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A Scale-Invariant Adaptive Test for IFR Alternatives Based on Cumulative Residual Entropy Under Proportional Hazards.

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Title: A Scale-Invariant Adaptive Test for IFR Alternatives Based on Cumulative Residual Entropy Under Proportional Hazards.
Authors: Alshehri, Mashael A.1 (AUTHOR)
Source: Mathematics (2227-7390). Aug2026, Vol. 14 Issue 16, p2902. 29p.
Subject Terms: *Proportional hazards models, *Statistical hypothesis testing, *Distribution (Probability theory), *Monte Carlo method, *Nonparametric statistics, *Entropy (Information theory)
Abstract: Highlights: The Adaptive CRE-PH Test provides scale-invariant, nonparametric detection of IFR-type departures from exponentiality within a unified proportional-hazards and Tsallis-entropy framework. Exact finite-sample null distributions, means, and covariances are obtained via Dirichlet spacings, yielding a joint characterization of the adaptive maximum statistic. Joint asymptotic normality and consistency under fixed alternatives are established for the dependent score-vector family. A prespecified moderate tuning grid balances numerical stability, representative score geometry, and multiplicity control without retrospective alternative-specific optimization. Monte Carlo studies demonstrate accurate size control, power close to the best fixed-q component, and effective detection of IFRA-but-not-IFR alternatives, with accompanying illustrative R scripts for a representative fixed-q simulation and graphical diagnostics. Testing exponentiality against increasing failure rate alternatives is central to reliability theory and lifetime data analysis. This paper develops the Adaptive Cumulative Residual Entropy Test under Proportional Hazards (Adaptive CRE-PH Test), a scale-invariant nonparametric procedure that unifies a Tsallis-entropy departure functional with a proportional-hazards transformation. For each tuning value, the fixed- q statistic admits a normalized-spacing representation. Under exponentiality, the spacing proportions follow a Dirichlet distribution, yielding exact finite-sample means, covariances, and a joint null characterization of the adaptive maximum. Joint asymptotic normality and consistency under fixed alternatives are established for the complete dependent score vector. Structural analysis of the score family motivates a prespecified moderate grid governed by endpoint stability, directional diversity, and multiplicity economy, rather than retrospective power optimization. Monte Carlo experiments demonstrate accurate size control, explicitly quantify calibration stability, and show power close to the best fixed- q component under linear failure rate, Makeham, and Weibull alternatives. A dedicated power experiment confirms substantial detection capability against an IFRA-but-not-IFR benchmark, showing that the broader population sign condition has practical as well as theoretical relevance. Additional DFR and bathtub experiments clarify directional specificity: rejection provides evidence against exponentiality in the IFR-sensitive direction but does not, without shape-specific inference, establish a globally increasing hazard. Three real-data applications illustrate the practical importance of distinguishing formal directional inference from exploratory Q–Q and total-time-on-test diagnostics. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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  – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=22277390&ISBN=&volume=14&issue=16&date=20260815&spage=2902&pages=2902-2930&title=Mathematics (2227-7390)&atitle=A%20Scale-Invariant%20Adaptive%20Test%20for%20IFR%20Alternatives%20Based%20on%20Cumulative%20Residual%20Entropy%20Under%20Proportional%20Hazards.&aulast=Alshehri%2C%20Mashael%20A.&id=DOI:10.3390/math14162902
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  Data: A Scale-Invariant Adaptive Test for IFR Alternatives Based on Cumulative Residual Entropy Under Proportional Hazards.
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  Data: <searchLink fieldCode="AR" term="%22Alshehri%2C+Mashael+A%2E%22">Alshehri, Mashael A.</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%282227-7390%29%22">Mathematics (2227-7390)</searchLink>. Aug2026, Vol. 14 Issue 16, p2902. 29p.
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  Data: *<searchLink fieldCode="DE" term="%22Proportional+hazards+models%22">Proportional hazards models</searchLink><br />*<searchLink fieldCode="DE" term="%22Statistical+hypothesis+testing%22">Statistical hypothesis testing</searchLink><br />*<searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br />*<searchLink fieldCode="DE" term="%22Monte+Carlo+method%22">Monte Carlo method</searchLink><br />*<searchLink fieldCode="DE" term="%22Nonparametric+statistics%22">Nonparametric statistics</searchLink><br />*<searchLink fieldCode="DE" term="%22Entropy+%28Information+theory%29%22">Entropy (Information theory)</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Highlights: The Adaptive CRE-PH Test provides scale-invariant, nonparametric detection of IFR-type departures from exponentiality within a unified proportional-hazards and Tsallis-entropy framework. Exact finite-sample null distributions, means, and covariances are obtained via Dirichlet spacings, yielding a joint characterization of the adaptive maximum statistic. Joint asymptotic normality and consistency under fixed alternatives are established for the dependent score-vector family. A prespecified moderate tuning grid balances numerical stability, representative score geometry, and multiplicity control without retrospective alternative-specific optimization. Monte Carlo studies demonstrate accurate size control, power close to the best fixed-q component, and effective detection of IFRA-but-not-IFR alternatives, with accompanying illustrative R scripts for a representative fixed-q simulation and graphical diagnostics. Testing exponentiality against increasing failure rate alternatives is central to reliability theory and lifetime data analysis. This paper develops the Adaptive Cumulative Residual Entropy Test under Proportional Hazards (Adaptive CRE-PH Test), a scale-invariant nonparametric procedure that unifies a Tsallis-entropy departure functional with a proportional-hazards transformation. For each tuning value, the fixed- q statistic admits a normalized-spacing representation. Under exponentiality, the spacing proportions follow a Dirichlet distribution, yielding exact finite-sample means, covariances, and a joint null characterization of the adaptive maximum. Joint asymptotic normality and consistency under fixed alternatives are established for the complete dependent score vector. Structural analysis of the score family motivates a prespecified moderate grid governed by endpoint stability, directional diversity, and multiplicity economy, rather than retrospective power optimization. Monte Carlo experiments demonstrate accurate size control, explicitly quantify calibration stability, and show power close to the best fixed- q component under linear failure rate, Makeham, and Weibull alternatives. A dedicated power experiment confirms substantial detection capability against an IFRA-but-not-IFR benchmark, showing that the broader population sign condition has practical as well as theoretical relevance. Additional DFR and bathtub experiments clarify directional specificity: rejection provides evidence against exponentiality in the IFR-sensitive direction but does not, without shape-specific inference, establish a globally increasing hazard. Three real-data applications illustrate the practical importance of distinguishing formal directional inference from exploratory Q–Q and total-time-on-test diagnostics. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196618722
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        Value: 10.3390/math14162902
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      – Code: eng
        Text: English
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        PageCount: 29
        StartPage: 2902
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      – SubjectFull: Proportional hazards models
        Type: general
      – SubjectFull: Statistical hypothesis testing
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Monte Carlo method
        Type: general
      – SubjectFull: Nonparametric statistics
        Type: general
      – SubjectFull: Entropy (Information theory)
        Type: general
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      – TitleFull: A Scale-Invariant Adaptive Test for IFR Alternatives Based on Cumulative Residual Entropy Under Proportional Hazards.
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              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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