weighted cumulative entropy. We call it increasing dynamic weighted cumulative entropy (IDWCE) class. Several properties of the class are presented. Finally, we provide few applications of the proposed measures.
Log-sum inequality, weighted mean inactivity time, reversed hazard rate, proportional reversed hazard model, non-singular transformation, IDWCE class.
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