An elliptically symmetric angular Gaussian distribution

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

Abstract

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.

Citation

Paine, P., Preston, S. P., Tsagris, M., & Wood, A. T. (2018). An elliptically symmetric angular Gaussian distribution. Statistics and Computing, 28(3), 689-697. https://doi.org/10.1007/s11222-017-9756-4

• 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
• DOI: https://doi.org/10.1007/s11222-017-9756-4
• Keywords: Angular Gaussian, Bootstrap, Kent distribution, Spherical distribution
• Public URL: https://nottingham-repository.worktribe.com/output/861491
• Publisher URL: http://link.springer.com/article/10.1007%2Fs11222-017-9756-4
• Contract Date: May 23, 2017