The new discrete distribution with application to COVID-19 Data.

Area of Science:

• Statistics
• Epidemiology
• Probability Theory

Background:

• Discrete distributions are crucial for analyzing count data, such as disease incidence.
• The Marshall-Olkin family and inverse Toppe-Leone distribution are important in statistical modeling.
• Modeling infectious diseases like COVID-19 requires robust statistical tools.

Purpose of the Study:

• To introduce a novel two-parameter discrete distribution, the discrete Marshall-Olkin Inverse Toppe-Leone (DMOITL) distribution.
• To model COVID-19 data from various countries (Italy, Puerto Rico, Singapore).
• To evaluate the performance of classical (maximum likelihood) and Bayesian estimation methods for the new distribution.

Main Methods:

• A new discrete distribution was derived using the survival discretization method.
• Properties such as reliability measures and moment functions were derived.
• Parameter estimation was performed using maximum likelihood and Bayesian methods.
• Monte Carlo simulations were used to compare estimation techniques.
• Highest posterior density (HPD) credible intervals were utilized with Markov Chain Monte Carlo (MCMC).

Main Results:

• The DMOITL distribution was successfully formulated and its properties derived.
• Both maximum likelihood and Bayesian methods provided valid parameter estimations.
• Simulation results offered insights into the comparative performance of the estimation techniques.
• HPD intervals demonstrated the utility of MCMC in assessing parameter uncertainty.

Conclusions:

• The DMOITL distribution offers a flexible new tool for count data analysis, including epidemiological modeling.
• The study validates the application of both maximum likelihood and Bayesian estimation for the DMOITL distribution.
• The findings contribute to the statistical methodology for disease modeling and parameter estimation.