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Method for Estimating Time Series Data of COVID-19 Deaths using a Gumbel Model

Author(s): Furutani H, Hiroyasu T, Okuhara Y

The purpose of the present paper is to introduce a method for forecasting the daily number of COVID-19 associated deaths. We apply the Gumbel distribution function for the analysis of time series data of the first-wave outbreak. The Gumbel distribution function FG(t) has the property of having a mode (peak) point b, where FG(b)=1/2.718. The probability density function of FG(t) has a single-peaked and right-skewed form. Using this distribution, we can estimate the total number of deaths N, and forecast daily numbers in the decreasing phase. We study the early-stage data of Italy, Canada, Belgium, Switzerland, the Netherlands, Sweden, Germany, China, France, and the United Kingdom. The data of New York City and England are also analyzed. In general, the Gumbel distribution reasonably reproduces the time series data of daily counts. However, significant discrepancies between theory and data are observed for China, France, and Sweden. We re-analyze the data of these countries and the Netherlands using different approaches.

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