Scaled von Mises-Fisher distributions

The best-known distribution on the sphere for statistical purposes is the Fisher, or von Mises-Fisher, distribution. However, this distribution possesses rotational symmetry which is too strong an assumption for many applications. This seminar presents a new distribution, called the scaled von Mises-Fisher (SvMF) distribution, which has ellipse-like contours yet has a simple normalising constant. The SvMF distribution will be compared and contrasted with two other distributions on the sphere with ellipse-like symmetry, the Kent and the elliptically symmetric angular Gaussian distributions. A main goal for developing this distribution is to use it for regression modelling of paleomagnetic data with a directional response. Applications to such data will be described. This is joint work with Janice Scealy (ANU).