Graphical interface for goodness-of-fit evaluation and clustering of probability distributions in environmental...

Area of Science:

• Environmental Science
• Data Science
• Statistical Modeling

Background:

• Classical Goodness-of-Fit (GoF) tests like Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) show inconsistencies with heterogeneous environmental data.
• Previous approaches often analyzed clustering or mixture modeling independently, missing integrated automated estimation and adaptive weighting.

Purpose of the Study:

• To develop a unified framework integrating GoF evaluation, K-Means++ clustering, and a KS-weighted mixture model for improved environmental data distribution selection.
• To automate and enhance the robustness of distribution selection for complex environmental datasets.

Main Methods:

• A novel framework combining GoF testing, K-Means++ clustering, and a KS-weighted mixture model was developed.
• Seventeen univariate probability distributions were evaluated on Black Sea chlorophyll concentration data using KS, AD tests, and information criteria.
• A MATLAB GUI was created to automate clustering, estimation, model selection, and evaluation, demonstrating adaptability across various sample sizes and variables.

Main Results:

• The KS-weighted mixture model demonstrated stable and improved fits for complex, heterogeneous environmental datasets.
• The integrated framework enhanced the interpretability of distribution selection, reducing reliance on single-distribution assumptions.
• The MATLAB GUI proved adaptable and robust for automated environmental data analysis.

Conclusions:

• The developed framework and KS-weighted mixture model offer a robust solution for selecting appropriate probability distributions in environmental science.
• This approach enhances the monitoring of marine ecosystem health, supporting Sustainable Development Goal 14 (SDG 14) through improved modeling of chlorophyll concentration.
• The study positions mixture modeling as a valuable tool within environmental data analysis, offering a reproducible workflow via the MATLAB GUI.