The Neutrosophic Weibull-Rayleigh Distribution: A Flexible Lifetime Model under Indeterminacy - Adnan Amin; Mehran khan (Journal of Analytical Uncertainty, 2026)
The classical Weibull-Rayleigh distribution is widely used in survival, reliability, and environmental studies. However, in many real-world applications, the model parameters are not precisely known due to measurement errors, incomplete data, or ambiguous information. Classical statistics cannot adequately handle such indeterminacy. This paper introduces the neutrosophic Weibull-Rayleigh distribution by extending the classical Weibull-Rayleigh distribution. We derive the neutrosophic probability density function, cumulative distribution function, survival function, hazard function, moments, moment generating function, and Shannon entropy. A simulation study demonstrates that as indeterminacy increases, all summary statistics become intervals rather than point estimates, with band widths that quantify parameter uncertainty. The proposed distribution is recommended for modeling lifetime data in medical diagnosis (incomplete patient records), environmental monitoring (sensor failures), and reliability engineering (imprecise component specifications) where indeterminacy is inherent.