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

Goodness-of-Fit (GoF) tests are applied to assess the suitability of probability distributions for environmental data. However, classical methods such as Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) often yield inconsistent outcomes in heterogeneous datasets. Previous studies employed clustering or mixture modeling separately, lacking integration with automated estimation and adaptive weighting. This study introduces a unified framework combining GoF evaluation, K-Means++ clustering, and a KS-weighted mixture model to enhance distribution selection. Seventeen univariate probability distributions were tested on chlorophyll concentration data from the Black Sea, with adequacy assessed via KS and AD tests and five information criteria. The framework was implemented via a MATLAB GUI to automate clustering, estimation, model selection, and evaluation steps. Tested across multiple sample sizes and extended to variables, the GUI demonstrated adaptability and robustness. Model performance showed that the KS-weighted mixture model provided stable fits for complex datasets, improving interpretability and reducing reliance on single-distribution assumptions.