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.