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 that Wuhan, China reported as the disease's first official case. Turkey is one of the most impacted nations in the globe because to the high number of infected patients. To comprehend the pattern of the virus's propagation and its impacts, it is crucial of examine the pandemic statistics of Turkey. The Gumbel distribution is used to model the maximum distribution of several samples with various distributions. Therefore, we used the Gumbel distribution to estimate the daily number of COVID-19-related deaths. In this study, based on the RMSE, R2, and Theil coefficient method's multi-objective programming approach, the parameter estimation of Gumbel distribution is proposed. A comprehensive Monte-Carlo simulation study was conducted to examine the performance 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 for 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, while RMSE was a better estimator for autumn and autumn-winter data.