The coronavirus disease 2019 (COVID-19) pandemic caused by the coronavirus strain has had massive global impact, and has interrupted economic and social activity. The daily confirmed COVID-19 cases in Saudi Arabia are shown to be affected by some explanatory variables that are recorded daily: recovered COVID-19 cases, critical cases, daily active cases, tests per million, curfew hours, maximal temperatures, maximal relative humidity, maximal wind speed, and maximal pressure. Restrictions applied by the Saudi Arabia government due to the COVID-19 outbreak, from the suspension of Umrah and flights, and the lockdown of some cities with a curfew are based on information about COVID-15. The aim of the paper is to propose some predictive regression models similar to generalized linear models (GLMs) for fitting COVID-19 data in Saudi Arabia to analyze, forecast, and extract meaningful information that helps decision makers. In this direction, we propose some regression models on the basis of inverted exponential distribution (IE-Reg), Bayesian (BReg) and empirical Bayesian regression (EBReg) models for use in conjunction with inverted exponential distribution (IE-BReg and IE-EBReg). In all approaches, we use the logarithm (log) link function, gamma prior and two loss functions in the Bayesian approach, namely, the zero-one and LINEX loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey's bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IE-Reg, IE-BReg, and IE-EBReg using some criteria, such as Akaike's information criterion (AIC), Bayesian information criterion (BIC), deviance (D), and mean squared error (MSE). Finally, we apply the collected data of the daily confirmed from March 23 - June 21, 2020 with the corresponding explanatory variables to the theoretical findings. IE-EBReg shows good model for the COVID-19 cases in Saudi Arabia compared with the other models.
Keywords: Bayesian generalized linear models; Huber's function; LINEX loss function; Tukey's bisquare function; empirical Bayesian; log link function; zero-one loss function.