Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order $\alpha$

Anija C. R; Smitha; S.; Sudheesh; K. Kattumannil

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arXiv · 2609.08434

Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order $\alpha$

Anija C. R·Smitha·S.·Sudheesh·K. Kattumannil

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Abstract

In this paper, we study the properties of cumulative residual Mathai--Haubold entropy of order $\alpha$. 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 $\alpha$ 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 $\alpha$, 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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Anija C. R, Smitha, S., Sudheesh, K. Kattumannil. 2026-09-08. Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order $\alpha$. https://arxiv.org/abs/2609.08434

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