Directional Statistics

Author : Kanti V. Mardia,Peter E. Jupp
Publisher : John Wiley & Sons
Page : 472 pages
File Size : 55,9 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015053172394

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Directional Statistics by Kanti V. Mardia,Peter E. Jupp Pdf

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.

Author : Christophe Ley,Thomas Verdebout
Publisher : CRC Press
Page : 201 pages
File Size : 45,7 Mb
Release : 2017-08-03
Category : Computers
ISBN : 9781351645782

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Modern Directional Statistics by Christophe Ley,Thomas Verdebout Pdf

Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory. The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory,high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Société Française de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics. Thomas Verdebout is professor of mathematical statistics at Université libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high- dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis.

Author : Kanti V. Mardia,Peter E. Jupp
Publisher : John Wiley & Sons
Page : 460 pages
File Size : 48,9 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317815

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Directional Statistics by Kanti V. Mardia,Peter E. Jupp Pdf

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.

Author : K. V. Mardia
Publisher : Academic Press
Page : 380 pages
File Size : 44,9 Mb
Release : 2014-07-03
Category : Mathematics
ISBN : 9781483218663

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Statistics of Directional Data by K. V. Mardia Pdf

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Statistics of Directional Data aims to provide a systematic account of statistical theory and methodology for observations which are directions. The publication first elaborates on angular data and frequency distributions, descriptive measures, and basic concepts and theoretical models. Discussions focus on moments and measures of location and dispersion, distribution function, corrections for grouping, calculation of the mean direction and the circular variance, interrelations between different units of angular measurement, and diagrammatical representation. The book then examines fundamental theorems and distribution theory, point estimation, and tests for samples from von Mises populations. The text takes a look at non-parametric tests, distributions on spheres, and inference problems on the sphere. Topics include tests for axial data, point estimation, distribution theory, moments and limiting distributions, and tests of goodness of fit and tests of uniformity. The publication is a dependable reference for researchers interested in probability and mathematical statistics.

Author : Christophe Ley,Thomas Verdebout
Publisher : CRC Press
Page : 300 pages
File Size : 44,6 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781351856522

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Applied Directional Statistics by Christophe Ley,Thomas Verdebout Pdf

This book collects important advances in methodology and data analysis for directional statistics. It is the companion book of the more theoretical treatment presented in Modern Directional Statistics (CRC Press, 2017). The field of directional statistics has received a lot of attention due to demands from disciplines such as life sciences or machine learning, the availability of massive data sets requiring adapted statistical techniques, and technological advances. This book covers important progress in bioinformatics, biology, astrophysics, oceanography, environmental sciences, earth sciences, machine learning and social sciences.

Author : Ashis SenGupta,Barry C. Arnold
Publisher : Springer Nature
Page : 487 pages
File Size : 48,9 Mb
Release : 2022-06-15
Category : Mathematics
ISBN : 9789811910449

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Directional Statistics for Innovative Applications by Ashis SenGupta,Barry C. Arnold Pdf

In commemoration of the bicentennial of the birth of the “lady who gave the rose diagram to us”, this special contributed book pays a statistical tribute to Florence Nightingale. This book presents recent phenomenal developments, both in rigorous theory as well as in emerging methods, for applications in directional statistics, in 25 chapters with contributions from 65 renowned researchers from 25 countries. With the advent of modern techniques in statistical paradigms and statistical machine learning, directional statistics has become an indispensable tool. Ranging from data on circles to that on the spheres, tori and cylinders, this book includes solutions to problems on exploratory data analysis, probability distributions on manifolds, maximum entropy, directional regression analysis, spatio-directional time series, optimal inference, simulation, statistical machine learning with big data, and more, with their innovative applications to emerging real-life problems in astro-statistics, bioinformatics, crystallography, optimal transport, statistical process control, and so on.

