The parameter estimation of the COVID-19 death based on the Gumbel distribution through the multi-objective programming: Turkey case

Abstract

Nearly all nations, including Turkey, were impacted by the 2019 new coronavirus (COVID-19) infections reported by Wuhan, China, as the disease's first official case. Turkey is one of the most impacted nations in the globe due to the high number of infected patients. To comprehend the pattern of the virus's propagation and its impacts, it is crucial to examine the pandemic statistics in Turkey. The Gumbel distribution is utilized when describing the maximum or minimum of several samples with different distributions. Therefore, we used the Gumbel distribution to estimate the daily number of COVID-19-related deaths. This study proposes a multi-objective programming methodology for Gumbel distribution parameter estimation based on the RMSE, R2, and Theil coefficient methods. A comprehensive Monte-Carlo simulation research is performed to examine the effectiveness of single-objective RMSE, R2, Theil’s coefficient and multi-objective RMSE-R2, RMSE-Theil, R2-Theil, RMSE-R2-Theil programming estimation methods. When the simulation results were analyzed, the case formed by the RMSE-R2-Theil estimator has the best Def value across all cases. The application of the real dataset containing COVID-19 death data is examined, and it can be seen that Theil, RMSE-Theil, and R2-Theil were better estimators for winter data. At the same time, RMSE was a better estimator for autumn and autumn-winter data.

Keywords

• Gumbel distribution
• Multi-objective optimization
• NSGA-II
• COVID-19-related deaths

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