arXiv:2610.36227 · v1

Directional Statistics on Circles and Spheres: A New Angle on Data

首次提交 2026-10-27 04:05

版本更新 2026-10-27 04:05

雷达观测 2026-10-29 00:35

摘要

Two compass bearings near north can have an ordinary arithmetic mean pointing south: the difficulty is that angles live on a circle, not a straight line. Using real wind observations, diffusion-MRI orientations, and geometric examples from machine learning, this article introduces circular and axial averages, directional variability, and probability models on circles and spheres. The guiding principle is to identify the geometry and symmetries of the observations before choosing a statistical method.

作者备注：11 pages, 5 figures. Expository article with real-data examples and reproducible R code. Submitted to Resonance: Journal of Science Education