A note on the geodesic normal distribution on the sphere
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908146544410624 |
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| author | Chacón, José E. Meilán-Vila, Andrea |
| author_facet | Chacón, José E. Meilán-Vila, Andrea |
| contents | 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 hypersphere 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14899 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the geodesic normal distribution on the sphere Chacón, José E. Meilán-Vila, Andrea Statistics Theory Metric Geometry Probability 60E05, 62E10, 62H11 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 hypersphere 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. |
| title | A note on the geodesic normal distribution on the sphere |
| topic | Statistics Theory Metric Geometry Probability 60E05, 62E10, 62H11 |
| url | https://arxiv.org/abs/2411.14899 |