In this study, the maximum likelihood estimators (MLEs) and Bayes estimators for the shape and scale parameters of Inverse Exponential Power (IEP) distribution are derived. As closed-form solutions for the Bayes estimators are not available, approximate estimators are obtained through Lindley’s and Tierney–Kadane’s approximation methods, along with the Markov Chain Monte Carlo (MCMC) method, under the squared-error loss (SEL) function. Also, the approximate Bayes estimates are evaluated against the maximum likelihood estimates based on mean square error (MSE) and bias values using Monte Carlo simulation. In addition, the coverage probabilities of the parametric bootstrap estimates are computed. Finally, real data sets belonging to the COVID-19 Pandemic Case Fatality Rate across World Health Organization (WHO) and Organization fo Economic Co-Operation and Development (OECD) regions data is investigated as an important indicator to achieve United Nations’ Sustainable Development Goal 3 (SDG 3) are employed to display the emprical results associated with both non-bayesian and bayesian estimations of the IEP distribution presented. By offering improved estimation techniques for flexible health indicator distributions, the results contribute to the broader effort of enhancing statistical tools used in global health analytics—particularly in areas such as survival modeling, biomedical reliability, and chronic disease monitoring aligned with SDG 3.