Uncertain growth model for the cumulative number of COVID-19 infections in China
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Uncertain growth model for the cumulative number of COVID-19 infections in China Zhe Liu1 Accepted: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract As a type of coronavirus, COVID-19 has quickly spread around the majority of countries worldwide, and seriously threatens human health and security. This paper aims to depict cumulative numbers of COVID-19 infections in China using the growth model chosen by cross validation. The residual plot does not look like a null plot, so we can not find a distribution function for the disturbance term that is close enough to the true frequency. Therefore, the disturbance term can not be characterized as random variables, and stochastic regression analysis is invalid in this case. To better describe this pandemic automatically, this paper first employs uncertain growth models with the help of uncertain hypothesis tests to detect and modify outliers in data. The forecast value and confidence interval for the cumulative number of COVID-19 infections in China are provided. Keywords Uncertainty theory · Uncertain statistics · Uncertain regression analysis · Uncertain hypothesis test · COVID-19
1 Introduction Regression analysis estimates relationships among variables. Although stochastic regression analysis has a long history of development, they are all considered under the framework of probability theory. However, the premise of probability theory, i.e., the estimated distribution being close enough to the true frequency, cannot be satisfied in many cases. Motivated by this, Liu (2007, 2009) founded uncertainty theory based on normality, duality, subadditivity, and product axioms to better address the inaccuracy of the human system. Currently, this theory has been successfully applied in uncertain statistics (Liu 2010). For example, Yang and Liu (2019) first presented uncertain time series analysis to predict future values based on imprecise observations. Following that,
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Zhe Liu [email protected] School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China
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Z. Liu
more research interests (Yang and Ni 2020; Liu and Yang 2020b; Tang 2020) were drawn to study and extend this topic. Especially, Ye and Yang (2020) applied uncertain time series to modelling cumulative numbers of COVID-19 infections. Uncertain regression analysis has been developed to address relationships between variables under the framework of uncertainty theory. Yao and Liu (2018) proposed least squares estimations for unknown parameters in uncertain multiple regression models. Motivated by this, researchers considered other estimations such as least absolute deviations estimations (Liu and Yang 2020a), Tukey’s biweight estimations (Chen 2020), and maximum likelihood estimations (Lio and Liu 2020). In addition, Lio and Liu (2018) provided the confidence interval for the response variable. To evaluate different uncertain regression models, cross-validation methods (Liu and Jia 2020; Liu 2019) have attracted some scholars’ att
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