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Directional Statistics

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.

Author : Kanti V. Mardia

Release : 2009-09-25

Publisher : John Wiley & Sons

ISBN : 0470317817

File Size : 41.31 MB

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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.

Directional Statistics

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.

Author : Kanti V. Mardia

Release : 2000

Publisher : Wiley-Blackwell

ISBN :

File Size : 22.22 MB

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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.

Directional statistics

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Statistics of Directional Data

THE BACKGROUND The interest in developing techniques to analyse directional
data is as old as the subject of mathematical statistics itself. Indeed, the theory of
errors was developed by Gauss primarily to analyse certain directional ...

Author : K. V. Mardia

Release : 2014-07-03

Publisher : Academic Press

ISBN : 148321866X

File Size : 40.84 MB

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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.

Modern Directional Statistics

Fisher used as illustrating example the direction of remanent magnetism found in
igneous or sedimentary rocks. The impact of the Fisher (1953) paper led to a
methodological and systematic study of directional data holding account of their ...

Author : Christophe Ley

Release : 2017-08-03

Publisher : CRC Press

ISBN : 1351645781

File Size : 66.46 MB

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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.

Applied Directional Statistics

Aim of the book Directional statistics are concerned with data that are directions.
The typical supports for directional data are the unit circle and unit (hyper-)sphere
, or more generally Riemannian manifolds. The nonlinear nature of these ...

Author : Christophe Ley

Release : 2018-09-03

Publisher : CRC Press

ISBN : 1351856529

File Size : 25.34 MB

Format : PDF

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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.

Topics in Circular Statistics

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 : S. Rao Jammalamadaka

Release : 2001

Publisher : World Scientific

ISBN : 9789812779267

File Size : 79.78 MB

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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.

Circular Statistics in R

Arthur Pewsey, Markus Neuhäuser, Graeme D Ruxton. von Mises distribution.
Biometrika, 72,647–52. [105] Lund, U. (1999). Least circular distance regression
for directional data. Journal of Applied Statistics, 26, 723–33. [170] Lund, U. (
2002).

Author : Arthur Pewsey

Release : 2013-09-26

Publisher : OUP Oxford

ISBN : 0191650773

File Size : 46.95 MB

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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.

Applied Directional Statistics

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).

Author : Taylor & Francis Group

Release : 2020-12-18

Publisher : CRC Press

ISBN : 9780367733452

File Size : 52.43 MB

Format : PDF, ePub, Mobi

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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.

Advances in Directional and Linear Statistics

degree at the Indian Statistical Institute (ISI), Kolkata. ... C.R. Rao, and D. Basu
among others, and worked with Professor C.R. Rao for his Ph.D. (1969) on path-
breaking research in the then newly emerging area of directional data analysis.

Author : Martin T. Wells

Release : 2010-11-04

Publisher : Springer Science & Business Media

ISBN : 9783790826289

File Size : 40.87 MB

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The present volume consists of papers written by students, colleagues and collaborators of Sreenivasa Rao Jammalamadaka from various countries, and covers a variety of research topics which he enjoys and contributed immensely to.

Statistics on Special Manifolds

Examples of Orientation Statistics The Special k = l Case The directional statistics
in this case may be put into two categories, directed (spherical) and undirected (
axial). They are, respectively, the observations from the Stiefel manifold Vl m, ...

Author : Yasuko Chikuse

Release : 2003-02-06

Publisher : Springer Science & Business Media

ISBN : 9780387001609

File Size : 69.13 MB

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Covering statistical analysis on the two special manifolds, the Stiefel manifold and the Grassmann manifold, this book is designed as a reference for both theoretical and applied statisticians. It will also be used as a textbook for a graduate course in multivariate analysis. It is assumed that the reader is familiar with the usual theory of univariate statistics and a thorough background in mathematics, in particular, knowledge of multivariate calculation techniques.

