Harmonic mixture weibull normal regression with applications in biomedicine

In medical and biomedical research, real data sets often exhibit characteristics such as bimodality, unimodality, or asymmetry. Among the generalized regression models commonly employed for analyzing such data are the Kumaraswamy and gamma-normal models. This study introduces two new generalized regression models based on the Harmonic Mixture Weibull-Normal distribution: one with varying dispersion and the other with constant dispersion. Additionally, a novel experimental design model was developed using the same distribution framework. The proposed models demonstrated the capability to effectively capture symmetric, asymmetric, and bimodal response variables. Model parameters were estimated using the maximum likelihood method, and simulation experiments were conducted to assess the behavior of the model coefficients. Empirical results revealed that the newly developed models outperformed several established alternatives, making them more practical for biomedical applications. Residual analysis further confirmed the adequacy of the proposed models, supporting their suitability for analyzing complex data in biomedical research.