Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, we deﬁne a new measure of information based on cumulative distribution function, which is called “weighted cumulative entropy” (WCE). The above-mentioned model is a “Shift-dependent uncertainty measure”. In addition, we examine some of the properties of WCE and obtain some bounds for this measure. In order to estimate this new information measure, we put forward empirical WCE. Furthermore, in some theorems we have some characterization results. We explore that if the ﬁrst (last) order statistics are equal for two distributions, then this two distributions will be equal.