A new extended Chen distribution for modelling COVID-19 data

Area of Science:

• Statistics
• Probability Theory
• Biostatistics
• Epidemiological Modeling

Background:

• Existing statistical distributions often lack the flexibility to accurately model diverse real-world data patterns.
• The need for distributions capable of capturing various hazard rate shapes (increasing, decreasing, bathtub) is critical in fields like epidemiology.
• The Chen and exponentiated Chen distributions serve as foundational models but have limitations in capturing complex data behaviors.

Purpose of the Study:

• To introduce and define a novel, flexible statistical distribution: the Topp-Leone Exponentiated Chen (TLEC) distribution.
• To establish the theoretical statistical properties of the TLEC distribution, including its PDF, CDF, moments, and hazard rate.
• To demonstrate the TLEC distribution's superior performance in modeling real-world data, specifically COVID-19 datasets.

Main Methods:

• Derivation of key statistical properties: probability density function (PDF), cumulative distribution function (CDF), moments, and hazard rate function.
• Application of Maximum Likelihood Estimation (MLE) for parameter estimation of the TLEC distribution.
• Conducting simulation studies to validate the efficiency and robustness of the MLE method for TLEC parameters.

Main Results:

• The TLEC distribution was successfully derived, encompassing its fundamental statistical characteristics.
• Simulation studies confirmed the efficiency of the Maximum Likelihood Estimation method for parameter estimation.
• Application to COVID-19 data demonstrated that the TLEC distribution provides a better fit than several competing statistical models.

Conclusions:

• The proposed Topp-Leone Exponentiated Chen (TLEC) distribution offers enhanced flexibility and superior fitting capabilities for complex datasets.
• The TLEC distribution proves effective in modeling real-world phenomena, particularly demonstrated by its performance with COVID-19 data.
• This novel distribution represents a significant advancement for accurate and flexible statistical modeling in various scientific applications.