A new Weibull distribution for modeling complex biomedical data

Classical models like the Weibull distribution often struggle to capture the high variability and complexity inherent in biomedical data. To address these limitations, we introduced the odd beta prime-Weibull (OBP-Weibull) distribution, derived from the odd beta prime class, which provides enhanced flexibility and greater kurtosis than the traditional Weibull model. The OBP-Weibull model is designed to accommodate a range of distribution shapes, from skewed (both right and left) to symmetric and J-shaped, as well as various hazard rate patterns, including increasing, bathtub, and decreasing. These features make it particularly adaptable for statistical modeling in biomedical research. Key properties of the OBP-Weibull distribution are outlined, with parameter estimation conducted using the least squares, weighted least squares, and maximum likelihood estimation methods. Monte Carlo simulations confirm the model's robustness across diverse scenarios. Using the OBP-Weibull model, we analyze three real-world biomedical datasets: COVID-19 mortality data, pathological clinic data, and remission times in acute bone cancer patients. Results show that the OBP-Weibull model outperforms classical models in capturing data complexities. This study establishes the OBP-Weibull distribution as a valuable tool for complex data modeling in biomedical research, providing essential insights and applications.