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arXiv · 2610.13310

Arctan-skewing: a new skewing scheme on the hypertorus

Christophe Ley·Sophia Loizidou
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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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Christophe Ley, Sophia Loizidou. 2026-10-09. Arctan-skewing: a new skewing scheme on the hypertorus. https://arxiv.org/abs/2610.13310

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