Application of Extreme Value Theory to Crash Data Analysis

Area of Science:

• Statistical modeling
• Extreme value theory
• Data analysis

Background:

• Parametric models often fail to accurately estimate data tails.
• Standard methods may not capture extreme event distributions effectively.
• Accurate tail estimation is crucial for predicting rare phenomena.

Purpose of the Study:

• To apply extreme value theory (EVT) for improved tail distribution fitting.
• To enhance the predictive accuracy of models for extreme events.
• To analyze vehicle crash data using the peak-over-threshold (POT) approach.

Main Methods:

• Utilized the peak-over-threshold (POT) approach from extreme value theory.
• Implemented constraints for optimal threshold selection to minimize data sensitivity.
• Applied maximum likelihood estimation with the Generalized Pareto Distribution (GPD) for tail modeling.

Main Results:

• The POT approach with GPD provided superior tail distribution fits compared to overall distribution methods.
• Accurate estimation of extreme values and probabilities of rare events (e.g., high-speed crashes) was achieved.
• Demonstrated effectiveness in analyzing airbag inflator pressure, crash velocity, and mass distributions.

Conclusions:

• The peak-over-threshold approach is a valuable tool for analyzing vehicle crash, biomechanics, and injury tolerance data.
• EVT enhances the estimation of occurrence probabilities for extreme phenomena.
• This method improves the reliability of predictions for rare and high-impact events.