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Directional (version 6.1)

A Collection of Functions for Directional Data Analysis

Description

A collection of functions for directional data (including massive data, with millions of observations) 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 a) 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. . b) Tsagris M. and Alenazi A. (2019). Comparison of discriminant analysis methods on the sphere. Communications in Statistics: Case Studies, Data Analysis and Applications 5(4):467--491. . c) P. J. Paine, S. P. Preston, M. Tsagris and Andrew T. A. Wood (2020). Spherical regression models with general covariates and anisotropic errors. Statistics and Computing 30(1): 153--165. . d) Tsagris M. and Alenazi A. (2022). An investigation of hypothesis testing procedures for circular and spherical mean vectors. Communications in Statistics-Simulation and Computation (Accepted for publication). . e) Tsagris M. and Alzeley O. (2023). Circular and spherical projected Cauchy distributions. .

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Version

Install

install.packages('Directional')

Monthly Downloads

735

Version

6.1

License

GPL (>= 2)

Maintainer

Michail Tsagris

Last Published

July 17th, 2023

Functions in Directional (6.1)

Circular correlations between one and many circular variables

Circular correlations between two circular variables
Column-wise MLE of the angular Gaussian and the von Mises Fisher distributions

Column-wise MLE of the angular Gaussian and the von Mises Fisher distributions
Rotation axis and angle of rotation given a rotation matrix

Rotation axis and angle of rotation given a rotation matrix
Directional-package

This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.
Column-wise uniformity Watson test for circular data

Column-wise uniformity tests for circular data
Circular distance correlation between two circular variables

Circular distance correlation between two circular variables
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
Circular correlations between two circular variables

Circular correlations between two circular variables
Tuning of the k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
Summary statistics for circular data

Summary statistics for circular data
Circular-linear correlation

Circular-linear correlation
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
Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
Density of the SESPC distribution

Density of the SESPC distribution
Cross validation for estimating the classification rate

Cross validation for estimating the classification rate
Density of some circular distributions

Density of some circular distributions
Euclidean transformation

Euclidean transformation
MLE of the ESAG distribution

MLE of the ESAG distribution
k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
Density of some (hyper-)spherical distributions

Density of some (hyper-)spherical distributions
Saddlepoint approximations of the Fisher-Bingham distributions

Saddlepoint approximations of the Fisher-Bingham distributions
Density of the Wood bimodal distribution on the sphere

Density of the Wood bimodal distribution on the sphere
Spherical regression using the ESAG distribution

Spherical regression using the ESAG distribution
Rotation matrix on SO(3) from three Euler angles

Construct a rotation matrix on SO(3) from the Euler angles.
Simulation of random values from a Bingham distribution

Simulating from a Bingham distribution
Density of a mixture of von Mises-Fisher distributions

Density of a mixture of von Mises-Fisher distributions
Goodness of fit test for grouped data

Goodness of fit test for grouped data
Summary statistics for grouped circular data

Summary statistics for grouped circular data
The k-nearest neighbours using the cosinus distance

The k-nearest neighbours using the cosinus distance
Density of the spherical ESAG and Kent distributions

Density of the spherical ESAG and Kent distributions
Hypothesis test for von Mises-Fisher distribution over Kent distribution

Hypothesis test for von Mises-Fisher distribution over Kent distribution
Prediction in discriminant analysis based on ESAG distribution

Prediction of a new observation using discriminant analysis based on ESAG distribution
Contour plot (on the plane) of the ESAG and Kent distributions without any data

Contour plot (on the plane) of the ESAG and Kent and ESAG distributions without any data
Bootstrap ANOVA for (hyper-)spherical data

Bootstrap ANOVA for (hyper-)spherical data
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Cross validation with ESAG discrminant analysis

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

MLe of the Kent distribution
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
Inverse of Lambert's equal area projection

Inverse of Lambert's equal area projection
Anova for circular data

Analysis of variance for circular data
Anova for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Haversine distance matrix

Harvesine distance matrix
Generate random folds for cross-validation

Generate random folds for cross-validation
Permutation based 2-sample mean test for (hyper-)spherical data

Permutation based 2-sample mean test for (hyper-)spherical data
Bootstrap 2-sample mean test for (hyper-)spherical data

Bootstrap 2-sample mean test for (hyper-)spherical data
Transform unit vectors to angular data

Transform unit vectors to angular data
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
Spherical regression using the projected normal or the von Mises-Fisher distribution

