Treffer: A DISCRIMINANT FRAMEWORK FOR MIXED AND HEAVY-TAILED DATA: EVALUATING THE GENERALIZED EXPONENTIAL POWER DISTRIBUTION WITH MODIFIED VARIANCE TRANSFORMATION.

This study proposes a flexible distributional framework the Generalized Exponential Power Distribution with Modified Variance Transformation (GEPDMVT) designed to improve classification accuracy in datasets characterized by skewness, heavy tails, and mixed-variable structures. Traditional classifiers like Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis QDA, and Support Vector Machine (SVM) often rely on restrictive assumptions such as normality and equal covariances, which may not hold in real-world data. The GEPDMVT modifies the variance structure of the multivariate exponential power distribution to align the shape and scale parameters, enhancing robustness. A novel Multivariate Discriminant Analysis (MVDA) classifier was developed based on this distribution and evaluated using simulated data across sample sizes (n = 20 to 10,000) and four benchmark datasets (Iris, Wine, Pima, and Glass). Results show that while MVDA slightly underperforms in small samples, it competes favourably and even surpasses existing methods in large datasets, achieving 99.92% accuracy at n = 10,000. MVDA outperformed all methods on the Wine dataset and was comparable in others, confirming its adaptability and resilience in heterogeneous and complex data scenarios. The findings demonstrate the potential of GEPDMVT-based MVDA in enhancing classification performance across a wide range of real-world applications, especially where data deviates from traditional parametric assumptions. [ABSTRACT FROM AUTHOR]

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