Arctan-skewing: a new skewing scheme on the hypertorus
Abstract
In this paper we propose and study arctan-skewing, a general approach to skew any symmetric distribution on the unit hypertorus. Arctan-skewing retains the main advantages of the popular sine-skewing mechanism, but improves on it by overcoming its two major limitations. These are a condition on the skewness parameter and a singular Fisher Information matrix in the vicinity of symmetry when combined with well-known symmetric models from the literature such as the circular von Mises or bivariate Cosine models. Arctan-skewing thus represents a compelling alternative to model skewed data on the circle and torus, notably from the field of protein bioinformatics. After a thorough investigation of its stochastic properties, we present a maximum likelihood estimation procedure and devise optimal tests for symmetry against our new class of skewed alternatives. Finally we show that arctan-skewed models better fit protein data compared to their sine-skewed counterparts.
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BibTeX
@misc{ley2026arctanskewing,
title = {{Arctan-skewing: a new skewing scheme on the hypertorus}},
author = {Christophe Ley and Sophia Loizidou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13310},
eprint = {2610.13310},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13310},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Arctan-skewing: a new skewing scheme on the hypertorus
AU - Christophe Ley
AU - Sophia Loizidou
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13310
UR - https://arxiv.org/abs/2610.13310
AB - In this paper we propose and study arctan-skewing, a general approach to skew any symmetric distribution on the unit hypertorus. Arctan-skewing retains the main advantages of the popular sine-skewing mechanism, but improves on it by overcoming its two major limitations. These are a condition on the skewness parameter and a singular Fisher Information matrix in the vicinity of symmetry when combined with well-known symmetric models from the literature such as the circular von Mises or bivariate Cosine models. Arctan-skewing thus represents a compelling alternative to model skewed data on the circle and torus, notably from the field of protein bioinformatics. After a thorough investigation of its stochastic properties, we present a maximum likelihood estimation procedure and devise optimal tests for symmetry against our new class of skewed alternatives. Finally we show that arctan-skewed models better fit protein data compared to their sine-skewed counterparts.
ER -