On weighted interval entropy

Measures of uncertainty in past and residual lifetime distributions have been proposed in the information-theoretic literature. Recently, Di Crescenzo and Longobardi (2006) introduced weighted differential entropy and its dynamic versions. These information-theoretic uncertainty measures are shift-dependent. In this paper, we study the weighted differential information measure for two-sided truncated random variables. This new measure is a generalization of recent dynamic weighted entropy measures. We study various properties of this measure, including its connection with weighted residual and past entropies, and we obtain its upper and lower bounds.