Bayesian estimation of the inverse Exponential Power distribution for COVID-19 case fatality analysis under SDG 3

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Accurate statistical estimation is vital for global health analytics, particularly for indicators related to Sustainable Development Goal 3 (SDG 3).
• The Inverse Exponential Power (IEP) distribution offers flexibility in modeling various health-related phenomena.

Purpose of the Study:

• To derive Maximum Likelihood Estimators (MLEs) and Bayes estimators for the shape and scale parameters of the IEP distribution.
• To develop and evaluate approximate Bayes estimators using Lindley's, Tierney-Kadane's, and Markov Chain Monte Carlo (MCMC) methods.
• To assess the performance of these estimators using Monte Carlo simulations and real-world health data.

Main Methods:

• Derivation of MLEs for IEP distribution parameters.
• Application of Lindley's, Tierney-Kadane's approximation, and MCMC methods for approximate Bayes estimation under squared-error loss.
• Monte Carlo simulation to compare MLEs and Bayes estimators based on Mean Square Error (MSE) and bias.
• Computation of parametric bootstrap coverage probabilities.
• Empirical analysis using COVID-19 Case Fatality Rate data from WHO and OECD regions.

Main Results:

• Approximate Bayes estimators were successfully derived for the IEP distribution parameters when closed-form solutions were unavailable.
• Simulation studies provided insights into the performance characteristics (MSE, bias) of both Bayesian and non-Bayesian estimation methods.
• Parametric bootstrap confidence intervals were evaluated for their coverage probabilities.
• The utility of the proposed estimation techniques was demonstrated using real-world COVID-19 data.

Conclusions:

• The study provides advanced estimation techniques for the IEP distribution, enhancing its applicability in health indicator analysis.
• The findings contribute to improving statistical tools for global health analytics, supporting SDG 3 objectives in areas like survival modeling and disease monitoring.
• The developed methods offer a valuable resource for researchers and policymakers in public health and biomedical fields.