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Modelling such data requires flexible distribution families on the hypertorus. Common choices are the von Mises and the wrapped normal distributions. In this work we investigate the <jats:italic>inverse stereographic normal distribution<\/jats:italic> as an alternative distribution family both from a theoretical and applied perspective. We first generalize unimodality results to arbitrary dimensions by proving that the inverse stereographic normal distribution is unimodal if and only if all eigenvalues of the covariance matrix are less than or equal to 0.5. We then analyze the flexibility by fitting mixtures of shifted inverse stereographic normal distributions via gradient descent to several examples of toroidal data.<\/jats:p>","DOI":"10.1007\/s11222-025-10563-4","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T21:17:10Z","timestamp":1736803030000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An analysis of the modality and flexibility of the inverse stereographic normal distribution"],"prefix":"10.1007","volume":"35","author":[{"given":"Florian B.","family":"Hinz","sequence":"first","affiliation":[]},{"given":"Amr H.","family":"Mahmoud","sequence":"additional","affiliation":[]},{"given":"Markus A.","family":"Lill","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,13]]},"reference":[{"issue":"26","key":"10563_CR1","doi-asserted-by":"publisher","first-page":"8932","DOI":"10.1073\/pnas.0801715105","volume":"105","author":"W Boomsma","year":"2008","unstructured":"Boomsma, W., Mardia, K.V., Taylor, C.C., Ferkinghoff-Borg, J., Krogh, A., Hamelryck, T.: A generative, probabilistic model of local protein structure. 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