On residual cumulative generalized exponential entropy and its application in human health

Hanan H. Sakr; Mohamed S. Mohamed; Hanan H. Sakr; Mohamed S. Mohamed

doi:10.3934/era.2025077

Electronic Research Archive

2025, Volume 33, Issue 3: 1633-1666. doi: 10.3934/era.2025077

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Research article

On residual cumulative generalized exponential entropy and its application in human health

Hanan H. Sakr ^{1,2
,
,},
Mohamed S. Mohamed ²

1.
Department of Management Information Systems, College of Business Administration in Hawtat Bani Tamim, Prince Sattam Bin Abdulaziz University, Saudi Arabia
2.
Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11341, Egypt

Received: 05 February 2025 Revised: 05 March 2025 Accepted: 12 March 2025 Published: 20 March 2025

Numerous adaptations of traditional entropy concepts and their residual counterparts have emerged in statistical research. While some methodologies incorporate supplementary variables or reshape foundational assumptions, many ultimately align with conventional formulations. This study introduces a novel extension termed residual cumulative generalized exponential entropy to broaden the scope of residual cumulative entropy for continuous distributions. Key attributes of the proposed measure include non-negativity, bounds, its relationship to the continuous entropy measure, and stochastic comparisons. Practical implementations are demonstrated through case studies involving established probability models. Additionally, insights into order statistics are derived to characterize the measure's theoretical underpinnings. The residual cumulative generalized exponential entropy framework bridges concepts such as Bayesian risk assessment and excess wealth ordering. For empirical implementation, non-parametric estimation strategies are devised using data-driven approximations of residual cumulative generalized exponential entropy, with two distinct estimators of the cumulative distribution function evaluated. A practical application is showcased, using clinical diabetes data. The study further explores the role of generalized exponential entropy in identifying distributional symmetry, mainly through its application to uniform distributions to pinpoint symmetry thresholds in ordered data. Finally, the utility of generalized exponential entropy is examined in pattern analysis, with a diabetes dataset serving as a benchmark for evaluating its classification performance.
- exponential entropy,
- order statistics,
- non-parametric estimation,
- residual cumulative entropy,
- pattern recognition,
- stochastic order
Citation: Hanan H. Sakr, Mohamed S. Mohamed. On residual cumulative generalized exponential entropy and its application in human health[J]. Electronic Research Archive, 2025, 33(3): 1633-1666. doi: 10.3934/era.2025077

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Abstract

Numerous adaptations of traditional entropy concepts and their residual counterparts have emerged in statistical research. While some methodologies incorporate supplementary variables or reshape foundational assumptions, many ultimately align with conventional formulations. This study introduces a novel extension termed residual cumulative generalized exponential entropy to broaden the scope of residual cumulative entropy for continuous distributions. Key attributes of the proposed measure include non-negativity, bounds, its relationship to the continuous entropy measure, and stochastic comparisons. Practical implementations are demonstrated through case studies involving established probability models. Additionally, insights into order statistics are derived to characterize the measure's theoretical underpinnings. The residual cumulative generalized exponential entropy framework bridges concepts such as Bayesian risk assessment and excess wealth ordering. For empirical implementation, non-parametric estimation strategies are devised using data-driven approximations of residual cumulative generalized exponential entropy, with two distinct estimators of the cumulative distribution function evaluated. A practical application is showcased, using clinical diabetes data. The study further explores the role of generalized exponential entropy in identifying distributional symmetry, mainly through its application to uniform distributions to pinpoint symmetry thresholds in ordered data. Finally, the utility of generalized exponential entropy is examined in pattern analysis, with a diabetes dataset serving as a benchmark for evaluating its classification performance.

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