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An elliptically symmetric angular Gaussian distribution

Paine, P.J.; Preston, Simon P.; Tsagris, Michail; Wood, Andrew T.A.


P.J. Paine

Professor of Statistics and Applied Mathematics

Michail Tsagris

Andrew T.A. Wood


We define a distribution on the unit sphere Sd−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.


Paine, P., Preston, S. P., Tsagris, M., & Wood, A. T. (2018). An elliptically symmetric angular Gaussian distribution. Statistics and Computing, 28(3), 689-697.

Journal Article Type Article
Acceptance Date May 9, 2017
Online Publication Date May 22, 2017
Publication Date 2018-05
Deposit Date May 23, 2017
Publicly Available Date May 23, 2017
Journal Statistics and Computing
Print ISSN 0960-3174
Electronic ISSN 1573-1375
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 28
Issue 3
Pages 689-697
Keywords Angular Gaussian, Bootstrap, Kent distribution, Spherical distribution
Public URL
Publisher URL


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