Distributions conditioned on extrapolated events via copula and extreme value theory

Area of Science:

• Traffic Safety
• Probability Theory
• Statistical Modeling

Background:

• Road user interactions involve interdependent proximity and speed, often modeled using Copula distributions.
• Estimating marginal distributions for proximity is difficult due to multi-peaked histograms.

Purpose of the Study:

• To develop a robust method for approximating marginal distributions in traffic safety.
• To leverage extreme value theory for tail region approximation of proximity distributions.
• To enable conditional distribution estimation beyond observed data.

Main Methods:

• Partitioning the outcome space to apply extreme value theory.
• Utilizing Copula functions to model multivariate dependencies between road user proximity and speed.
• Employing extreme value theory for approximating tail distributions.

Main Results:

• The proposed method effectively approximates marginal distributions in monotone density regions.
• It allows for the estimation of conditional distributions even when specific conditions are absent in the dataset.
• Demonstrates enhanced accuracy in modeling extreme proximity events.

Conclusions:

• The integration of Copula and extreme value theory offers a powerful approach for traffic safety research.
• This methodology improves the understanding of road user behavior, particularly in critical scenarios.
• Enables more accurate risk assessment and the development of targeted safety interventions.