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Circular Statistics in R 1st Edition by Arthur Pewsey, Markus Neuhäuser, Graeme Ruxton 0199671133 9780199671137

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Circular Statistics in R 1st Edition A. Pewsey Digital Instant Download

Author(s): A. Pewsey, M. Neuhauser, G. D Ruxton
ISBN(s): 9780199671137, 0199671133
Edition: 1
File Details: PDF, 1.48 MB
Year: 2014
Language: english
SKU: EB-5230550 Category: Tags: , ,

Circular Statistics in R 1st Edition by Arthur Pewsey, Markus Neuhäuser, Graeme Ruxton – Ebook PDF Instant Download/Delivery: 0199671133, 9780199671137

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ISBN 10: 0199671133 

ISBN 13: 9780199671137

Author: Arthur Pewsey; Markus Neuhäuser; Graeme D Ruxton

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.

Circular Statistics in R 1st Table of contents:

1. Introduction
1.1 What is Circular Statistics?
1.2 What is R?
1.3 Getting Started with R
1.4 R’s Circular Package
1.5 Web-based R Code and the CircStatsInR Workspace
1.6 Circular Statistics in Other Software Environments
1.7 Related Types of Data
1.8 Aims of the Book
1.9 The Book’s Structure and Use
1.10 A Note on Resampling Methods

2. Graphical Representation of Circular Data
2.1 Introduction
2.2 Raw Circular Data Plots
2.3 Rose Diagrams
2.4 Kernel Density Estimates
2.5 Linear Histograms

3. Circular Summary Statistics
3.1 Introduction
3.2 Sample Trigonometric Moments
3.3 Measures of Location
3.3.1 Sample Mean Direction
3.3.2 Sample Median Direction
3.4 Measures of Concentration and Dispersion
3.4.1 Sample Mean Resultant Length
3.4.2 Sample Circular Variance and Standard Deviation
3.4.3 Other Sample Dispersion Measures
3.5 Measures of Skewness and Kurtosis
3.6 Corrections for Grouped Data
3.7 Axial Data

4. Distribution Theory and Models for Circular Random Variables
4.1 Introduction
4.2 Circular Distribution Theory
4.2.1 Circular Distribution and Probability Density Functions
4.2.2 Circular Characteristic Function, Trigonometric Moments and Fourier Series Expansion
4.2.3 Basic Population Measures
4.2.4 Symmetric Distributions
4.2.5 Large-sample Distribution of Key Circular Summaries
4.3 Circular Models
4.3.1 General Approaches for Generating Circular Distributions
4.3.2 Discrete Circular Uniform Distribution
4.3.3 Continuous Circular Uniform Distribution
4.3.4 Cardioid Distribution
4.3.5 Cartwright’s Power-of-Cosine Distribution
4.3.6 Wrapped Cauchy Distribution
4.3.7 Wrapped Normal Distribution
4.3.8 Von Mises Distribution
4.3.9 Jones–Pewsey Family
4.3.10 Unimodal Symmetric Transformation of Argument Families
4.3.11 Sine-skewed Distributions
4.3.12 Unimodal Asymmetric Transformation of Argument Families
4.3.13 Inverse Batschelet Distributions
4.3.14 Summary of Continuous Circular Models
4.3.15 Other Models for Unimodal Data
4.3.16 Multimodal Models
4.3.17 Models for Toroidal Data
4.3.18 Models for Cylindrical Data

5. Basic Inference for a Single Sample
5.1 Testing for Uniformity
5.1.1 Testing for Uniformity Against any Alternative
5.1.2 Testing for Uniformity Against a Unimodal Alternative with a Specified Mean Direction
5.2 Testing for Reflective Symmetry
5.2.1 Large-sample Test for Reflective Symmetry
5.2.2 Bootstrap Test for Reflective Symmetry
5.3 Inference for Key Circular Summaries
5.3.1 Bias-corrected Point Estimation
5.3.2 Bias-corrected Confidence Intervals
5.3.3 Testing for a Specified Mean Direction

6. Model Fitting for a Single Sample
6.1 Introduction
6.2 Fitting a von Mises Distribution
6.2.1 Maximum Likelihood Based Point Estimation
6.2.2 Confidence Interval Construction
6.2.3 Goodness-of-fit
6.3 Fitting a Jones–Pewsey Distribution
6.3.1 Maximum Likelihood Point Estimation
6.3.2 Confidence Interval Construction
6.3.3 Model Comparison and Reduction
6.3.4 Goodness-of-fit
6.3.5 Modelling Grouped Data
6.4 Fitting an Inverse Batschelet Distribution
6.4.1 Maximum Likelihood Point Estimation
6.4.2 Confidence Interval Construction
6.4.3 Model Comparison and Reduction
6.4.4 Goodness-of-fit

7. Comparing Two or More Samples of Circular Data
7.1 Exploratory Graphical Comparison of Samples
7.1.1 Multiple Raw Circular Data Plot
7.1.2 Angular Q-Q Plot
7.2 Tests for a Common Mean Direction
7.2.1 Watson’s Large-sample Nonparametric Test
7.2.2 Bootstrap Version of Watson’s Nonparametric Test
7.2.3 Watson–Williams Test for von Mises Distributions
7.3 Tests for a Common Median Direction
7.3.1 Fisher’s Nonparametric Test
7.3.2 Randomization Version of Fisher’s Nonparametric Test
7.4 Tests for a Common Concentration
7.4.1 Wallraff’s Nonparametric Test
7.4.2 Fisher’s Test for von Mises Distributions
7.4.3 Randomization Version of Fisher’s Test
7.5 Tests for a Common Distribution
7.5.1 Chi-squared Test for Grouped Data
7.5.2 Large-sample Mardia–Watson–Wheeler Test
7.5.3 Randomization Version of the Mardia–Watson–Wheeler Test
7.5.4 Watson’s Two-sample Test
7.5.5 Randomization Version of Watson’s Two-sample Test
7.6 Moore’s Test for Paired Circular Data

8. Correlation and Regression
8.1 Introduction
8.2 Linear–Circular Association
8.2.1 Johnson–Wehrly–Mardia Correlation Coefficient
8.2.2 Mardia’s Rank Correlation Coefficient
8.3 Circular–Circular Association
8.3.1 Fisher–Lee Correlation Coefficient for Rotational Dependence
8.3.2 Fisher–Lee Correlation Coefficient for Toroidal-Monotonic Association
8.3.3 Jammalamadaka–Sarma Correlation Coefficient
8.3.4 Rothman’s Test for Independence
8.4 Regression for a Linear Response and a Circular Regressor
8.4.1 Basic Cosine Regression Model
8.4.2 Extended Cosine Regression Model
8.4.3 Skew Cosine Regression Model
8.4.4 Symmetric Flat-Topped and Sharply Peaked Cosine Regression Model
8.5 Regression for a Circular Response and Linear Regressors
8.6 Regression for a Circular Response and a Circular Regressor
8.7 Multivariate Regression with Circular Regressors

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Tags: Arthur Pewsey, Markus Neuhäuser, Graeme Ruxton, Circular