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What is Learnable in Valiant's Theory of the Learnable? 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The Cumulative Residual Mathai--Haubold Entropy and its Non-parametric Inference
Anija C. R, Smitha S., Sudheesh K. Kattumannil · 2025-12-11 · via math.ST updates on arXiv.org

We introduce the cumulative residual Mathai--Haubold entropy (CRMHE) and investigate its properties. We then propose a dynamic counterpart, the dynamic cumulative residual Mathai--Haubold entropy (DCRMHE), and establish its uniqueness in characterizing the distribution function. Non-parametric estimators for the CRMHE and DCRMHE are developed based on the kernel density estimation of the survival function. The efficacy of the estimators is assessed through a comprehensive Monte Carlo simulation study. The relevance of the proposed DCRMHE estimator is illustrated using two real-world datasets: on the failure times of 70 aircraft windshields and failure times of 40 randomly selected mechanical switches.

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