Author : Christophe Ley,Thomas Verdebout
Publisher : CRC Press
Page : 300 pages
File Size : 42,8 Mb
Release : 2020-12-18
Category : Circular data
ISBN : 0367733455

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Applied Directional Statistics by Christophe Ley,Thomas Verdebout Pdf

This book collects important advances in methodology and data analysis for directional statistics. It is the companion book of the more theoretical treatment presented in Modern Directional Statistics (CRC Press, 2017). The field of directional statistics has received a lot of attention due to demands from disciplines such as life sciences or machine learning, the availability of massive data sets requiring adapted statistical techniques, and technological advances. This book covers important progress in bioinformatics, biology, astrophysics, oceanography, environmental sciences, earth sciences, machine learning and social sciences.

Author : N. I. Fisher
Publisher : Cambridge University Press
Page : 300 pages
File Size : 43,7 Mb
Release : 1995-10-12
Category : Mathematics
ISBN : 0521568900

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Statistical Analysis of Circular Data by N. I. Fisher Pdf

A unified, up-to-date account of circular data-handling techniques, useful throughout science.

Author : S. Rao Jammalamadaka,Ambar Sengupta,Ashis Sengupta
Publisher : World Scientific
Page : 348 pages
File Size : 48,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9812779264

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Topics in Circular Statistics by S. Rao Jammalamadaka,Ambar Sengupta,Ashis Sengupta Pdf

This research monograph on circular data analysis covers some recent advances in the field, besides providing a brief introduction to, and a review of, existing methods and models. The primary focus is on recent research into topics such as change-point problems, predictive distributions, circular correlation and regression, etc. An important feature of this work is the S-plus subroutines provided for analyzing actual data sets. Coupled with the discussion of new theoretical research, the book should benefit both the researcher and the practitioner. Contents: Circular Probability Distributions; Some Sampling Distributions; Estimation of Parameters; Tests for Mean Direction and Concentration; Tests for Uniformity; Nonparametric Testing Procedures; Circular Correlation and Regression; Predictive Inference for Directional Data; Outliers and Related Problems; Change-Point Problems; Miscellaneous Topics; Some Facts on Bessel Functions; How to Use the CircStats Package. Readership: Researchers and practitioners dealing with circular data.

Author : Jens Breckling
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236887

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The Analysis of Directional Time Series: Applications to Wind Speed and Direction by Jens Breckling Pdf

Given a series of wind speeds and directions from the port of Fremantle the aim of this monograph is to detect general weather patterns and seasonal characteristics. To separate the daily land and sea breeze cycle and other short-term disturbances from the general wind, the series is divided into a daily and a longer term, synoptic component. The latter is related to the atmospheric pressure field, while the former is studied in order i) to isolate particular short-term events such as calms, storms and oscillating winds, and ii) to determine the land and sea breeze cycle which dominates the weather pattern for most of the year. All these patterns are described in detail and are related to the synoptic component of the data. Two time series models for directional data and a new measure of angular association are introduced to provide the basis for certain parts of the analysis.

Author : Arthur Pewsey,Markus Neuhäuser,Graeme D Ruxton
Publisher : OUP Oxford
Page : 192 pages
File Size : 46,8 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780191650765

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Circular Statistics in R by Arthur Pewsey,Markus Neuhäuser,Graeme D Ruxton Pdf

