An elliptically symmetric angular Gaussian distribution |
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Authors: | P J Paine S P Preston M Tsagris Andrew T A Wood |
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Institution: | 1.School of Mathematics and Statistics,University of Sheffield,Sheffield,UK;2.School of Mathematical Sciences,University of Nottingham,Nottingham,UK;3.Department of Computer Science,University of Crete,Heraklion,Greece |
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Abstract: | 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. |
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