# Distributions on an ellipsoid?

This is my first question. I hope somebody can help me with this. I am after the name of a distribution and references would be incredibly useful. I am looking for a generalisation of the von-Mises distribution (on the unit circle) or von-Mises Fisher distribution (on the unit sphere) to an ellipsoid. I assume this has been done before, but I have not been successful in finding any relevant literature.

• In what way do you wish to make the analogue on an ellipse? What properties should the function have and how will they be defined? The reason that I am asking is because for circular distribution I am always thinking about a parameter with a uniform metric like the angle, ranging from 0 to 2pi. But what is it for an ellipse? Also an angle ranging from 0 to 2pi, but with some different metric? – Sextus Empiricus May 19 '20 at 7:59
• Hi, thank you for responding. I am interested in distributions akin to the ones above, but on an ellipsoid not an ellipse. Although, if you happen to know generalisations to an ellipse (for vM), than that would also be useful. What I am looking for is a symmetric unimodal distribution that is like the normal distribution in Euclidean space, but on an ellipisoid. I did try searching, but couldn't find any distributions defined on an ellipisoid or even an ellipse. – dataMonkey May 19 '20 at 8:21
• "that is like the normal distribution in Euclidean space" What do you mean by 'is like'? – Sextus Empiricus May 19 '20 at 8:37
• Because an ellipsoid is a sphere when the coordinate axes are aligned with the ellipsoid's axes and suitably scaled, there's nothing to do: all spherical distributions can be applied to ellipsoids without modification. That might explain why it's hard to find literature specific to ellipsoids. – whuber May 19 '20 at 11:34
• @whuber: do you want to post your comment(s) as an answer? Better to have a short answer than no answer at all. Anyone who has a better answer can post it. – Stephan Kolassa Jul 24 '20 at 6:49