A Pathway Idea for Model Building.

Area of Science:

• Mathematical and Stochastic Modeling
• Data Analysis Across Scientific Disciplines

Background:

• Existing models often struggle to capture complex data distributions.
• The need for flexible modeling approaches that can adapt to diverse datasets is critical.

Purpose of the Study:

• To examine mathematical and stochastic models capable of transitioning between different functional forms.
• To demonstrate how pathway parameters enable capturing intermediate stages of distributions.
• To provide a unified framework for selecting appropriate models across various scientific domains.

Main Methods:

• Investigated a pathway of models including generalized beta (type-1 and type-2), generalized gamma, generalized Mittag-Leffler, and Lévy distributions.
• Utilized pathway parameters to connect different families of functions.
• Employed graphical representations to illustrate model behavior, including tail characteristics.

Main Results:

• Demonstrated that pathway models can approximate data from biological, physical, engineering, and social sciences.
• Showcased the ability of these models to capture transitional behaviors between established distributions.
• Visualized how pathway parameters influence model properties such as tail thickness and right-tail cutoff.

Conclusions:

• Flexible mathematical and stochastic models connected by pathway parameters offer a powerful tool for data analysis.
• These models provide a means to find suitable approximations, even for complex or transitional data patterns.
• The framework facilitates improved understanding of data characteristics through analysis of tail behaviors.