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

Year 2025, Early View, 1 - 1

Ecem Demir Yurtseven , Emre Koçak , H. Hasan Örkcü

https://doi.org/10.35378/gujs.1393264

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

References

• [1] Ekiz, T., Ilıman, E., Dönmez, E., “Comparison of health anxiety level and control perception of COVID-19”, International Journal of Health Management and Strategies Research, 6(1): 139-154, (2020).
• [2] Hekler, E. B., Lambert, J., Leventhal, E., Levethal, H., Jahn, E, Contrada, R. J., “Commonsense Illness Beliefs, Adherence Behaviors and Hypertension Control Among African Americans”, Journal of Behavioral Medicine, 31: 391-400, (2008).
• [3] https://covid19.who.int/. Access date: 05.04.2022
• [4] Chen, J. M., “Novel statistics predict the COVID-19 pandemic could terminate in 2022”, Journal of Medical Virology, 94(6): 2845-2848, (2022).
• [5] Bello-Chavolla, O. Y., Antonio-Villa, N. E., Ortiz-Brizuela, E., Vargas-Vázquez, A., González-Lara, M. F., de Leon, A. P., Sifuentes-Osornio, J., Aguilar-Salinas, C. A., “Validation and repurposing of the MSL-COVID-19 score for prediction of severe COVID-19 using simple clinical predictors in a triage setting: The Nutri-CoV score”, PLoS One, 15(12), (2020).
• [6] Pelinovsky, E., Kokoulina, M., Epifanova, A., Kurkin, A., Kurkina, O., Tang, M., Macau, E., Kirillin, M., “Gompertz model in COVID-19 spreading simulation”, Chaos, Solitons and Fractals, 154: 111699, (2022).
• [7] Haghighat, F., “Predicting the trend of indicators related to Covid-19 using the combined MLP-MC model”, Chaos, Solitons and Fractals, 152: 111399, (2021).
• [8] Ekinci, A., “Modelling and forecasting of the growth rate of new COVID-19 cases in top nine affected countries: Considering conditional variance and asymmetric effect”, Chaos, Solitons and Fractals, 151: 0111227, (2021).
• [9] Mishra, B. K., Keshri, A. K., Saini, D. K., Ayesha, S., Mishra, B. K., Rao, Y. S., “Mathematical model, forecast and analysis on the spread of COVID-19”, Chaos, Solitons and Fractals, 147: 110995, (2021).
• [10] Gumbel, E. J., “The return period of flood flows”, The annals of mathematical statistics, 12(2): 163-190, (1941).
• [11] Kang, D., Ko, K., Huh, J., “Determination of extreme wind values using the Gumbel distribution”, Energy, 86: 51-58, (2015).
• [12] Niemann, H. J., Diburg, S., “Statistics of extreme climatic actions based on the Gumbel probability distributions with an upper limit”, Computers and Structures, 126: 193-198, (2013).
• [13] García, Bustos, S. L., Navarrete, S., Chancay, A., Mendoza, M., Pincay, M., Teran, M., “Zoning of Ecuador According to Maximum Magnitudes of Earthquakes and their Frequency of Occurrence using Statistical Models Estimated by Maximum Likelihood”, Gazi University Journal of Science, 34(3): 916-935, (2021).
• [14] Aydın, D., Şenoğlu, B., “Monte Carlo Comparison of the Parameter Estimation Methods for the Two-Parameter Gumbel Distribution”, Journal of Modern Applied Statistical Methods, 14(2): 123-140, (2015).
• [15] Dietrich, D., Hüsler, H., “Minimum distance estimators in extreme value distributions”, Communications in Statistics - Theory and Methods, 25(4): 695–703, (1996).
• [16] Mousa, M. A., Jaheen, Z. F., Ahmad, A. A., “Bayesian estimation, prediction and characterization for the Gumbel model based on records”, Statistics: A Journal of Theoretical and Applied Statistics, 36(1): 65-74, (2002).
• [17] Mahdi, S., Cenac, M., “Estimating parameters of Gumbel distribution using the methods moments, probability weighted moments and maximum likelihood”, Revista de Matemática: Teoría y Aplicaciones, 12: 151-156, (2005).
• [18] Yılmaz, A., Kara, M., Özdemir, O., “Comparison of different estimation methods for extreme value distribution”, Journal of Applied Statistics, 48: 2259-2284, (2021).
• [19] Furutani, H., Hiroyasu, T., Okuhara, Y., “Simple Method for Estimating Daily and Total COVID-19 Deaths Using a Gumbel Model”, Researchsquare, (2020).
• [20] Furutani, H., Hiroyasu, T., Okuhara, Y., “Method for Estimating Time Series Data of COVID-19 Deaths Using a Gumbel Model”, Archives of Clinical and Biomedical Research, 6(1): 50-64, (2022).
• [21] Hee, O., “Tests for Predictability of Statistical Models”, Journal of Farm Economics, 48(5):1479-1484, (1996).
• [22] Deb, K., Pratab, A., Agarwal, S., Meyarivan, T., “A fast and elitist multi-objective genetic algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, 6(29): 182-197, (2002).