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Complex elliptical distributions with application to shape analysis. (English) Zbl 1094.62062

Summary: 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 the 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 shapes and obtain confidence bounds and credible regions for shapes. The methodology is illustrated through an example where estimation of the shape of mouse vertebrae is desired.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62F15 Bayesian inference
62H12 Estimation in multivariate analysis
62H11 Directional data; spatial statistics
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