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A note on inverse stereographic projection of elliptical distributions. (English) Zbl 06861780

Summary: This note concerns a family of distributions on the unit sphere obtained by inverse stereographic projection of elliptical distributions. We give some properties of these distributions with emphasis on the study of unimodality. This construction encompasses many known families of distributions on the unit sphere. Finally, we show that it is possible to define new families of unimodal distributions that allow anisotropy.

MSC:

62H11 Directional data; spatial statistics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:

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