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![A comparison of convergence rates demonstrates that the Standard Kolmogorov metric stagnates due to tail noise, achieving a rate of [latex]n^{-0.25}[/latex], while a Weighted Metric-with a parameter of [latex]q=1.2[/latex]-successfully filters outliers to restore the optimal Gaussian convergence rate of [latex]n^{-0.5}[/latex], thereby accelerating model validation for Student-t distributions ([latex]\nu=2.5[/latex]).](https://arxiv.org/html/2601.04490v1/figs/compare_student.png)