Extensions of entropy-based concomitant models for ordered systems with applications to radiation monitoring data in the Kingdom of Saudi Arabia

Mohamed Said Mohamed; Hanan H. Sakr; Mohamed Said Mohamed; Hanan H. Sakr

doi:10.3934/math.20261109

AIMS Mathematics

2026, Volume 11, Issue 9: 27728-27765. doi: 10.3934/math.20261109

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Extensions of entropy-based concomitant models for ordered systems with applications to radiation monitoring data in the Kingdom of Saudi Arabia

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

1.
Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Hawtat Bani Tamim 16511, Saudi Arabia
2.
Mathematics Department, Faculty of Education, Ain Shams University, Cairo 11341, Egypt

Received: 23 June 2026 Revised: 02 August 2026 Accepted: 25 August 2026 Published: 01 September 2026
MSC : 60G05, 94-08, 94A17

In this study, a generating informational function is introduced for concomitants of $ p $-generalized order statistics, providing a unified framework that incorporates several classical entropy-type measures as special cases. The proposed formulation extends existing entropy-based models by combining concomitant structures with generalized order statistics under the Huang–Kotz extension. Since closed-form expressions are generally difficult to obtain, a tractable representation based on the uniform distribution is developed and subsequently applied to several lifetime distributions through suitable transformations. New stochastic ordering properties of the proposed generating informational function are established, and corresponding characterization results are derived for the uniform and exponential distributions. In addition, explicit analytical bounds are obtained to approximate the proposed measure in situations where exact evaluation is analytically intractable. From an inferential perspective, two non-parametric estimators for the generating informational function are proposed, and their consistency properties are investigated. A corrected estimator is further introduced to improve estimation efficiency. The asymptotic behavior of the estimators is numerically illustrated through histogram-based analysis. Numerical studies based on Monte Carlo simulations, bootstrap convergence analysis, and real lifetime datasets demonstrate the effectiveness, stability, and practical applicability of the proposed estimation procedures.
- generating informational function,
- generalized order statistics,
- concomitants,
- stochastic ordering,
- non-parametric estimation
Citation: Mohamed Said Mohamed, Hanan H. Sakr. Extensions of entropy-based concomitant models for ordered systems with applications to radiation monitoring data in the Kingdom of Saudi Arabia[J]. AIMS Mathematics, 2026, 11(9): 27728-27765. doi: 10.3934/math.20261109

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Abstract

In this study, a generating informational function is introduced for concomitants of $ p $-generalized order statistics, providing a unified framework that incorporates several classical entropy-type measures as special cases. The proposed formulation extends existing entropy-based models by combining concomitant structures with generalized order statistics under the Huang–Kotz extension. Since closed-form expressions are generally difficult to obtain, a tractable representation based on the uniform distribution is developed and subsequently applied to several lifetime distributions through suitable transformations. New stochastic ordering properties of the proposed generating informational function are established, and corresponding characterization results are derived for the uniform and exponential distributions. In addition, explicit analytical bounds are obtained to approximate the proposed measure in situations where exact evaluation is analytically intractable. From an inferential perspective, two non-parametric estimators for the generating informational function are proposed, and their consistency properties are investigated. A corrected estimator is further introduced to improve estimation efficiency. The asymptotic behavior of the estimators is numerically illustrated through histogram-based analysis. Numerical studies based on Monte Carlo simulations, bootstrap convergence analysis, and real lifetime datasets demonstrate the effectiveness, stability, and practical applicability of the proposed estimation procedures.

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