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SUMMARY A complex version of the Bingham distribution is defined on the unit complex sphere in Ck. Various statistical properties, including asymptotic normality under high concentration, are derived. Symmetries in the distribution make it a natural tool for the analysis of the shape of landmark data in two dimensions. Strengths and weaknesses of this approach are investigated. Links and contrasts with Bookstein co-ordinates are discussed. A hybrid approach to principal component analysis based on complex and real co-ordinates is suggested.
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John T. Kent (1994) studied this question.
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