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Directional statistics is the discipline of statistics that deals with directions (unit vectors in $\mathbb{R}^n$), axes (lines through the origin in $\mathbb{R}^n$) or rotations in $\mathbb{R}^n$.

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This is more like an extended comment rather than a full answer. I am working on a problem that is, I think, somewhat related to the question so I share my thoughts. In what sense are you interested …
answered Sep 26 '14 by Kristóf Marussy