Annals of Communications in Mathematics

AbstractProbability 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.

ABSTRACT. Probability distributions are essential tools for modeling, prediction, and statistical inference. In recent years, several generalized families of distributions have been proposed to extend classical models and increase their flexibility in capturing complex data behaviors. This paper reviews selected generalized families published between 2023 and 2025, focusing on their construction mechanisms, statistical properties, estimation methods, and real-world applications. The families discussed include trigonometric-based, inverse, Lomax-generated, Topp–Leone, and hybrid forms. To illustrate their performance, five families were combined with the exponential distribution and fitted to a real dataset. The comparison shows that all extended models provide an adequate fit, while the standard exponential model performs poorly. The findings confirm the practical value of generalized families in improving data modeling.