# Unveiling Uniform Shifted Power Law in Stochastic Human and Autonomous Driving Behavior

arXiv: https://arxiv.org/abs/2511.00659 · HTML: https://mlsanity.com/paper/2511.00659/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [SSP-DMGTimeNet: Physics-Constrained Learning for Spatiotemporal Trajectory Prediction of Vehicle Platoons](https://mlsanity.com/paper/2609.06961/) (2026)

## Abstract (arXiv)

Accurately simulating rare but safety-critical driving behaviors is essential for the evaluation and certification of autonomous vehicles (AVs). However, current models often fail to reproduce realistic collision rates when calibrated on real-world data, largely due to inadequate representation of long-tailed behavioral distributions. Here, we uncover a simple yet unifying shifted power law that robustly characterizes the stochasticity of both human-driven vehicle (HV) and AV behaviors, especially in the long-tail regime. The model adopts a parsimonious analytical form with only one or two parameters, enabling efficient calibration even under data sparsity. Analyzing large-scale, micro-level trajectory data from global HV and AV datasets, the shifted power law achieves an average R2 of 0.97 and a nearly identical tail distribution, uniformly fits both frequent behaviors and rare safety-critical deviations, significantly outperforming existing Gaussian-based baselines. When integrated into an agent-based traffic simulator, it enables forward-rolling simulations that reproduce realistic crash patterns for both HVs and AVs, achieving rates consistent with real-world statistics and improving the fidelity of safety assessment without post hoc correction. This discovery offers a unified and data-efficient foundation for modeling high-risk behavior and improves the fidelity of simulation-based safety assessments for mixed AV/HV traffic. The shifted power law provides a promising path toward simulation-driven validation and global certification of AV technologies.