A novel extension of the Rayleigh distribution for biomedical data: Properties, estimation and performance

Alhaji Modu Isa; Sule Omeiza Bashiru

doi:10.32890/jcia2026.5.1.2

Authors

Alhaji Modu Isa Borno State University, Nigeria
Sule Omeiza Bashiru Confluence University of Science and Technology, Nigeria

DOI:

https://doi.org/10.32890/jcia2026.5.1.2

Keywords:

Maximum Likelihood Estimation Method, moment, Rayleigh Distribution, Sine Type II Topp-Leone G, survival data

Abstract

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.

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