In this paper, we study the properties of cumulative residual Mathai--Haubold entropy of order $α$. A dynamic version of this entropy measure is then proposed, and its properties are examined within the framework of reliability modeling. We show that the dynamic cumulative residual Mathai--Haubold entropy of order $α$ uniquely determines the survival function. Characterization results for the exponential and generalized Pareto distributions are derived using the proposed measure. Furthermore, we develop nonparametric estimators for the cumulative residual Mathai--Haubold entropy and its dynamic counterpart of order $α$, based on the kernel estimation of the survival function. The performance of these estimators is evaluated through a Monte Carlo simulation study. Finally, the practical relevance of the proposed dynamic estimator is illustrated using two real data; failure-time data from aircraft windshields and failure-time data from 40 randomly selected mechanical switches.

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