An elliptically symmetric angular Gaussian distribution
Phillip J. Paine, Simon Preston, Michail Tsagris, Andrew T. A. Wood · Statistics and Computing · 2017
We define a distribution on the unit sphere $$\mathbb {S}^{d-1}$$ called the elliptically symmetric angular Gaussian distribution. This distribution, which to our knowledge has not been studied before, is a subfamily of the angular Gaussian distribution closely analogous to the Kent subfamily of the general Fisher–Bingham distribution. Like the Kent distribution, it has ellipse-like contours, enabling modelling of rotational asymmetry about the mean direction, but it has the additional advantages of being simple and fast to simulate from, and having a density and hence likelihood that is easy and very quick to compute exactly. These advantages are especially beneficial for computationally intensive statistical methods, one example of which is a parametric bootstrap procedure for inference for the directional mean that we describe.