An elliptically symmetric angular Gaussian distribution
Paine, P.J.; Preston, Simon P.; Tsagris, Michail; Wood, Andrew T.A.
Simon P. Preston
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 elliptical 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.
|Journal Article Type||Article|
|Journal||Statistics and Computing|
|Peer Reviewed||Peer Reviewed|
|APA6 Citation||Paine, P., Preston, S. P., Tsagris, M., & Wood, A. T. (in press). An elliptically symmetric angular Gaussian distribution. Statistics and Computing, https://doi.org/10.1007/s11222-017-9756-4|
|Keywords||Angular Gaussian, Bootstrap, Kent distribution, Spherical distribution|
|Copyright Statement||Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0|
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
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