The complex Watson distribution and shape analysis

The complex Watson distribution is an important simple distribution on the complex sphere which is used in statistical shape analysis. We describe the density, obtain the integrating constant and provide large sample approxim ations. Maximum likelihood estimation and hypothesis testing procedures for one and two samples are described. The particular connection with shape an alysis is discussed and we consider an application examining shape differen ces between normal and schizophrenic brains. We make some observations abou t Bayesian shape inference and finally we describe a more general rotationa lly symmetric family of distributions.