Contagious statistical distributions: k-connections and applications in infectious disease environments

Area of Science:

• Statistics
• Probability Theory

Background:

• Contagious statistical distributions are crucial for modeling phenomena with dependencies.
• Existing research highlights strong associations among certain distributions (e.g., binomial, hypergeometric, Pólya, uniform) under specific conditions.
• Understanding these relationships aids in managing contagion and analyzing complex systems.

Purpose of the Study:

• To elucidate the strong association between specific contagious statistical distributions using factorial moments.
• To introduce novel methods for simplifying the analysis of these distributional relationships.
• To define and explore the properties of k-connected chains of distributions.

Main Methods:

• Utilizing factorial moments to establish and demonstrate the strong association between distributions.
• Introducing novel elements to simplify the derivation of these relationships.
• Generalizing the concept of distribution relationships to k-connected chains.

Main Results:

• Demonstrated a method using factorial moments to reveal strong associations among binomial, hypergeometric, Pólya, and uniform distributions.
• Introduced novel techniques that simplify the analysis of these statistical relationships.
• Defined and characterized k-connected chains of distributions, extending existing models.

Conclusions:

• Factorial moments provide a simplified and effective approach to understanding associations among contagious statistical distributions.
• The concept of k-connected chains offers a generalized framework for analyzing relationships in statistical modeling.
• The findings have implications for managing contagion and analyzing diverse real-world applications.