Spherical regression using the projected normal or the von Mises-Fisher distribution
Permutation based 2-sample mean test for circular data

Permutation based 2-sample mean test for circular data
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
Bootstrap ANOVA for circular data

Bootstrap ANOVA for circular data
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Bootstrap 2-sample mean test for circular data

Bootstrap 2-sample mean test for circular data
MLE of the Matrix Fisher distribution on SO(3)

MLE of the Matrix Fisher distribution on SO(3)
Test for a given mean direction

Test for a given mean direction
Uniformity test for circular data

Uniformity tests for circular data.
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.
Normalised spatial median for directional data

Normalised spatial median for directional data
Maps of the world and the continents

maps of the world and the continents
Simulation from a Matrix Fisher distribution on SO(3)

Simulation from a Matrix Fisher distribution on SO(3)
Simulation of random values from a mixture of von Mises-Fisher distributions

Simulation of random values from a mixture of von Mises-Fisher distributions
Probability density function of the circular Purkayastha distribution

Probability density function of the circular Purkayastha distribution
Lambert's equal area projection

Lambert's equal area projection
Cross validation with Purkayastha discrminant analysis

Cross validation for estimating the classification rate of a discrminant analysis for directional data assuming a Purkayastha distribution
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
Mixtures of Von Mises-Fisher distributions

Mixtures of Von Mises-Fisher distributions
Simulation of random values from the ESAG distribution

Simulation of random values from the ESAG distribution
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
Prediction in discriminant analysis based on Purkayastha distribution

Prediction of a new observation using discriminant analysis based on Purkayastha distribution
MLE of some circular distributions with multiple samples

MLE of some circular distributions with multiple samples
Hypothesis test for SIPC distribution over the SESPC distribution

Hypothesis test for SIPC distribution over the SESPC distribution
Read a file as a Filebacked Big Matrix

Read a file as a Filebacked Big Matrix
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Probability density function of the circular (wrapped) exponential distribution

Probability density function of the circular (wrapped) exponential distribution
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Simulation of random values from some circular distributions

Simulation of random values from some circular distributions
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Probability density function of the von Mises-Fisher distribution

Probability density function of the von Mises-Fisher distribution
Converting an unsigned unit quaternion to rotation matrix on SO(3)

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

Compute the Euler angles from a rotation matrix on SO(3).
MLE of the SESPC distribution

MLE of the SESPC distribution
Simulation of random values from rotationally symmetric distributions

Simulation of random values from rotationally symmetric distributions
Simulation of random values from the SESPC distribution

Simulation of random values from the SESPC distribution
Spherical-spherical regression

Spherical-Spherical regression
Contour plot (on the sphere) of the SESPC distribution

Contour plot (on the sphere) of the SESPC distribution
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Spherical-spherical correlation

Spherical-spherical correlation
Spherical and hyper-spherical distance correlation

Spherical and hyper-spherical distance correlation
Contour plot (on the sphere) of the ESAG and Kent distributions

Contour plot (on the sphere) of the ESAG and Kent distributions
Contour plot (on the sphere) of a mixture of von Mises-Fisher distributions

Contour plot (on the sphere) of a mixture of von Mises-Fisher distributions
Generation of unit vector(s) with a given angle

Generation of unit vector(s) with a given angle
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
Contour plots of some rotational symmetric distributions

Contour plots of some rotational symmetric distributions
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
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
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
MLE of (hyper-)spherical rotational symmetric distributions

MLE of (hyper-)spherical rotational symmetric distributions
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
Naive Bayes classifiers for circular data

Naive Bayes classifiers for directional data
Contour plot (on the sphere) of some spherical rotational symmetric distributions

Contour plot (on the sphere) of some spherical rotational symmetric distributions
Test for equality of concentration parameters for spherical data

Test for equality of concentration parameters for spherical data
MLE of some circular distributions

MLE of some circular distributions
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
Tuning of the bandwidth parameter in the von Mises kernel

Tuning of the bandwidth parameter in the von Mises kernel for circular data
Circular or angular regression

Circular or angular regression
Interactive 3D plot of spherical data

Interactive 3D plot of spherical data
Forward Backward Early Dropping selection for circular data using the SPML regression

Forward Backward Early Dropping selection for circular data using the SPML regression
Many simple circular or angular regressions

Many simple circular or angular regressions
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
Prediction with some naive Bayes classifiers for circular data

Prediction with some naive Bayes classifiers for circular data
MLE of the Wood bimodal distribution on the sphere

MLE of the Wood bimodal distribution on the sphere