# ぱらぱらめくる『Directional Statistics』

install.packages("circular")
library(circular)

• 目次
• 1 Circular Data
• 2 Summary Statistics
• 3 Basic Concepts and Models
• 4 Fundamental Theorems and Distribution Theory
• 5 Point Estimation
• 6 Tests of Uniformity and Tests of Goodness-of-Fit
• 7 Tests on von Mises Distributions
• 8 Non-parametric Methods
• 9 Distributions on Spheres
• 10 Inference on Spheres
• 11 Correlation and Regression
• 12 Modern Methodology
• 13 General Sample Spaces
• 14 Shape Analysis
• 細目次
• 1 Circular Data
• Introduction
• Diagrammatical representation
• Forms of frequency distributions
• Further examples of directional data
• 2 Summary Statistics
• Introduction
• Measures of location
• Measures of concentration and dispersion
• Trigonometric moments
• Corerctions for grouping
• 3 Basic Concepts and Models
• Introduction
• The distribution function
• The characteristic function
• Moments and measures of location and dispersion
• Circular models
• Multiply-wrapped distributions
• Distributions on the torus and the cylinder
• 4 Fundamental Theorems and Distribution Theory
• Introduction
• Properties of characteristic functions
• Limit theorems
• The distributions of and from the uniform distribution
• Distribution of C, S and R for A von Mises population
• Distributions related to the multi-sample problem for non Mises Populations
• Moments of • Limiting distributions of circular statistics
• 5 Point Estimation
• Introduction
• Unbiased estimators and a Cramer-Rao bound
• von Mises distributions
• Wrapped cauchy distributions
• Mixtures of von Mises distributions
• 6 Tests of Uniformity and Tests of Goodness-of-Fit
• Introduction
• Graphical assessment of uniformity
• Tests of uniformity
• Tests of goodness-of-fit
• 7 Tests on von Mises Distributions
• Introduction
• Single-sample tests
• Two-sample tests
• Multi-sample tests
• Testing von Misesness
• 8 Non-parametric Methods
• Introduction
• Tests of symmetry
• Two-sample tests
• Multi-sample tests
• 9 Distributions on Spheres
• Spherical data
• Descriptive measures
• Models for spherical data
• Models for axial data
• Distribution theory
• Moments and limiting distributions
• 10 Inference on Spheres
• Introduction
• Point estimation
• Single-sample tests
• Two-sample tests
• Multi-sample tests
• Tests on axial distributions
• A general framework for testing uniformity
• 11 Correlation and Regression
• Introduction
• Measures of correlation
• Regression models
• Bivariate models
• Directional time series
• 12 Modern Methodology
• Introduction
• Outliers
• Goodness-of-fit
• Robust methods
• Bootstrap methods
• Density estimation
• Bayesian methods
• Curve fitting and smoothing
• Other methods
• 13 General Sample Spaces
• Introduction
• Frames and rotations
• Subspaces
• Other sample spaces
• 14 Shape Analysis
• Introduction
• Mean shape and variation
• Shape coordinate systems and uniform distributions
• A test of uniformity
• Shape distributions
• Complex bingham distributions
• Complex watson distributions
• The complex angular gaussian model
• A rotationality symmetric shape family
• Shapes in higher dimensions