Annals of Communications in Mathematics

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.

Abstract:The cosine Gompertz distribution has been proposed as an extension of the classical Gompertz model; however, its hazard rate is restricted to an increasing shape. To overcome this limitation, we introduce the Exponentiated Cosine Gompertz Distribution (ECGD) by applying the exponentiated family approach to the cosine Gompertz distribution. The proposed model offers greater flexibility in describing different hazard-rate patterns, including decreasing, increasing, and bathtub-shaped behaviors. Some mathematical properties of the ECGD are derived, and its parameters are estimated using the methods of maximum likelihood, maximum product of spacings, Anderson–Darling, and Cramér–von Mises. A simulation study is conducted to assess the performance of these estimation methods, with the results indicating satisfactory estimation performance across the considered scenarios. The practical applicability of the ECGD is demonstrated using a real-world dataset, where it provides a better fit than several competing models. These results indicate that the proposed distribution is a useful and flexible model for reliability analysis.