Complex elliptical distributions with application to shape analysis

We introduce a general class of complex elliptical distributions on a complex sphere that includes many of the most commonly used distributions, like the complex Watson, Bingham, angular central Gaussian and several others. We study properties of this family of distributions and apply the distribution theory for modeling shapes in two dimensions. We develop maximum likelihood and Bayesian methods of estimation to describe shape and obtain confidence bounds and credible regions for shapes. The methodology is illustrated through an example where estimation of shape of mouse vertebrae is desired.