Proposing a Deep Learning based Regional Goodness-of-Fit test for identification of regional distribution

Regional frequency analysis relies heavily on robust goodness-of-fit (GOF) testing for selecting an appropriate probability distribution, which directly influences the accuracy of estimated quantiles. However, existing statistical approaches often involve strong assumptions and computational overheads that limit their effectiveness, particularly for large regional datasets. The widely used L-moment-based approach requires scaling each site’s data by its own mean, which raises concerns about potential distortion of the original distributional characteristics. To overcome this limitation, the present study proposes a novel Deep Learning (DL)-based GOF test that identifies the regional distribution without performing mean-based scaling. The proposed methodology employs a Deep Neural Network (DNN) trained to classify regional distributions based on the distinctive behavior of Generalized Extreme Value, Generalized Pareto, Generalized Logistic, Generalized Normal, and Pearson Type III distributions under specific mathematical transformations. These transformations yield distribution-specific signatures that form the basis of the DNN training process. For a given dataset, the transformations are applied, and kernel density estimates derived from the transformed data are used as inputs to a pre-trained DNN model to identify the most suitable regional distribution. The DNN classifier achieved an accuracy of 95.09% on the training dataset and 94.86% on the test dataset. A comprehensive simulation study was conducted for multiple regional configurations to assess the performance of the proposed DL-based GOF test. The results were compared against the conventional L-moment-based GOF approach. The proposed method demonstrated comparable classification accuracy for smaller region sizes and marginally improved accuracy for larger datasets. The proposed DL-based GOF framework shows significant promise, particularly due to its substantially lower computational cost compared to the conventional L-moment methodology. The findings suggest that this approach can facilitate accurate and efficient estimation of quantiles, thereby supporting informed decision-making planning, management and risk assessment.