The Khalil New Generalized Rayleigh (KNGR) Distribution:Statistical Properties, Estimation, and Applications

Abstract

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.