Statistics of Directional Data (Probability & Mathematical Statistics Monograph) - Hardcover

Mardia, K. V.

Hardcover

ISBN 10: 0124711502 ISBN 13: 9780124711501

Publisher: Academic Press Inc, 1972

Synopsis

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.

About this title

Review

"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)

"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) "...written as a drastic revision and major extension to Statistics of Directional Data....definitive reference on this subject...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)

From the Back Cover

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.

Edition details

• Publisher: Academic Press Inc
• Publication date: 1972
• Language: English
• ISBN 10: 0124711502
• ISBN 13: 9780124711501
• Binding: Hardcover
• Number of pages: 357