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A note on the geodesic normal distribution on the sphere

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  • Chacón, José E.
  • Meilán-Vila, Andrea

Abstract

This paper presents an alternative formulation of the geodesic normal distribution on the sphere, building on the work of Hauberg (2018). While the isotropic version of this distribution is naturally defined on the sphere, the anisotropic version requires projecting points from the sphere onto the tangent space. In contrast, our approach removes the dependence on the tangent space and defines the geodesic normal distribution directly on the sphere. Moreover, we demonstrate that the density contours of this distribution are exactly ellipses on the sphere, providing intriguing alternative characterizations for describing this locus of points.

Suggested Citation

  • Chacón, José E. & Meilán-Vila, Andrea, 2026. "A note on the geodesic normal distribution on the sphere," Statistics & Probability Letters, Elsevier, vol. 227(C).
    • Handle: RePEc:eee:stapro:v:227:y:2026:i:c:s0167715225001774
    DOI: 10.1016/j.spl.2025.110532
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    References listed on IDEAS

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    1. You, Kisung & Suh, Changhee, 2022. "Parameter estimation and model-based clustering with spherical normal distribution on the unit hypersphere," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. J. L. Scealy & Andrew T. A. Wood, 2019. "Scaled von Mises–Fisher Distributions and Regression Models for Paleomagnetic Directional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1547-1560, October.
    3. Jean-François Coeurjolly & Nicolas Bihan, 2012. "Geodesic normal distribution on the circle," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 977-995, October.
    4. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
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