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Abstract
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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.
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