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Directional (version 3.7)

Directional Statistics

Description

A collection of functions for directional data analysis. Hypothesis testing, discriminant and regression analysis, MLE of distributions and more are included. The standard textbook for such data is the "Directional Statistics" by Mardia, K. V. and Jupp, P. E. (2000). Other references include Phillip J. Paine, Simon P. Preston Michail Tsagris and Andrew T. A. Wood (2018). An elliptically symmetric angular Gaussian distribution. Statistics and Computing 28(3): 689-697. , P. J. Paine, S. P. Preston, M. Tsagris and Andrew T. A. Wood (2019). Spherical regression models with general covariates and anisotropic errors. Statistics and Computing (to appear). .

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Version

Install

install.packages('Directional')

Monthly Downloads

629

Version

3.7

License

GPL-2

Maintainer

Michail Tsagris

Last Published

April 19th, 2019

Functions in Directional (3.7)

MLE of the angular central Gaussian distribution

MLE of the angular central Gaussian distribution
Random values generation from the ESAG distribution

Random values generation from the ESAG distribution
Euclidean transformation

Euclidean transformation
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Summary statistics for grouped circular data

Summary statistics for grouped circular data
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
BIC for the model based clustering using mixtures of von Mises-Fisher distributions

BIC to choose the number of components in a model based clustering using mixtures of von Mises-Fisher distributions
Converting an unsigned unit quaternion to rotation matrix on SO(3)

Converting an unsigned unit quaternion to rotation matrix on SO(3)
Mixtures of Von Mises-Fisher distributions

Mixtures of Von Mises-Fisher distributions
Probability density function of the von Mises-Fisher distribution

Probability density function of the von Mises-Fisher distribution
Spherical-spherical correlation

Spherical-spherical correlation
Circurlar correlations between two circular variables

Circurlar correlations between two circular variables
Spherical-spherical regression

Spherical-Spherical regression
Rotation matrix on SO(3) from three Euler angles

Construct a rotation matrix on SO(3) from the Euler angles.
Tuning of the bandwidth parameter in the von Mises kernel

Tuning of the bandwidth parameter in the von Mises kernel for circular data
MLE of the Wood bimodal distribution on the sphere

MLe of the Wood bimodal distribution on the sphere
k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance
Simulation of random values from a Bingham distribution

Simulating from a Bingham distribution
Tuning of the k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
Cross validation with ESAG discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming an ESAG distribution
Density of the ESAG distribution

Density of the ESAG distribution
Prediction in discriminant analysis based on ESAG distribution

Prediction of a new observation using discriminant analysis based on ESAGdistribution
Circular-linear correlation

Circular-linear correlation
Rotation axis and angle of rotation given a rotation matrix

Rotation axis and angle of rotation given a rotation matrix
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
Hypothesis test for von Mises-Fisher distribution over Kent distribution

Hypothesis test for von Mises-Fisher distribution over Kent distribution
Saddlepoint approximations of the Fisher-Bingham distributions

Saddlepoint approximations of the Fisher-Bingham distributions
Contour plot of the Kent distribution for some data

Contour plot of the Kent distribution for some data
Test of equality of the concentration parameters for circular data

A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data
Contour plot of the Kent distribution without any data

Contour plot of the Kent distribution without any data
Anova for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Density of the von Mises-Fisher and the spherical Kent distributions

Density of the spherical Kent distribution
MLE of the ESAG distribution

MLE of the ESAG distribution
Directional-package

This is an R package that provides methods for the statistical analysis of Directional data.
Anova for circular data

Analysis of variance for circular data
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
Contour plot of a mixture of von Mises-Fisher distributions model

Contour plot of a mixture of von Mises-Fisher distributions model for spherical data only.
Spherical regression using the projected normal or the von Mises-Fisher distribution

Spherical regression using the projected normal or the von Mises-Fisher distribution
Uniformity test for circular data

Uniformity tests for circular data.
MLE of the spherical projected normal distribution

MLE of the spherical projected normal distribution
Cross validation for estimating the classification rate

Cross validation for estimating the classification rate
Simulation of random values from a mixture of von Mises-Fisher distributions

Random values simulation from a mixture of von Mises-Fisher distributions
Lambert's equal area projection

Lambert's equal area projection
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
Inverse of Lambert's equal area projection

Inverse of Lambert's equal area projection
Generate random folds for cross-validation

Generate random folds for cross-validation
MLE of the von Mises-Fisher distribution

MLE of von Mises-Fisher distribution
von Mises kernel density estimation

Kernel density estimation of circular data with a von Mises kernel
Prediction in discriminant analysis based on von Mises-Fisher distribution

Prediction of a new observation using discriminant analysis based on von Mises-Fisher distribution
Tuning of the bandwidth parameter in the von Mises-Fisher kernel

Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical data
Simulation from a Matrix Fisher distribution on SO(3)

Simulation from a Matrix Fisher distribution on SO(3)
Circurlar correlations between one and many circular variables

Circurlar correlations between two circular variables
Simulation of random values from a von Mises-Fisher distribution

Random values simulation from a von Mises-Fisher distribution
Random values simulation from a von Mises distribution

Random values simulation from a von Mises distribution
Unit vector(s) with a given angle

Unit vector(s) with a given angle
A test for testing the equality of the concentration parameters for ciruclar data

A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar data
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
Density of the von Mises distribution

Density of the von Mises distribution
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
Test for equality of concentration parameters for spherical data

Test for equality of concentration parameters for spherical data
Summary statistics for circular data

Summary statistics for circular data
MLE of the generalised von Mises distribution

MLE of the geometrically generalised von Mises distribution
Interactive 3D plot of spherical data

Interactive 3D plot of spherical data
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Goodness of fit test for grouped data

Goodness of fit test for grouped data
MLE of the Kent distribution

MLe of the Kent distribution
Mle of the Matrix Fisher distribution on SO(3)

Mle of the Matrix Fisher distribution on SO(3)
MLE of some circular distributions

MLE of some circular distributions
Circular or angular regression

Circular or angular regression
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
Test for a given mean direction

Test for a given mean direction
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Contour plot of spherical data using a von Mises-Fisher kernel density estimate

Contour plot of spherical data using a von Mises-Fisher kernel density estimate
Euler angles from a rotation matrix on SO(3)

Compute the Euler angles from a rotation matrix on SO(3).
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Contour plots of the von Mises-Fisher distribution

Contour plots of the von Mises-Fisher distribution on the sphere
Cross validation in von Mises-Fisher discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming a von Mises-Fisher distribution