Presents new and up-dated material on both the underlying theory and the practical methodology of directional statistics, helping the reader to utilise and develop the techniques appropriate to their work.
The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of good-of-fit, inference on von Mises distributions and non-parametric methods. The second part considers statistics on spheres of arbitrary dimension, and includes a detailed account of inference on the main distributions on spheres. Recent material on correlation, regression time series, robust techniques, bootstrap methods, density estimation and curve fitting is presented. The third part considers statistics on more general sample spaces, in particular rotation groups, Stiefel manifolds, Grassmann manifolds and complex projective spaces. Shape analysis is considered from the perspective of directional statistics.
Written by leading authors in the field, this text will be invaluable not only to researchers in probability and statistics interested in the latest developments in directional statistics, but also to practitioners and researchers in many scientific fields, including astronomy, biology, computer vision, earth sciences and image analysis.
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alternatives analogue angles angular central Gaussian Appendix approximation axial data Cauchy distributions central Gaussian distributions characteristic function circular data combined sample complex Bingham distribution concentration parameter conditional distribution conﬁdence regions conﬁguration considered in Section corresponding data set decomposition deﬁned denotes directional statistics distribution function eigenvalues eigenvector exponential model ﬁnd ﬁrst Fisher distribution follows generalisation given gives Hg for large high-concentration independent Jupp Kent landmarks large values large-sample asymptotic distribution likelihood ratio statistic likelihood ratio test manifolds Mardia maximum likelihood estimate mean resultant length Mises distribution Mises-Fisher distribution null distribution null hypothesis observations obtained orthogonal plot points preshape probability density function Procrustes quantiles random sample random variables Rayleigh test reﬂection regression rejects Hg rejects uniformity respectively rotational symmetry sample mean sample mean direction satisﬁes score test space sphere spherical data Stiefel manifolds Table test of uniformity triangles uniform distribution uniform scores unit vectors variance Watson distribution