Some families of distributions on higher shape spaces (Q2809705)

The chapter under review is in the volume dedicated to Kanti Mardia, who has been influential in the development of shape analysis. It starts by describing the main parametric families of distributions that have been used on shape spaces. The authors conclude that on higher shape spaces only a few families of distributions have been explored. They proceed by introducing generalizations of the complex angular central Gaussian distributions. Next, remarking that the introduced distributions and the shape Bingham distributions [the authors, J. Multivariate Anal. 88, No. 1, 163--176 (2004; Zbl 1041.62047)] are invariant under reflection, the authors modify them to the end of obtaining shape distributions that allow departures from such symmetry. Also, a test of symmetry under reflection is proposed.NEWLINENEWLINEFor the entire collection see [Zbl 1332.62011].