A New Exponential Gompertz Distribution: Theory and Applications

With the rise of numerous phenomena that require interpretation and investigation, developing novel distributions has become an important need. This research introduced a new probability distribution called New Exponential Gompertz distribution based on the new exponential-X family to enhance flexibility and improve performance. The most significant benefit of this novel distribution is that its hazard function could be increasing, decreasing and bathtub which reflects the flexibility of the distribution to fit various applications. Furthermore, its density can adopt a variety of symmetric and asymmetric possible shapes. Some of the theoretical characteristics such as quantile, order statistic and moment are provided. The parameter estimates are derived using five different estimation methods including maximum likelihood, ordinary least square, weighted least square, Cramér-von mises and maximum product of spacing methods. Simulation studies are conducted to assess the effectiveness of the five estimation methods. The maximum likelihood estimate shows the most reliable estimate for estimating parameters since it provides the smallest mean square error While the maximum product of spacing method is less efficient. The performance of the proposed distribution is assessed through real-world applications in medical, engineering and physics with competitive distributions. The results indicate that the new distribution efficiently represents various types of data compared to other distributions.