Weighted entropies and their estimations

Abstract

In this article, some new results and inequalities of dynamic failure entropy (DFE) defined by the author Abbasnejad in 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 new information measures.

Keywords:

• Cumulative entropy
• Empirical cumulative entropy
• Lifetime distributions
• Proportional reversed hazard rate model
• Uncertainty measure