Asymptotic properties of the Bingham distribution in arbitrary dimensions

Dawei Wu; Lei Zhang; Pingwen Zhang

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arXiv · 2609.07121

Asymptotic properties of the Bingham distribution in arbitrary dimensions

Dawei Wu·Lei Zhang·Pingwen Zhang

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Abstract

The Bingham distribution is widely used to model directional data with antipodal symmetry, and a central analytical object is the normalizing constant $Z$. Even though efficient algorithms exist for bounded or moderate parameter values, its singular behavior in general dimensions remains underexplored in the literature. We use a well-known integral representation to obtain asymptotic series of $Z$ and its derivatives, which lead to asymptotic profiles of its moments. Then, we also study the asymptotic behavior of the Bingham entropy, and prove its decomposition into an explicit logarithmic leading term and a Lipschitz continuous correction term. The degeneration of higher-dimensional Bingham distributions to their lower-dimensional counterparts is observed in both the asymptotic series and the entropy.

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Dawei Wu, Lei Zhang, Pingwen Zhang. 2026-09-07. Asymptotic properties of the Bingham distribution in arbitrary dimensions. https://arxiv.org/abs/2609.07121

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