A Novel Extension of the Rayleigh Distribution for Biomedical Data: Properties, Estimation and Performance

This study introduces a new compound distribution by combining the Rayleigh distribution with the sine type II Topp-Leone (STIITL) generator, resulting in the sine type II Topp-Leone Rayleigh (STIITLR) distribution. The proposed model incorporates a trigonometric function and an additional shape parameter, offering greater flexibility in modelling diverse data behaviours. Several statistical properties of the distribution are derived, including moments, the moment-generating function, hazard and survival functions, and entropy. To estimate the model parameters, four methods were employed: maximum likelihood, Anderson-Darling, Cramér-von Mises, and maximum product of spacings. A simulation study was conducted to evaluate the consistency and accuracy of these estimators. As sample sizes increased, the estimators showed improved performance, with reductions in bias and root-mean-square error. The STIITLR model was then applied to a biomedical dataset involving survival times of patients with acute myeloid leukaemia. Compared to competing distributions, the proposed model provided a superior fit. These findings demonstrate that the STIITLR distribution is a promising tool for modelling complex survival patterns in biomedical research, where flexibility and adaptability are essential.