The complex Watson distribution and shape analysis

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 61; no. 4; pp. 913 - 926
• Main Authors: Mardia, K. V., Dryden, I. L.
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers Ltd 1999; Blackwell Publishers; Blackwell; Royal Statistical Society
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Approximation; Brain; Complex Bingham distribution; Complex sphere; Complex Watson distribution; Distribution; Distribution theory; Eigenvalues; Exact sciences and technology; G. S. Watson; Geometric shapes; Inference; Landmarks; Mathematical economics; Mathematics; Maximum likelihood; Maximum likelihood estimation; Nonparametric inference; Parametric inference; Probability and statistics; Ratio test; Samples; Schizophrenia; Sciences and techniques of general use; Shape; Shape analysis; Statistics; Symmetry; Bayes estimation; Hypothesis test; Parameter estimation; Statistical estimation; Maximum likelihood; Sampling
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/1467-9868.00210

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 approximations. Maximum likelihood estimation and hypothesis testing procedures for one and two samples are described. The particular connection with shape analysis is discussed and we consider an application examining shape differences between normal and schizophrenic brains. We make some observations about Bayesian shape inference and finally we describe a more general rotationally symmetric family of distributions.