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<p>In this paper, we introduce the cumulative residual Burg entropy as a survival-based extension of the classical Burg entropy. Consequently, we define a relative version of this measure and a Jensen–cumulative residual Burg entropy divergence to quantify dispersion between two survival functions. We derive key properties and bounds for the proposed entropy under proportional survival functions and establish its equivalence with proportional hazard structures. Furthermore, the proposed entropy and its relative divergence are explored for geometric and harmonic mixture survival models. A nonparametric estimator for the cumulative residual Burg entropy is proposed, and its convergence properties are examined. Finally, we present an application demonstrating the utility of the relative cumulative residual Burg divergence as a model selection criterion using a real dataset on water capacities of the Shasta Reservoir in California.</p>

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Burg entropy in terms of survival function and its application in model selection

  • 期刊论文

  • 发表日期：

    2025年10月30日

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  • Omid Kharazmi,
  • Shital Saha,
  • Suchandan Kayal

摘要

In this paper, we introduce the cumulative residual Burg entropy as a survival-based extension of the classical Burg entropy. Consequently, we define a relative version of this measure and a Jensen–cumulative residual Burg entropy divergence to quantify dispersion between two survival functions. We derive key properties and bounds for the proposed entropy under proportional survival functions and establish its equivalence with proportional hazard structures. Furthermore, the proposed entropy and its relative divergence are explored for geometric and harmonic mixture survival models. A nonparametric estimator for the cumulative residual Burg entropy is proposed, and its convergence properties are examined. Finally, we present an application demonstrating the utility of the relative cumulative residual Burg divergence as a model selection criterion using a real dataset on water capacities of the Shasta Reservoir in California.