Directional Statistics. Wiley Series in Probability and Statistics

  • ID: 2176085
  • Book
  • 456 Pages
  • John Wiley and Sons Ltd
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Observations which are directions, axes or rotations occur in many sciences, including astronomy, biology, earth sciences, image analysis, and medicine. To analyse such data it is necessary to use the techniques of directional statistics, in which the special structure of circles, spheres and rotation groups is taken into account. This book gives a unified and comprehensive account of directional statistics, presenting both the underlying statistical theory and the practical methodology. The book is divided into three parts. The first part concentrates on statistics on the circle. Topics covered include tests of uniformity, tests of goodness–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. 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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I: Circular data;

2. Summary Statistics;

3 Basic Concepts and Models;

4 Fundamental Theorems and Distribution Theory;

5 Point Estimation;

6 Tests of Uniformity and Tests of Goodness–of–Fit;

7. Tests on von Mises Distributions

8 Non–parametric Methods

9 Distributions on Spheres

10 Inference on Spheres

11 Correlation and Regression

12 Modern Methodology

13 General Sample Spaces

14 Shape Analysis
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"This book provides essential material that is very timely and interesting and provides an excellent treatise on the theory, methodology, and applications of directional and axial statistics." (Technometrics, November 2008)

"This book has been written as a drastic revision and major extension to Statistics of Directional Data. It is a worthy successor to that book and will surely become the definitive reference on this subject are for many years." (Short Book Reviews, Vol. 20, No. 3, December 2000)

"The text will be an invaluable source of reference for researchers and practitioners alike working with directional data..." (The Statistician, Vol. 50, 2001)

"...a highly valuable and nicely written contribution" (Statistics and Decisions, Vol 19/2, 2001)

"In coverage and presentation, the current book dominates?the starting place for anyone wanting to make inferences using directional data or wishing to pursue research in this area." (Mathematical Reviews, 2003b)

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