Weighted entropies and their estimations

In this paper, some new results and inequalities of dynamic failure entropy (DFE) defined by Abbasnejad (2011) will be obtained. Then weighted versions of failure and survival entropies of order β introduced and some properties and inequalities based on these uncertainty measures found. Then weighted DFE will be introduced and some properties investigated. Finally, empirical cumulative entropy is applied to estimate the new information measures.