Weighted power Maxwell distribution: Statistical inference and COVID-19 applications

Area of Science:

• Statistics and Data Science
• Machine Learning

Background:

• Novel statistical distributions are crucial for advancing data science and machine learning.
• Existing distributions may lack desirable mathematical properties for certain applications.

Purpose of the Study:

• To introduce and analyze a new statistical distribution with superior properties.
• To assess the fuzzy reliability function of the novel distribution.
• To demonstrate the utility of the new distribution in data science and machine learning.

Main Methods:

• Mathematical analysis of the distribution's properties, including its cumulative distribution function (CDF) and probability density function (PDF).
• Development and assessment of a fuzzy reliability function.
• Application of both traditional and Bayesian methodologies for parameter estimation.
• Comparative analysis of classical and Bayesian estimators using a test setup.
• Empirical validation using Covid-19 death data.

Main Results:

• A novel statistical distribution with a closed-form CDF and PDF was successfully developed.
• The fuzzy reliability function was mathematically characterized.
• Both classical and Bayesian estimation methods were evaluated for their effectiveness.
• The new distribution demonstrated its applicability and effectiveness through Covid-19 death data analysis.

Conclusions:

• The proposed novel distribution offers significant advantages, including closed-form functions, making it highly valuable for data science.
• The distribution is particularly useful for machine learning applications.
• The study successfully validated the new model's performance using real-world data, highlighting its practical utility.