Recently, Tahmasebi and Eskandarzadeh introduced a new extended cumulative entropy
(ECE). In this paper, we present results on shift-dependent measure of ECE and its dynamic past
version. These results contain stochastic order, upper and lower bounds, the symmetry property and
some relationships with other reliability functions. We also discuss some properties of conditional
weighted ECE under some assumptions. Finally, we propose a nonparametric estimator of this new
measure and study its practical results in blind image quality assessment.