Circular Statistics in R provides the most comprehensive guide to the analysis of circular data in over a decade. Circular data arise in many scientific contexts whether it be angular directions such as: observed compass directions of departure of radio-collared migratory birds from a release point; bond angles measured in different molecules; wind directions at different times of year at a wind farm; direction of stress-fractures in concrete bridge supports; longitudes of earthquake epicentres or seasonal and daily activity patterns, for example: data on the times of day at which animals are caught in a camera trap, or in 911 calls in New York, or in internet traffic; variation throughout the year in measles incidence, global energy requirements, TV viewing figures or injuries to athletes. The natural way of representing such data graphically is as points located around the circumference of a circle, hence their name. Importantly, circular variables are periodic in nature and the origin, or zero point, such as the beginning of a new year, is defined arbitrarily rather than necessarily emerging naturally from the system. This book will be of value both to those new to circular data analysis as well as those more familiar with the field. For beginners, the authors start by considering the fundamental graphical and numerical summaries used to represent circular data before introducing distributions that might be used to model them. They go on to discuss basic forms of inference such as point and interval estimation, as well as formal significance tests for hypotheses that will often be of scientific interest. When discussing model fitting, the authors advocate reduced reliance on the classical von Mises distribution; showcasing distributions that are capable of modelling features such as asymmetry and varying levels of kurtosis that are often exhibited by circular data. The use of likelihood-based and computer-intensive approaches to inference and modelling are stressed throughout the book. The R programming language is used to implement the methodology, particularly its "circular" package. Also provided are over 150 new functions for techniques not already covered within R. This concise but authoritative guide is accessible to the diverse range of scientists who have circular data to analyse and want to do so as easily and as effectively as possible.

Author : S. Rao Jammalamadaka,Ambar Sengupta
Publisher : World Scientific
Page : 336 pages
File Size : 53,9 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810237783

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Topics in Circular Statistics by S. Rao Jammalamadaka,Ambar Sengupta Pdf

This research monograph on circular data analysis covers some recent advances in the field, besides providing a brief introduction to, and a review of, existing methods and models. The primary focus is on recent research into topics such as change-point problems, predictive distributions, circular correlation and regression, etc. An important feature of this work is the S-plus subroutines provided for analyzing actual data sets. Coupled with the discussion of new theoretical research, the book should benefit both the researcher and the practitioner.

Author : Christophe Ley,Thomas Verdebout
Publisher : CRC Press
Page : 191 pages
File Size : 51,6 Mb
Release : 2017-08-03
Category : Computers
ISBN : 9781498706667

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Modern Directional Statistics by Christophe Ley,Thomas Verdebout Pdf

Modern Directional Statistics collects important advances in methodology and theory for directional statistics over the last two decades. It provides a detailed overview and analysis of recent results that can help both researchers and practitioners. Knowledge of multivariate statistics eases the reading but is not mandatory. The field of directional statistics has received a lot of attention over the past two decades, due to new demands from domains such as life sciences or machine learning, to the availability of massive data sets requiring adapted statistical techniques, and to technological advances. This book covers important progresses in distribution theory,high-dimensional statistics, kernel density estimation, efficient inference on directional supports, and computational and graphical methods. Christophe Ley is professor of mathematical statistics at Ghent University. His research interests include semi-parametrically efficient inference, flexible modeling, directional statistics and the study of asymptotic approximations via Stein’s Method. His achievements include the Marie-Jeanne Laurent-Duhamel prize of the Société Française de Statistique and an elected membership at the International Statistical Institute. He is associate editor for the journals Computational Statistics & Data Analysis and Econometrics and Statistics. Thomas Verdebout is professor of mathematical statistics at Université libre de Bruxelles (ULB). His main research interests are semi-parametric statistics, high- dimensional statistics, directional statistics and rank-based procedures. He has won an annual prize of the Belgian Academy of Sciences and is an elected member of the International Statistical Institute. He is associate editor for the journals Statistics and Probability Letters and Journal of Multivariate Analysis.

Author : Arthur Pewsey,Markus Neuhäuser,Graeme D Ruxton
Publisher : Oxford University Press
Page : 198 pages
File Size : 45,5 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780199671137

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Circular Statistics in R by Arthur Pewsey,Markus Neuhäuser,Graeme D Ruxton Pdf

Measurements like mass, length and speed are "linear"; but compass direction or the time of the year are "circular". Circular data have a repeating nature and an arbitrary zero: 12 months after the 1st of July it is the 1st of July again. This book explains how to easily and effectively analyse circular data statistically.

Author : Kantilal Varichand Mardia
Publisher : Unknown
Page : 429 pages
File Size : 41,6 Mb
Release : 1999
Category : Distribution (Probability theory)
ISBN : OCLC:1035778443

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Directional Statistics by Kantilal Varichand Mardia Pdf