Topics in Circular Statistics

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 : S Rao Jammalamadaka

Release : 2001-04-30

Publisher : World Scientific

ISBN : 9814495247

File Size : 73.36 MB

Format : PDF, Mobi

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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 DistributionsSome Sampling DistributionsEstimation of ParametersTests for Mean Direction and ConcentrationTests for UniformityNonparametric Testing ProceduresCircular Correlation and RegressionPredictive Inference for Directional DataOutliers and Related ProblemsChange-Point ProblemsMiscellaneous TopicsSome Facts on Bessel FunctionsHow to Use the CircStats Package Readership: Researchers and practitioners dealing with circular data. Keywords:Directional Statistics;Circular Data;CircStat Programs;Von Mises Density;Circular Normal Distribution;Wrapped Stable Family;Spacings Tests;Circular Correlation and Regression;Two-Dimensional Directions;Circadian Rhythms;Cosinor Analysis;Tests of Isotropy or Uniformity

Statistics for Earth and Environmental Scientists

10.1 Introduction Examples of directional data include wind, geologic faults,
movement of animals, ocean currents, and paleomagnetism. Directional data
occur in two or three dimensions. Wind direction is an example of circular data in
two ...

Author : John H. Schuenemeyer

Release : 2011-04-12

Publisher : John Wiley & Sons

ISBN : 1118102215

File Size : 37.42 MB

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A comprehensive treatment of statistical applications for solvingreal-world environmental problems A host of complex problems face today's earth science community,such as evaluating the supply of remaining non-renewable energyresources, assessing the impact of people on the environment,understanding climate change, and managing the use of water. Propercollection and analysis of data using statistical techniquescontributes significantly toward the solution of these problems.Statistics for Earth and Environmental Scientists presentsimportant statistical concepts through data analytic tools andshows readers how to apply them to real-world problems. The authors present several different statistical approaches tothe environmental sciences, including Bayesian and nonparametricmethodologies. The book begins with an introduction to types ofdata, evaluation of data, modeling and estimation, randomvariation, and sampling—all of which are explored throughcase studies that use real data from earth science applications.Subsequent chapters focus on principles of modeling and the keymethods and techniques for analyzing scientific data,including: Interval estimation and Methods for analyzinghypothesis testingof means time series data Spatial statistics Multivariate analysis Discrete distributions Experimental design Most statistical models are introduced by concept andapplication, given as equations, and then accompanied by heuristicjustification rather than a formal proof. Data analysis, modelbuilding, and statistical inference are stressed throughout, andreaders are encouraged to collect their own data to incorporateinto the exercises at the end of each chapter. Most data sets,graphs, and analyses are computed using R, but can be worked withusing any statistical computing software. A related websitefeatures additional data sets, answers to selected exercises, and Rcode for the book's examples. Statistics for Earth and Environmental Scientists is anexcellent book for courses on quantitative methods in geology,geography, natural resources, and environmental sciences at theupper-undergraduate and graduate levels. It is also a valuablereference for earth scientists, geologists, hydrologists, andenvironmental statisticians who collect and analyze data in theireveryday work.

Phenological Research

Circular statistics is an area of statistics not very much used by ecologists nor by
other researchers from the biological ... Nevertheless, the connection between
the evaluation of temporal, recurring events and the analysis of directional data ...

Author : Irene L. Hudson

Release : 2009-11-24

Publisher : Springer Science & Business Media

ISBN : 9789048133352

File Size : 21.73 MB

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As climate change continues to dominate the international environmental agenda, phenology – the study of the timing of recurring biological events – has received increasing research attention, leading to an emerging consensus that phenology can be viewed as an ‘early warning system’ for climate change impact. A multidisciplinary science involving many branches of ecology, geography and remote sensing, phenology to date has lacked a coherent methodological text. This new synthesis, including contributions from many of the world’s leading phenologists, therefore fills a critical gap in the current biological literature. Providing critiques of current methods, as well as detailing novel and emerging methodologies, the book, with its extensive suite of references, provides readers with an understanding of both the theoretical basis and the potential applications required to adopt and adapt new analytical and design methods. An invaluable source book for researchers and students in ecology and climate change science, the book also provides a useful reference for practitioners in a range of sectors, including human health, fisheries, forestry, agriculture and natural resource management.

