Journal
STATISTICS AND COMPUTING
Volume 28, Issue 3, Pages 689-697Publisher
SPRINGER
DOI: 10.1007/s11222-017-9756-4
Keywords
Angular Gaussian; Bootstrap; Kent distribution; Spherical distribution
Funding
- Engineering and Physical Sciences Research Council [EP/K022547/1]
- Engineering and Physical Sciences Research Council [EP/K022547/1] Funding Source: researchfish
- EPSRC [EP/K022547/1] Funding Source: UKRI
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We define a distribution on the unit sphere 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.
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