A New Exponential Gompertz Distribution:Theory and Applications

With the rise of numerous phenomena that require interpretation and inves-tigation, developing novel distributions has become an important need. Thisresearch introduced a new probability distribution called New ExponentialGompertz distribution based on the new exponential-X family to enhanceflexibility and improve performance. The most significant benefit of thisnovel distribution is that its hazard function could be increasing, decreasingand bathtub which reflects the flexibility of the distribution to fit variousapplications. Furthermore, its density can adopt a variety of symmetric andasymmetric possible shapes. Some of the theoretical characteristics such asquantile, order statistic and moment are provided. The parameter estimatesare derived using five different estimation methods including maximumlikelihood, ordinary least square, weighted least square, Cram er-von misesand maximum product of spacing methods. Simulation studies are conductedto assess the effectiveness of the five estimation methods. The maximumlikelihood estimate shows the most reliable estimate for estimating param-eters since it provides the smallest mean square error While the maximum product of spacing method is less efficient. The performance of the proposeddistribution is assessed through real-world applications in medical, engineer-ing and physics with competitive distributions. The results indicate that thenew distribution efficiently represents various types of data compared to otherdistributions