Advances in the characterization of curvature of two-dimentional probability manifolds
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911762917359616 |
|---|---|
| author | Giacopelli, Giuseppe De Gaetano, Andrea |
| author_facet | Giacopelli, Giuseppe De Gaetano, Andrea |
| contents | In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information Geometry sense even when the generatrix is non-even or non-smooth. A novel formula is obtained for the computation of curvature in the case of exponential families: this formula implies some new flatness criteria in dimension 2. Finally, it is observed that many two parameter distributions, widely used in applications, are locally hyperbolic, which highlights the role of hyperbolic geometry in the study of commonly employed probability manifolds. These results have benefited from the use of explainable computational tools, which can substantially boost scientific productivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12270 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Advances in the characterization of curvature of two-dimentional probability manifolds Giacopelli, Giuseppe De Gaetano, Andrea Statistics Theory Probability In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information Geometry sense even when the generatrix is non-even or non-smooth. A novel formula is obtained for the computation of curvature in the case of exponential families: this formula implies some new flatness criteria in dimension 2. Finally, it is observed that many two parameter distributions, widely used in applications, are locally hyperbolic, which highlights the role of hyperbolic geometry in the study of commonly employed probability manifolds. These results have benefited from the use of explainable computational tools, which can substantially boost scientific productivity. |
| title | Advances in the characterization of curvature of two-dimentional probability manifolds |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2401.12270 |