Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.09959 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917078138617856 |
|---|---|
| author | Fukushi, Ayumu Nakanishi-Ohno, Yoshinori Matsuda, Takeru |
| author_facet | Fukushi, Ayumu Nakanishi-Ohno, Yoshinori Matsuda, Takeru |
| contents | In Wasserstein geometry, one-dimensional location-scale models are flat both intrinsically and extrinsically-that is, they are curvature-free as well as totally geodesic in the space of probability distributions. In this study, we introduce a class of one-dimensional statistical models, termed the location-scale-shape model, which generalizes several distributions used in extreme-value theory. This model has a shape parameter that specifies the tail heaviness. We investigate the Wasserstein geometry of the location-scale-shape model and show that it is intrinsically flat but extrinsically curved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flatness of location-scale-shape models under the Wasserstein metric Fukushi, Ayumu Nakanishi-Ohno, Yoshinori Matsuda, Takeru Statistics Theory Differential Geometry 62F99 (Primary) 53B20 (Secondary) In Wasserstein geometry, one-dimensional location-scale models are flat both intrinsically and extrinsically-that is, they are curvature-free as well as totally geodesic in the space of probability distributions. In this study, we introduce a class of one-dimensional statistical models, termed the location-scale-shape model, which generalizes several distributions used in extreme-value theory. This model has a shape parameter that specifies the tail heaviness. We investigate the Wasserstein geometry of the location-scale-shape model and show that it is intrinsically flat but extrinsically curved. |
| title | Flatness of location-scale-shape models under the Wasserstein metric |
| topic | Statistics Theory Differential Geometry 62F99 (Primary) 53B20 (Secondary) |
| url | https://arxiv.org/abs/2511.09959 |