Quantifying Deviations from Gaussianity with Application to Flight Delay Distributions

Area of Science:

• Statistics
• Data Analysis
• Air Traffic Management

Background:

• Gaussian distribution is a common assumption in data analysis.
• Deviations from Gaussianity, characterized by skewness and heavy tails, can impact model accuracy.
• Understanding these deviations is crucial for complex systems like air traffic.

Purpose of the Study:

• To develop a novel method for quantifying deviations from Gaussianity.
• To analyze the impact of skewness and heavy tails using stable distributions.
• To validate the methodology with real-world flight delay data.

Main Methods:

• Utilized Jensen-Shannon distance to measure statistical divergence.
• Employed stable distributions as a flexible modeling framework.
• Used phase-randomized surrogates as Gaussian references for comparison.
• Validated the approach with European and US flight delay datasets.

Main Results:

• Demonstrated significant deviations from Gaussianity in flight delay data.
• Identified particularly pronounced deviations at high-traffic airports.
• Observed systematic differences in air traffic patterns between Europe and the US.

Conclusions:

• The proposed Jensen-Shannon distance method effectively quantifies non-Gaussianity.
• Flight delays exhibit substantial deviations from Gaussian assumptions, especially in busy airspaces.
• The findings suggest underlying differences in air traffic management strategies between Europe and the US.