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Directional (version 7.0)

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) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (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) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (2020). "Spherical regression models with general covariates and anisotropic errors". Statistics and Computing 30(1): 153--165. . d) Tsagris M. and Alenazi A. (2024). "An investigation of hypothesis testing procedures for circular and spherical mean vectors". Communications in Statistics-Simulation and Computation, 53(3): 1387--1408. . e) Yu Z. and Huang X. (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statistics, 18(1): 301--334. . f) Tsagris M. and Alzeley O. (2024). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". Australian & New Zealand Journal of Statistics (Accepted for publication). . g) Tsagris M., Papastamoulis P. and Kato S. (2024). "Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution". .

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Install

install.packages('Directional')

Monthly Downloads

1,471

Version

7.0

License

GPL (>= 2)

Maintainer

Michail Tsagris

Last Published

December 5th, 2024

Functions in Directional (7.0)

k-NN algorithm using the arc cosinus distance

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

Circular correlations between two circular variables
Density of a mixture of rotationally symmetric distributions

Density of a mixture of rotationally symmetric distributions
Directional-package

This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.
Density of the SESPC distribution

Density of the SESPC distribution
The k-nearest neighbours using the cosinus distance

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

Density of the spherical ESAG and Kent distributions
Tuning of the k-NN algorithm using the arc cosinus distance

k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
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
Column-wise uniformity Watson test for circular data

Column-wise uniformity tests for circular 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
Conversion of cosines to azimuth and plunge

Conversion of cosines to azimuth and plunge
Transform unit vectors to angular data

Transform unit vectors to angular data
Density of the Wood bimodal distribution on the sphere

Density of the Wood bimodal distribution on the sphere
Summary statistics for circular data

Summary statistics for circular data
MLE of the ESAG distribution in arbitrary dimensions

MLE of the ESAG distribution
Prediction in discriminant analysis based on some distributions

Prediction of a new observation using discriminant analysis based on some distributions
Cross validation for estimating the classification rate

Cross validation for estimating the classification rate
Bootstrap 2-sample mean test for (hyper-)spherical data

Bootstrap 2-sample mean test for (hyper-)spherical data
Spherical regression using the ESAG distribution

Spherical regression using the ESAG distribution
Simulation of random values from a Bingham distribution

Simulating from a Bingham distribution
Spherical regression using rotationally symmetric distributions

Spherical regression using rotationally symmetric distributions
Circular-linear correlation

Circular-linear correlation
Saddlepoint approximations of the Fisher-Bingham distributions

Saddlepoint approximations of the Fisher-Bingham distributions
Density of some circular distributions

Density of some circular distributions
Euclidean transformation

Euclidean transformation
Anova for circular data

Analysis of variance for circular data
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
Density of some (hyper-)spherical distributions

Density of some (hyper-)spherical distributions
Hypothesis test for von Mises-Fisher distribution over Kent distribution

Hypothesis test for von Mises-Fisher distribution over Kent distribution
Haversine distance matrix

Harvesine distance matrix
Hypothesis test for IAG distribution over the ESAG distribution

Hypothesis test for IAG distribution over the ESAG distribution
k-NN regression

k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Inverse of the Euclidean transformation

Inverse of the Euclidean transformation
Logarithm of the Kent distribution normalizing constant

Logarithm of the Kent distribution normalizing constant
Tuning of the k-NN regression

Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variables
Rotation matrix on SO(3) from three Euler angles

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

MLe of the Kent distribution
Summary statistics for grouped circular data

Summary statistics for grouped circular data
Habeck's rotation matrix generation

Generation of three-dimensional random rotations using Habeck's algorithm.
Permutation based 2-sample mean test for (hyper-)spherical data

Permutation based 2-sample mean test for (hyper-)spherical data
Spherical and hyperspherical median

Fast calculation of the spherical and hyperspherical median
MLE of some circular distributions with multiple samples

MLE of some circular distributions with multiple samples
Mixtures of rotationally symmetric distributions

Mixtures of rotationally symmetric distributions
Bootstrap ANOVA for (hyper-)spherical data

Bootstrap ANOVA for (hyper-)spherical data
Rayleigh's test of uniformity

Rayleigh's test of uniformity
Goodness of fit test for grouped data

Goodness of fit test for grouped 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.
Inverse of Lambert's equal area projection

Inverse of Lambert's equal area projection
Simulation from a Bingham distribution using any symmetric matrix A

Simulation from a Bingham distribution using any symmetric matrix A
Anova for (hyper-)spherical data

Analysis of variance for (hyper-)spherical data
Bootstrap 2-sample mean test for circular data

Bootstrap 2-sample mean test for circular data
Normalised spatial median for directional data

Normalised spatial median for directional data
Score test for many simple CIPC and SMPL regressions

