Directional data arise in many fields, e.g. earth sciences, astronomy, meteorology and bioinformatics. The best-known distribution in directional statistics is the von Mises-Fisher (vMF) distribution. From a modelling point of view, however, the vMF distribution has the limitation that it is rotationally symmetric and it is therefore sometimes too restrictive as a model, depending on the particular dataset. An alternative to the vMF distribution, which has greater flexibility, is the Kent (1982, JRSSB) distribution. More recently, a new generalisation of the vMF distribution, called the scaled von Mises-Fisher distribution, has been proposed. In some respects the new distribution is more convenient to work with than the Kent distribution. The scaled vMF distribution will be compared and contrasted with the vMF and Kent distributions and the application of the new distribution in palaeomagnetism will be briefly described. The final part of the talk will discuss an approach to robust estimation on the sphere.
This talk is based on joint work with Janice Scealy (ANU).