Authors

• Malihe Mirali ¹
• Simin Baratpour ²

¹ Department of Statistics, International Campus, Ferdowsi University of Mashhad, Mashhad, Iran

² Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 91775-1159, Mashhad, Iran

Abstract

Considering Rao et al. (2004) and Di Crescenzo and Longobardi (2009) studies, Misagh et al. (2011) proposed a weighted information which is based on the cumulative entropy called Weighted Cumulative Entropy (WCE). The above-mentioned model is a Shiftdependent Uncertainty Measure. In this paper, we examine some of the properties of WCE and obtain some bounds for that. In order to estimate this information measure, we put forward empirical WCE. Furthermore, in some theorems, we have some characterization results. We explore that, if the WCE of the first (last) order statistic are equal for two distributions, then this two distributions will be equal.
 

Keywords

• Cumulative entropy‎
• ‎Cumulative residual entropy‎
• ‎Survival function‎
• ‎Weighted Shannon entropy