{"ID":2842061,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.09959","arxiv_id":"2511.09959","title":"Flatness of location-scale-shape models under the Wasserstein metric","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.","short_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...","url_abs":"https://arxiv.org/abs/2511.09959","url_pdf":"https://arxiv.org/pdf/2511.09959v1","authors":"[\"Ayumu Fukushi\",\"Yoshinori Nakanishi-Ohno\",\"Takeru Matsuda\"]","published":"2025-11-13T04:40:27Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.DG\"]","methods":"[]","has_code":false}