Nonparametric Inference on Manifolds

There are many areas of significant application of statistics on manifolds. For
example, directional statistics (statistics on the sphere S 2) are used to study
shifts in the Earth's magnetic poles over geological time, which have an important
 ...

Author : Abhishek Bhattacharya

Release : 2012-04-05

Publisher : Cambridge University Press

ISBN : 1107019583

File Size : 48.66 MB

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A systematic introduction to a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes.

Probability, Statistics, and Their Applications

Rudolf Beran University of California , Davis Abstract Consider a one - way layout
with one directional observation per factor level . Each observed direction is a
unit vector in Ro measured with random error . Information accompanying the ...

Author : Rabindra Nath Bhattacharya

Release : 2003

Publisher : IMS

ISBN : 9780940600553

File Size : 24.43 MB

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Models for Bivariate Directional Data and Angular-linear Data with Applications to Statistical Inference

Circular Statistics . Appl . Statist . , 24 , 147 - 150 . Rao , C . R . ( 1973 ) . Linear
Statistical Inference and Its Applications , 2nd ed . New York : John Wiley and
Sons . Rao , J . S . and Puri , M . L . ( 1975 ) . Problems of association for bivariate
 ...

Author : Thomas Edward Wehrly

Release : 1976

Publisher :

ISBN :

File Size : 58.56 MB

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Multivariate Statistics

... KROONENBERG · Applied Multiway Data Analysis KVAM and VIDAKOVIC ·
Nonparametric Statistics with Applications ... MARCHETTE · Random Graphs for
Statistical Pattern Recognition MARDIA and JUPP · Directional Statistics MASON,
 ...

Author : Yasunori Fujikoshi

Release : 2010-01-26

Publisher : John Wiley & Sons

ISBN : 0470411694

File Size : 70.37 MB

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A comprehensive examination of high-dimensional analysis ofmultivariate methods and their real-world applications Multivariate Statistics: High-Dimensional and Large-SampleApproximations is the first book of its kind to explore howclassical multivariate methods can be revised and used in place ofconventional statistical tools. Written by prominent researchers inthe field, the book focuses on high-dimensional and large-scaleapproximations and details the many basic multivariate methods usedto achieve high levels of accuracy. The authors begin with a fundamental presentation of the basictools and exact distributional results of multivariate statistics,and, in addition, the derivations of most distributional resultsare provided. Statistical methods for high-dimensional data, suchas curve data, spectra, images, and DNA microarrays, are discussed.Bootstrap approximations from a methodological point of view,theoretical accuracies in MANOVA tests, and model selectioncriteria are also presented. Subsequent chapters feature additionaltopical coverage including: High-dimensional approximations of various statistics High-dimensional statistical methods Approximations with computable error bound Selection of variables based on model selection approach Statistics with error bounds and their appearance indiscriminant analysis, growth curve models, generalized linearmodels, profile analysis, and multiple comparison Each chapter provides real-world applications and thoroughanalyses of the real data. In addition, approximation formulasfound throughout the book are a useful tool for both practical andtheoretical statisticians, and basic results on exact distributionsin multivariate analysis are included in a comprehensive, yetaccessible, format. Multivariate Statistics is an excellent book for courseson probability theory in statistics at the graduate level. It isalso an essential reference for both practical and theoreticalstatisticians who are interested in multivariate analysis and whowould benefit from learning the applications of analyticalprobabilistic methods in statistics.

Applied Statistics Using SPSS, STATISTICA and MATLAB

The book chapters provide a comprehensive coverage of the main statistical
analysis topics (data description, statistical inference, classification and
regression, factor analysis, survival data, directional statistics) that one faces in
practical ...

Author : J. P. Marques de Sá

Release : 2003

Publisher : Springer Science & Business Media

ISBN : 9783540011569

File Size : 21.98 MB

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Assuming no previous statistics education, this practical reference provides a comprehensive introduction and tutorial on the main statistical analysis topics, demonstrating their solution with the most common software packages. Intended for anyone applying statistical analysis to a wide variety of science and engineering problems, the book shows how to use SPSS, MATLAB, and STATISTICA for data analyses, such as data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics.