Discrete Harris Extended Inverse Exponential Distribution and Its Applications to COVID-19 Data

In this paper, we introduce a novel discrete probability distribution, referred to as the discrete Harris extended inverse exponential distribution, and explore its fundamental properties. We demonstrate that the proposed model serves as a generalization of the discrete Marshall-Olkin inverted exponential distribution. Key theoretical characteristics of the proposed model are derived, including its probability generating function, moments, hazard rate function, cumulative hazard rate function, reversed hazard rate function, mean residual life, and quantile function. Parameter estimation is performed using various estimation techniques, including the maximum likelihood estimation, Anderson-Darling, Cramér-von Mises, ordinary least squares, and weighted least squares. In addition, a simulation study is conducted to evaluate the performance of the estimators. The applicability of the proposed distribution is further illustrated through its fit to two discrete real-world data sets of COVID-19 from China and Pakistan.