ぱらぱらめくる『Directional Statistics』

Directional Statistics (Wiley Series in Probability and Statistics)

• 方向統計学のWiki記事(こちら)

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
  • Exploratory adta analysis
  • 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