Abstract

Probability distributions are essential for modeling and analyzing complex datasets across various scientific disciplines. However, classical distributions often fail to capture intricate features such as skewness, heavy tails, or high variability observed in real-world data. To address these limitations, this study proposes the Sine Type II Topp-Leone Gompertz (STIITLG) distribution, a novel extension of the Gompertz model based on the sine type II Topp-Leone family. The proposed model enhances the flexibility of the classical Gompertz distribution by incorporating an additional shape parameter, enabling it to better accommodate diverse data behaviors. Several key properties of the model, including moments, inverse moment, mean residual life function, entropy, and order statistics, were derived to establish its theoretical foundation. The model parameters were estimated using the maximum likelihood estimation method, and a comprehensive simulation study confirmed the consistency of these estimators. The practical utility of the model was demonstrated by applying it to two real-life datasets, where it outperformed several existing models based on goodness-of-fit criteria. These findings underscore the potential of the proposed distribution as a robust tool for modeling complex phenomena in diverse fields.