Score test for many simple CIPC and SPML regressions
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
Maps of the world and the continents

maps of the world and the continents
MLE of the SESPC distribution

MLE of the SESPC distribution
Permutation based 2-sample mean test for circular data

Permutation based 2-sample mean test for circular data
Naive Bayes classifiers for circular data

Naive Bayes classifiers for directional data
Generate random folds for cross-validation

Generate random folds for cross-validation
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
von Mises kernel density estimation

Kernel density estimation of circular data with a von Mises kernel
Bootstrap ANOVA for circular data

Bootstrap ANOVA for circular data
MLE of the Matrix Fisher distribution on SO(3)

MLE of the Matrix Fisher distribution on SO(3)
Rotation matrix from a rotation axis and angle of rotation

Rotation matrix from a rotation axis and angle of rotation
Hyper spherical-spherical regression

Hyper spherical-spherical regression
Lambert's equal area projection

Lambert's equal area projection
Uniformity test for circular data

Uniformity tests for circular data.
MLE of (hyper-)spherical rotationally symmetric distributions

MLE of (hyper-)spherical rotationally symmetric distributions
Converting an unsigned unit quaternion to rotation matrix on SO(3)

Converting an unsigned unit quaternion to rotation matrix on SO(3)
MLE of the Purkayashta distribution

MLE of the Purkayashta distribution
Angular central Gaussian random values simulation

Angular central Gaussian random values simulation
Cumulative distribution function of circular distributions

Cumulative distribution function of circular distributions
Simulation of random values from a spherical Fisher-Bingham distribution

Simulation of random values from a spherical Fisher-Bingham distribution
Euler angles from a rotation matrix on SO(3)

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

Simulation of random values from the SESPC distribution
Random sample of matrices in SO(p)

Random sample of matrices in SO(p)
Spherical-spherical correlation

Spherical-spherical correlation
Spherical and hyper-spherical distance correlation

Spherical and hyper-spherical distance correlation
Read a file as a Filebacked Big Matrix

Read a file as a Filebacked Big Matrix
Test for a given mean direction

Test for a given mean direction
Simulation of random values from the ESAG distribution

Simulation of random values from the ESAG distribution
Contour plots of some rotationally symmetric distributions

Contour plots of some rotationally symmetric distributions
Simulation of random values from a spherical Kent distribution

Simulation of random values from a spherical Kent distribution
von Mises-Fisher kernel density estimation for (hyper-)spherical data

Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernel
Hypothesis test for SIPC distribution over the SESPC distribution

Hypothesis test for SIPC distribution over the SESPC distribution
Projections based test of uniformity

Projections based test of uniformity
Spherical regression using the SESPC distribution

Spherical regression using the SESPC distribution
Simulation of random values from rotationally symmetric distributions

Simulation of random values from rotationally symmetric distributions
Two sample location test for (hyper-)spherical data

Two sample location test for (hyper-)spherical data
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
Simulation of random values from some circular distributions

Simulation of random values from some circular distributions
Generation of unit vector(s) with a given angle

Generation of unit vector(s) with a given angle
Contour plot (on the sphere) of some spherical rotationally symmetric distributions

Contour plot (on the sphere) of some spherical rotationally symmetric distributions
Simulation from a Matrix Fisher distribution on SO(3)

Simulation from a Matrix Fisher distribution on SO(3)
Check visually whether matrix Fisher samples is correctly generated or not

Check visually whether matrix Fisher samples is correctly generated or not.
Simulation of random values from a mixture of rotationally symmetric distributions

Simulation of random values from a mixture of rotationally symmetric 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
Converting a rotation matrix on SO(3) to an unsigned unit quaternion

Converting a rotation matrix on SO(3) to an unsigned unit quaternion
(Hyper-)spherical regression using rotational symmetric distributions

(Hyper-)spherical regression using the 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
Circular or angular regression

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

Tuning of the bandwidth parameter in the von Mises kernel for circular data
Rotation matrix to rotate a spherical vector along the direction of another

Rotation matrix to rotate a spherical vector along the direction of another
Spherical-spherical regression

Spherical-Spherical regression
Prediction with some naive Bayes classifiers for circular data

Prediction with some naive Bayes classifiers for circular data
Contour plot (on the sphere) of the SESPC distribution

Contour plot (on the sphere) of the SESPC distribution
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
MLE of the Wood bimodal distribution on the sphere

MLE of the Wood bimodal distribution on the sphere
Rotation axis and angle of rotation given a rotation matrix

Rotation axis and angle of rotation given a rotation matrix
Circular distance correlation between two circular variables

Circular distance correlation between two circular variables
BIC for the model based clustering using mixtures of rotationally symmetric distributions

BIC to choose the number of components in a model based clustering using mixtures of rotationally symmetric distributions
Circular correlations between one and many circular variables

Circular correlations between two circular variables