Performance Measure of the Simulated Dataset of OGED Compared to other Compound Distributions of Exponential

Abstract

Simulation studies are essential tools for investigating the performance and validation of new probability models through data generated under controlled settings. This study evaluates the performance of the simulated Odd Gompertz Exponential Distribution (OGED) dataset compared to extended distributions of Exponential, such as Exponentiated Weibull Exponential Distribution (EWED), Gompertz Exponential Distribution (GED), Kumaraswamy Exponential Distribution (KED), and the standard Exponential (Ex) distribution. The method of Maximum Likelihood Estimation (MLE) was employed to assess the efficiency, consistency, and robustness of parameters of the OGED at different sample sizes and parameter settings via performance metrics of bias and root mean square error (RMSE). A sample of 100 datasets was generated through the quantile function of the OGED and applied across all competing models. The Akaike Information Criterion (AIC) was used to evaluate the model's goodness-of-fit analysis. Results from the simulated OGED revealed consistent parameter estimates in the model with reduced bias and RMSE as the sample sizes increased. Comparative goodness-of-fit analysis shows that the OGED outperforms GE, EWE, KE, and Ex distributions. However, GED closely followed the OGED due to its strong modeling capabilities for the dataset. Furthermore, the results confirm that the OGED is highly effective in modeling the data from which it was generated and demonstrate its superior modeling performance compared to other competing distributions that share the same underlying exponential baseline.