A New Generalized- X Family for Analyzing the COVID-19 Data Set: a Case Study

Abstract

Nowadays, researchers in applied sectors are highly motivated to propose and study new generalizations of the existing distributions to provide the best fit to data. To provide a close fit to data in numerous sectors, a series of new distributions have been proposed. In this study, we propose a new family called the new generalized- $X$ (for short, “NG- $X$ ”) family of distributions. Based on the NG- $X$ method, a novel modification of the Weibull model called the new generalized-Weibull (for short, “NG-Weibull”) distribution is studied. The heavy-tailed characteristics of the NG- $X$ distributions are derived. The maximum likelihood estimators of the NG- $X$ distributions are also obtained. Based on the special case (i.e., NG-Weibull) of the NG- $X$ family, a simulation study is provided. The practical performance of the new NG-Weibull model is assessed by analyzing the COVID-19 data set. The fitting results of the NG-Weibull model are compared with three other competing models. Based on certain statistical measures, it is observed that the NG-Weibull model is the best competitive model.