Coronaviruses are enveloped RNA viruses from the Coronaviridae family affecting neurological, gastrointestinal, hepatic and respiratory systems. In late 2019 a new member of this family belonging to the Betacoronavirus genera (referred to as COVID-19) originated and spread quickly across the world calling for strict containment plans and policies. In most countries in the world, the outbreak of the disease has been serious and the number of confirmed COVID-19 cases has increased daily, while, fortunately the recovered COVID-19 cases have also increased. Clearly, forecasting the "confirmed" and "recovered" COVID-19 cases helps planning to control the disease and plan for utilization of health care resources. Time series models based on statistical methodology are useful to model time-indexed data and for forecasting. Autoregressive time series models based on two-piece scale mixture normal distributions, called TP-SMN-AR models, is a flexible family of models involving many classical symmetric/asymmetric and light/heavy tailed autoregressive models. In this paper, we use this family of models to analyze the real world time series data of confirmed and recovered COVID-19 cases.

In this research, the number of patients with Covid-19 and the number of deaths due to this disease in France, Germany, Iran, Italy, Spain, United Kingdom, and Unites States America are considered. First, the relations between the considered countries are studied using Pearson’s correlation. Then, based on the spread rate of Covid-19, these countries are categorized using principal component analysis.

The numbers of confirmed cases of new coronavirus (Covid-19) are increased daily in different countries. To determine the policies and plans, the study of the relations between the distributions of the spread of this virus in other countries is critical. In this work, the distributions of the spread of Covid-19 in Unites States America, Spain, Italy, Germany, United Kingdom, France, and Iran were compared and clustered using fuzzy clustering technique. At first, the time series of Covid-19 datasets in selected countries were considered. Then, the relation between spread of Covid-19 and population's size was studied using Pearson correlation. The effect of the population's size was eliminated by rescaling the Covid-19 datasets based on the population's size of USA. Finally, the rescaled Covid-19 datasets of the countries were clustered using fuzzy clustering. The results of Pearson correlation indicated that there were positive and significant between total confirmed cases, total dead cases and population's size of the countries. The clustering results indicated that the distribution of spreading in Spain and Italy was approximately similar and differed from other countries.