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Directional Statistics on Circles and Spheres: A New Angle on Data
Abstract
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.
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BibTeX
@misc{kulkarni2026directional,
title = {{Directional Statistics on Circles and Spheres: A New Angle on Data}},
author = {Siddhesh Kulkarni},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36227},
eprint = {2610.36227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36227},
}
RIS
TY - UNPB
TI - Directional Statistics on Circles and Spheres: A New Angle on Data
AU - Siddhesh Kulkarni
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36227
UR - https://arxiv.org/abs/2610.36227
AB - 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.
ER -