Annals of Communications in Mathematics

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.

Abstract. This study introduces a new probability distribution called the Cosine Exponential (CEX) Distribution, which combines the Cosine-G family of distributions with the Exponential distribution as the baseline model to create a more adaptable model. The aim is to improve modeling capabilities across various statistical applications. The paper presents expression of the density and distribution functions of the CEX model and investigates its key properties such as survival and hazard rate functions, reverse hazard function, cumulative hazard function, quantile function, moments, and moment generating function. It also outlines the methodology for estimating model parameters using maximum likelihood estimation. Through application to real datasets, the effectiveness of the proposed CEX distribution is demonstrated, showing significant enhancements over existing models. This paper highlights the potential of the CEX distribution as a robust tool for statistical modeling and analysis.