Circular statistics in R:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2013
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Enth. Literaturverz. S. [173] - 178 und Index |
| Physical Description: | XIV, 183 S. graph. Darst. |
| ISBN: | 9780199671137 0199671133 |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Introduction
........................................1
1.1
What is Circular Statistics?
1
1.2
What is R?
3
1.3
Getting Started with
R
3
1.4
R s Circular Package
4
1.5
Web-based
R
Code and the CircStatslnR Workspace
5
1.6
Circular Statistics in Other Software Environments
6
1.7
Related Types of Data
6
1.8
Aims of the Book
7
1.9
The Book s Structure and Use
8
1.10
A Note on Resampling Methods
9
Graphical Representation of Circular Data
...................11
2.1
Introduction
11
2.2
Raw Circular Data Plots
Π
2.3
Rose Diagrams
14
2.4
Kernel Density Estimates
15
2.5
Linear Histograms
17
Circular Summary Statistics
.............................21
3.1
Introduction
21
3.2
Sample Trigonometric Moments
22
3.3
Measures of Location
25
3.3.1
Sample Mean Direction
25
3.3.2
Sample Median Direction
26
3.4
Measures of Concentration and Dispersion
26
3.4.1
Sample Mean Resultant Length
26
3.4.2
Sample Circular Variance and Standard Deviation
27
3.4.3
Other Sample Dispersion Measures
28
3.5
Measures of Skewness and Kurtosis
29
3.6
Corrections for Grouped Data
30
3.7
Axial Data
32
Distribution Theory and Models for Circular Random
Variables
.........................................35
4.1
Introduction
35
4.2
Circular Distribution Theory
35
Xii
I CONTENTS
4.2.1
Circular Distribution and Probability Density Functions
36
4.2.2
Circular Characteristic Function, Trigonometric
Moments and Fourier Series Expansion
38
4Д.З
Basic Population Measures
40
4.2.4
Symmetric Distributions
41
4.2.5
Large-sample Distribution of Key Circular Summaries
42
4.3
Circular Models
44
4.3.1
General Approaches for Generating Circular Distributions
44
4.3.2
Discrete Circular Uniform Distribution
46
4.3.3
Continuous Circular Uniform Distribution
47
4.3.4
Cardioid Distribution
48
4.3.5
Cartwrighťs
Power-of-Cosine Distribution
50
4.3.6
Wrapped Cauchy Distribution
52
4.3.7
Wrapped Normal Distribution
54
4.3.8 Von
Mises
Distribution
56
4.3.9
Jones-Pewsey Family
58
4.3.10
Unimodal Symmetric Transformation of Argument Families
62
4.3.11
Sine-skewed Distributions
65
4.3.12
Unimodal Asymmetric Transformation of Argument Families
67
4.3.13
Inverse Batschelet Distributions
70
4.3.14
Summary of Continuous Circular Models
74
4.3.15
Other Models for Unimodal Data
75
4.3.16 Multimodal
Models
76
4.3.17
Models for Toroidal Data
77
4.3.18
Models for Cylindrical Data
77
Basic Inference for a Single Sample
........................79
5.1
Testing for Uniformity
80
5.1.1
Testing for Uniformity Against any Alternative
81
5.1.2
Testing for Uniformity Against a Unimodal Alternative
with a Specified Mean Direction
86
5.2
Testing for Reflective Symmetry
86
5.2.1
Large-sample Test for Reflective Symmetry
87
5.2.2
Bootstrap Test for Reflective Symmetry
88
5.3
Inference for Key Circular Summaries
90
5.3.1
Bias-corrected Point Estimation
90
5.3.2
Bias-corrected Confidence Intervals
91
5.3.3
Testing for a Specified Mean Direction
96
Model Fitting for a Single Sample
........................101
6.1
Introduction
101
6.2
Fitting a
von
Mises
Distribution
102
6.2.1
Maximum Likelihood Based Point Estimation
102
6.2.2
Confidence Interval Construction
102
6.2.3
Goodness-of-fit
103
C O.NT F. NÍS j
Xlii
6.3
Fitting a Jones-Pewsey Distribution
107
6.3.1
Maximum Likelihood Point Estimation
107
6.3.2
Confidence Interval Construction
108
6.3.3
Model Comparison and Reduction
113
6.3.4
Goodness-of-fit
115
6.3.5
Modelling Grouped Data
118
6.4
Fitting an Inverse Batschelet Distribution
123
6.4.1
Maximum Likelihood Point Estimation
124
6.4.2
Confidence Interval Construction
125
6.4.3
Model Comparison and Reduction
127
6.4.4
Goodness-of-fit
128
7
Comparing Two or More Samples of Circular Data
.............131
7.1
Exploratory Graphical Comparison of Samples
131
7.1.1
Multiple Raw Circular Data Plot
131
7.1.2
Angular QjdPlot
132
7.2
Tests for a Common Mean Direction
134
7.2.1
Watson s Large-sample Nonparametric Test
134
7.2.2
Bootstrap Version of Watson s Nonparametric Test
135
7.2.3
Watson-Williams Test for
von
Mises
Distributions
136
7.3
Tests for a Common Median Direction
137
7.3.1
Fisher s Nonparametric Test
137
7.3.2
Randomization Version of Fisher s Nonparametric Test
138
7.4
Tests for a Common Concentration
139
7.4.1 Wallraff
s
Nonparametric Test
139
7.4.2
Fisher s Test for
von
Mises
Distributions
139
7.4.3
Randomization Version of Fisher s Test
141
7.5
Tests for a Common Distribution
142
7.5.1
Chi-squared Test for Grouped Data
142
7.5.2
Large-sample Mardia-Watson-Wheeler Test
142
7.5.3
Randomization Version of the Mardia-Watson-Wheeler Test
143
7.5.4
Watson s Two-sample Test
144
7.5.5
