Flatness of location-scale-shape models under the Wasserstein metric
Abstract
Abstract 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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Statistical Mechanics and Entropy
Random Matrices and Applications
Publication details
- Journal / source
- Information Geometry
- Publisher
- Springer Science and Business Media LLC
- Volume
- 9
- Issue
- 2
- Pages
- 593-619
- Publication date
- 12 May 2026
- Language
- EN