Extension of the Weibull Survival Regression Based on Sine Type II Topp-Leone-G Family of Distribution: Properties and Application

This study introduces the Sine Type II Topp-Leone Weibull (STIITL-W) distribution, a novel statistical model designed to enhance flexibility in data modeling. The proposed distribution extends the classical Weibull distribution by incorporating the Sine Type II Topp-Leone family, offering improved adaptability for complex datasets. Key mathematical properties are derived, including moments, moment-generating functions, and reliability measures. Parameter estimation is performed using the maximum likelihood estimation (MLE) method, and a simulation study is conducted to evaluate the consistency and efficiency of the estimates. Additionally, a Sine Type II Topp-Leone Weibull Survival Regression (STIITL-WSR) model is developed for survival data analysis. The model's performance is assessed using real-world datasets, including transect stake distance measurements and liver cancer survival data. Comparative analysis based on the Akaike Information Criterion (AIC) demonstrates that the STIITL-W distribution outperforms competing models, such as the Topp-Leone Modified Weibull, Exponential, and Generalized Weibull distributions. Furthermore, the log-STIITL-Weibull survival regression model achieves a lower AIC compared to the log-TLG-Weibull regression model, confirming its superior performance in survival data modeling.