Quantifying Deviations from Gaussianity with Application to Flight Delay Distributions

We propose a novel approach for quantifying deviations from Gaussianity by leveraging the Jensen-Shannon distance. Using stable distributions as a flexible framework, we analyze the effects of skewness and heavy tails in synthetic sequences. We employ phase-randomized surrogates as Gaussian references to systematically evaluate the statistical distance between this reference and stable distributions. Our methodology is validated using real flight delay datasets from major airports in Europe and the United States, revealing significant deviations from Gaussianity, particularly at high-traffic airports. These results highlight systematic air traffic management strategy differences between the two geographic regions.