The new discrete distribution with application to COVID-19 Data

Abstract

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall–Olkin family and the inverse Toppe–Leone distribution, both of them were used to introduce a new discrete distribution called Marshall–Olkin inverse Toppe–Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall–Olkin Inverse Toppe–Leone (DMOITL). This new model possesses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte-Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).

Keywords

• Survival discretization
• Marshall–Olkin family
• Inverse Toppe–Leone
• Maximum likelihood estimation
• Bayesian estimation