This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of sequential order statistics under a conditional proportional hazard rates model. It is shown that the equality of the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution. Subsequently, we characterize the Weibull distribution on the basis of the ratio of the cumulative residual entropy of first sequential order statistics to the corresponding mean. Also, we consider characterizations based on the dynamic cumulative residual entropy and derive some bounds for the cumulative residual entropy of residual lifetime of the sequential order statistics.

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