Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and...

Area of Science:

• Computational statistics and probability theory.
• Development of scientific software and educational technology.

Background:

• Probability distributions are fundamental to modeling natural processes and physical phenomena.
• A vast number of distributions exist, but only a subset is commonly used.
• Existing tools lack comprehensive infrastructure for exploring and applying diverse distributions.

Purpose of the Study:

• To introduce the Distributome, a novel computational and graphical infrastructure.
• To facilitate the discovery, exploration, and application of a wide range of probability distributions.
• To support both computational research and science education.

Main Methods:

• Development of an extensible, open-source, community-built infrastructure accessible online.
• Implementation of interfaces for human and machine traversal, search, and navigation of distributions.
• Integration of tools for distribution modeling, analysis of inter-distribution relations, and computational utilization.

Main Results:

• The Distributome provides a unified framework for accessing and utilizing common probability distributions.
• Demonstrated applications in computational research, including simulation, data analysis, and model-fitting.
• Showcased potential for enhancing STEM education through interactive web applications and improved learning assessments.

Conclusions:

• The Distributome infrastructure significantly enhances the accessibility and application of probability distributions.
• It offers valuable resources for advancing computational modeling and enriching STEM education.
• The open-source and community-driven nature ensures portability, extensibility, and compatibility with modern web standards.