Randomization Version of Watson s Two-sample Test
145
7.6
Moore s Test for Paired Circular Data
146
8
Correlation and Regression
............................149
8.1
Introduction
149
8.2
Linear-Circular Association
149
8.2.1
Johnson-Wehrly-Mardia Correlation Coefficient
150
8.2.2
Mardia s Rank Correlation Coefficient
152
8.3
Circular-Circular Association
153
8.3.1
Fisher-Lee Correlation Coefficient for Rotational Dependence
153
8.3.2
Fisher-Lee Correlation Coefficient for Toroidal-
Monotonic Association
157
XIV
I CONTENTS
8.3.3
Jammalamadaka-Sarma Correlation Coefficient
157
8.3.4
Rothman s Test for Independence
158
8.4
Regression for a Linear Response and a Circular Regressor
160
8.4.1
Basic Cosine Regression Model
160
8.4.2
Extended Cosine Regression Model
162
8.4.3
Skew Cosine Regression Model
164
8.4.4
Symmetric Flat-Topped and Sharply Peaked Cosine
Regression Model
165
8.5
Regression for a Circular Response and Linear Regressors
166
8.6
Regression for a Circular Response and a Circular Regressor
168
8.7
Multivariate Regression with Circular Regressors
170
Appendix Further Reading
171
1
Books on Circular Statistics
171
2
Internet-based Resources
172
References
173
Index
179
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, both
from angular observations, and from daily or seasonal activity patterns. Examples of
the former include: observed compass directions of departure from a release point
of radio-collared migratory birds: bond angles measured in different molecules; wind
directions at different times of the year at a wind farm; direction of stress-fractures in
concrete bridge supports: longitudes of earthquake epicentres. Examples of the latter
include: times of the day at which animals are caught in a camera trap or
9
I I calls are
received in New York; variation throughout the year in measles incidence, global energy
requirements, TV viewing figures or injuries to athletes. The natural way to represent
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
numerica!
summaries used to represent circular data before
introducing distributions that might be used to model them. 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. Also provided are over I
50
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.
It s amazing how often I m asked for advice about circular statistics. Even
simple questions such as what s the mean direction? or are species active at
different times of day? require circular statistics and they are rarely catered for in
statistical texts. What Pewsey
et al.
have produced is a long-awaited guide to both
the theory and practice of circular statistics with a focus on R. It s a book I ll be
consulting frequently and recommending to students and colleagues alike.
Calvin Dytham. University of York
Arthur Pewsey is Associate Professor of Statistics in the Mathematics Department
at the University of
Extremadura
in Spain
Markus Neuhäuser
is Professor of Statistics at the RheinAhrCampus. Koblenz
University of Applied Sciences in Germany
Graeme D. Ruxton is Professor of Ecology at the University of St Andrews
in Scotland
tockphoto.corr
oto
ISBN
978-0-19-967113-7
UNIVERSITY PRESS
www,
ou
p
.
com
780199 671137
|
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| indexdate | 2024-07-10T00:59:36Z |
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| spelling | Pewsey, Arthur Verfasser (DE-588)105844834X aut Circular statistics in R Arthur Pewsey ; Markus Neuhäuser ; Graeme D. Ruxton 1. ed. Oxford Oxford Univ. Press 2013 XIV, 183 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Enth. Literaturverz. S. [173] - 178 und Index R Programm (DE-588)4705956-4 gnd rswk-swf Zirkuläre Statistik (DE-588)4312006-4 gnd rswk-swf R Programm (DE-588)4705956-4 s Zirkuläre Statistik (DE-588)4312006-4 s b DE-604 Neuhäuser, Markus Verfasser (DE-588)171794087 aut Ruxton, Graeme D. Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027001657&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027001657&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Pewsey, Arthur Neuhäuser, Markus Ruxton, Graeme D. Circular statistics in R R Programm (DE-588)4705956-4 gnd Zirkuläre Statistik (DE-588)4312006-4 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4312006-4 |
| title | Circular statistics in R |
| title_auth | Circular statistics in R |
| title_exact_search | Circular statistics in R |
| title_full | Circular statistics in R Arthur Pewsey ; Markus Neuhäuser ; Graeme D. Ruxton |
| title_fullStr | Circular statistics in R Arthur Pewsey ; Markus Neuhäuser ; Graeme D. Ruxton |
| title_full_unstemmed | Circular statistics in R Arthur Pewsey ; Markus Neuhäuser ; Graeme D. Ruxton |
| title_short | Circular statistics in R |
| title_sort | circular statistics in r |
| topic | R Programm (DE-588)4705956-4 gnd Zirkuläre Statistik (DE-588)4312006-4 gnd |
| topic_facet | R Programm Zirkuläre Statistik |
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