Exact and entropy-based nonparametric tests for exponentiality against increasing failure rate alternatives

Anfal A. Alqefari; Anfal A. Alqefari

doi:10.3934/math.2026519

AIMS Mathematics

2026, Volume 11, Issue 5: 12621-12649. doi: 10.3934/math.2026519

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Exact and entropy-based nonparametric tests for exponentiality against increasing failure rate alternatives

Anfal A. Alqefari ^,

Department of Statistics and Operations Research, College of Science, Qassim University, P.O. Box 6644, Buraydah 51482, Saudi Arabia

Received: 02 March 2026 Revised: 07 April 2026 Accepted: 10 April 2026 Published: 08 May 2026
MSC : 60E15, 62G10, 62N05, 94A17

Testing exponentiality against increasing failure rate (IFR) alternatives is a central problem in reliability theory with direct implications for aging characterization and maintenance optimization. In this paper, I introduce a novel entropy-based nonparametric test family constructed from fractional generalized cumulative residual entropy (FGCRE). The proposed statistics were formulated as scale-invariant L-functionals indexed by a tuning parameter, enabling adaptive sensitivity to diverse forms and magnitudes of IFR departures. A principal contribution of this work is the derivation of the exact finite-sample null distribution under exponentiality through a normalized spacing representation, thereby permitting fully exact, distribution-free inference without reliance on asymptotic approximations. Extensive Monte Carlo simulations demonstrated that the proposed test exhibits consistently strong and stable power, exceeding 0.85 in moderate sample sizes under Weibull alternatives and outperforming several established procedures, particularly in challenging discrimination regimes. Applications to real datasets from reliability engineering and environmental studies further confirmed the practical effectiveness of the proposed methodology in detecting positive aging behavior. Overall, the proposed framework offers a theoretically rigorous, flexible, and computationally efficient tool for exact and asymptotic testing of exponentiality against IFR alternatives.
- fractional generalized cumulative residual entropy,
- exponentiality testing,
- increasing failure rate,
- exact null distribution,
- L-statistics,
- reliability analysis,
- scale invariance
Citation: Anfal A. Alqefari. Exact and entropy-based nonparametric tests for exponentiality against increasing failure rate alternatives[J]. AIMS Mathematics, 2026, 11(5): 12621-12649. doi: 10.3934/math.2026519

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Abstract

Testing exponentiality against increasing failure rate (IFR) alternatives is a central problem in reliability theory with direct implications for aging characterization and maintenance optimization. In this paper, I introduce a novel entropy-based nonparametric test family constructed from fractional generalized cumulative residual entropy (FGCRE). The proposed statistics were formulated as scale-invariant L-functionals indexed by a tuning parameter, enabling adaptive sensitivity to diverse forms and magnitudes of IFR departures. A principal contribution of this work is the derivation of the exact finite-sample null distribution under exponentiality through a normalized spacing representation, thereby permitting fully exact, distribution-free inference without reliance on asymptotic approximations. Extensive Monte Carlo simulations demonstrated that the proposed test exhibits consistently strong and stable power, exceeding 0.85 in moderate sample sizes under Weibull alternatives and outperforming several established procedures, particularly in challenging discrimination regimes. Applications to real datasets from reliability engineering and environmental studies further confirmed the practical effectiveness of the proposed methodology in detecting positive aging behavior. Overall, the proposed framework offers a theoretically rigorous, flexible, and computationally efficient tool for exact and asymptotic testing of exponentiality against IFR alternatives.

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