Statistical reliability modeling via Entropy measures: Characterization and testing of log-symmetric lifetime distributions

Tahani Alshathri; Mohamed Kayid; Narayanaswamy Balakrishnan; Tahani Alshathri; Mohamed Kayid; Narayanaswamy Balakrishnan

doi:10.3934/math.2026581

AIMS Mathematics

2026, Volume 11, Issue 5: 14141-14171. doi: 10.3934/math.2026581

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Statistical reliability modeling via Entropy measures: Characterization and testing of log-symmetric lifetime distributions

1.
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2.
Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada

Received: 06 February 2026 Revised: 25 April 2026 Accepted: 12 May 2026 Published: 19 May 2026
MSC : 94A17, 62G10, 62N05

Statistical reliability modeling of lifetime data routinely encounters distributions that are asymmetric on the original scale yet exhibit fundamental structural balance after logarithmic transformation. Addressing this intrinsic feature of reliability and survival data, we developed a unified entropy-based reliability modeling framework for the characterization and testing of log-symmetry in continuous lifetime distributions. The proposed methodology was built upon distributional transformations induced by linear consecutive k-out-of-n reliability systems, which serve as structured mechanisms for probing how informational balance is preserved or disrupted under reliability-driven system behavior. Within this framework, Shannon entropy, Rényi entropy, and Kerridge inaccuracy were integrated to derive explicit and tractable characterization results that uniquely identified log-symmetric lifetime distributions through intrinsic information-theoretic relationships. These results led naturally to a nonparametric, computationally efficient statistical test for log-symmetry that avoided restrictive modeling assumptions and was well suited for practical reliability analysis. Comprehensive Monte Carlo simulations demonstrated that the proposed test achieved accurate type I error control and competitive power against a wide range of alternatives. Applications to real lifetime datasets from reliability settings further confirmed the effectiveness of the approach. Overall, the study demonstrated how entropy-based inference, when embedded within reliability system modeling, provides a rigorous and practically relevant framework for statistical analysis of lifetime distributions, thereby contributing theoretical insight and applied methodology to modern reliability modeling.
Citation: Tahani Alshathri, Mohamed Kayid, Narayanaswamy Balakrishnan. Statistical reliability modeling via Entropy measures: Characterization and testing of log-symmetric lifetime distributions[J]. AIMS Mathematics, 2026, 11(5): 14141-14171. doi: 10.3934/math.2026581

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Abstract

Statistical reliability modeling of lifetime data routinely encounters distributions that are asymmetric on the original scale yet exhibit fundamental structural balance after logarithmic transformation. Addressing this intrinsic feature of reliability and survival data, we developed a unified entropy-based reliability modeling framework for the characterization and testing of log-symmetry in continuous lifetime distributions. The proposed methodology was built upon distributional transformations induced by linear consecutive k-out-of-n reliability systems, which serve as structured mechanisms for probing how informational balance is preserved or disrupted under reliability-driven system behavior. Within this framework, Shannon entropy, Rényi entropy, and Kerridge inaccuracy were integrated to derive explicit and tractable characterization results that uniquely identified log-symmetric lifetime distributions through intrinsic information-theoretic relationships. These results led naturally to a nonparametric, computationally efficient statistical test for log-symmetry that avoided restrictive modeling assumptions and was well suited for practical reliability analysis. Comprehensive Monte Carlo simulations demonstrated that the proposed test achieved accurate type I error control and competitive power against a wide range of alternatives. Applications to real lifetime datasets from reliability settings further confirmed the effectiveness of the approach. Overall, the study demonstrated how entropy-based inference, when embedded within reliability system modeling, provides a rigorous and practically relevant framework for statistical analysis of lifetime distributions, thereby contributing theoretical insight and applied methodology to modern reliability modeling.

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