Abstract

Cumulative Entropy (CE) as a measure of uncertainty alternative to Shannon entropy is proposed by Di Crescenzo and Longobardi (2009). In this paper, some properties of the cumulative entropy are derived and under conditions are showed the cumulative entropy of the last order statistics can determine the distribution function uniquely. Weibull family is characterized by ratio of the cumulative entropy of the last order statistics to its expectation. Also, some inequalities are presented for the cumulative entropy of reversed residual lifetime of a parallel system.

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