Goodness-of-Fit and Composite Score Based Clustering for Optimal Probability Distribution

This study introduces an integrative framework that combines Goodness-of-Fit (GoF) statistics with Composite Score–based clustering to evaluate the suitability of probability distributions for environmental data. Traditional GoF methods, such as the Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) tests, often yield inconsistent results due to their differing sensitivities and methodological limitations. To overcome this, the proposed approach integrates KS and AD with five information-theoretic criteria—Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected AIC (AICc), Consistent AIC (CAIC), and Hannan–Quinn Criterion (HQC)—to construct a robust Composite Score. This unified score is applied within a clustering framework to systematically identify optimal probability distributions. The method is demonstrated using chlorophyll-a concentration data from the Black Sea, a region characterized by strong spatiotemporal variability. Clustering evaluation metrics, including the Silhouette Score and Davies–Bouldin Index, confirm the stability and interpretability of the resulting clusters. The analysis identifies Log-Normal, Nakagami, Weibull, Normal, and Logistic distributions as the best fits in Cluster 1; Rayleigh in Cluster 2; and the t Location–Scale distribution in Cluster 3. These findings demonstrate the framework’s effectiveness in capturing both asymmetric and heavy-tailed characteristics in environmental datasets. The approach is generalizable across domains such as hydrology, climatology, epidemiology, and economics, offering a scalable and objective decision-support tool for researchers handling complex statistical data. Moreover, this study supports Sustainable Development Goal (SDG) 14.1 by enhancing statistical tools for marine ecosystem monitoring through improved modeling of chlorophyll concentration—a key indicator of ocean health.