Statistical Evaluation of the Gompertz-Fréchet distribution: Statistical Elasticity Analysis Using Simulation, Estimation and Application

This paper deals with the analysis of the Gompertz-Fréchet (GoFr) distribution, which combines the Gompertz family and the Fréchet distribution, where the statistical properties of proposed distribution are studied and accurate estimation methods for the distribution parameters are developed. Monte Carlo simulation was employed to evaluate the performance of three estimation methods: the Maximal likelihood method (MLE), the least squares method (LSE), and weighted least squares method (WLSE). The simulation included different sample sizes ranging from n=50 to 200, and the results were analyzed using criteria such as bias, mean square error (MSE), and root mean square error (RMSE). The results showed that the MLE method is the most accurate and efficient, as the bias and MSE decreased with the increase in sample size. The GoFr distribution was also applied to real data and compared with six other distributions using statistical accuracy criteria such as AIC and BIC. The results confirmed that the GoFr distribution is superior in its fit to the data compared to other models, which reflects its flexibility and effectiveness in analyzing data of complex nature.