The Khalil New Generalized Rayleigh (KNGR) Distribution:Statistical Properties, Estimation, and Applications
DOI:
https://doi.org/10.14419/txpaq681Published
20-11-2025Keywords:
KNG-R Distribution; Lifetime Modeling; Reliability Analysis; Maximum Likelihood Estimation; Simulation StudyAbstract
This study introduces the Khalil New Generalized Rayleigh (KNG-R) distribution, a novel and flexible lifetime model derived by applying the Khalil New Generalized Family (KNGF) generator to the Rayleigh distribution. The proposed model extends the Ray-leigh family by incorporating additional parameters that enhance its ability to capture diverse data behaviors such as increasing, creasing, and bathtub-shaped hazard rates. Key statistical properties, including the probability density function, cumulative distribution function, moments, moment-generating function, entropy, and quantile function, were derived. Additionally, parameter estimation was conducted using the maximum likelihood method, and a Monte Carlo simulation confirms the consistency and efficiency of the estimators. The KNG-R distribution was applied to three real datasets and outperformed competing distributions, including the Weibull–Rayleigh, TIIEHL-PLo, SMR, and Rayleigh models, based on log-likelihood, AIC, BIC, and AICc criteria. The results demonstrate that the KNG-R is a powerful and adaptable distribution suitable for modeling complex lifetime and reliability data.
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