Abstract

Recently, an alternative measure of uncertainty termed by extropy was proposed by Lad et al. Accordingly, a cumulative residual extropy is also introduced by replacing the survival function in place of the density function in the extropy. In this paper, we define negative cumulative extropy (NCEX) measure of information and study several properties of this concept. We then elaborate the NCEX of coherent system’s lifetime when lifetimes of components are dependent and identically distributed. We also consider the conditional negative cumulative extropy and discuss some its properties. Finally, we propose the estimator of this measure using empirical approach and study it as a risk measure and large sample properties of this estimator.

摘要

最近，Lad 等人提出了另一种不确定性度量，称为 extropy。因此，还通过替换生存函数代替熵中的密度函数来引入累积剩余熵。在本文中，我们定义了信息的负累积熵（NCEX）度量，并研究了这个概念的几个属性。然后，我们详细说明了当组件的寿命依赖且同分布时相干系统寿命的 NCEX。我们还考虑了条件负累积熵并讨论了它的一些性质。最后，我们使用经验方法提出了该度量的估计量，并将其作为风险度量和该估计量的大样本特性进行了研究。