A Collection of Functions for Directional Data Analysis
Rotation axis and angle of rotation given a rotation matrix
BIC to choose the number of components in a model based clustering usi...
Circular correlations between two circular variables
Circular correlations between two circular variables
Circular distance correlation between two circular variables
Summary statistics for circular data
Circular-linear correlation
Column-wise MLE of the angular Gaussian and the von Mises Fisher distr...
Column-wise uniformity tests for circular data
A test for testing the equality of the concentration parameter among g...
Conversion of cosines to azimuth and plunge
The k-nearest neighbours using the cosinus distance
Density of the spherical ESAG and Kent distributions
Cross validation for estimating the classification rate
Prediction of a new observation using discriminant analysis based on s...
This is an R package that provides methods for the statistical analysi...
k-NN algorithm using the arc cosinus distance
k-NN algorithm using the arc cosinus distance. Tuning the k neigbours
Density of a mixture of rotationally symmetric distributions
Density of the SESPC distribution
Density of some circular distributions
Density of some (hyper-)spherical distributions
Density of the Wood bimodal distribution on the sphere
Contour plot (on the plane) of the ESAG and Kent and ESAG distribution...
MLE of the ESAG distribution
Spherical regression using the ESAG distribution
Transform unit vectors to angular data
Inverse of the Euclidean transformation
Euclidean transformation
Construct a rotation matrix on SO(3) from the Euler angles.
Simulating from a Bingham distribution
Saddlepoint approximations of the Fisher-Bingham distributions
Hypothesis test for von Mises-Fisher distribution over Kent distributi...
Goodness of fit test for grouped data
Summary statistics for grouped circular data
Generation of three-dimensional random rotations using Habeck's algori...
Harvesine distance matrix
Analysis of variance for (hyper-)spherical data
Bootstrap 2-sample mean test for (hyper-)spherical data
Analysis of variance for circular data
Permutation based 2-sample mean test for (hyper-)spherical data
Bootstrap ANOVA for (hyper-)spherical data
Bootstrap 2-sample mean test for circular data
Permutation based 2-sample mean test for circular data
Bootstrap ANOVA for circular data
Hyper spherical-spherical regression
Spherical regression using rotationally symmetric distributions
Hypothesis test for IAG distribution over the ESAG distribution
Logarithm of the Kent distribution normalizing constant
MLe of the Kent distribution
k-NN regression with Euclidean or (hyper-)spherical response and or pr...
Tuning of the k-NN regression with Euclidean or (hyper-)spherical resp...
Uniformity tests for circular data.
Inverse of Lambert's equal area projection
Lambert's equal area projection
Generate random folds for cross-validation
MLE of the Matrix Fisher distribution on SO(3)
Test for a given mean direction
Fast calculation of the spherical and hyperspherical median
Contour plot of a mixture of von Mises-Fisher distributions model for ...
Mixtures of rotationally symmetric distributions
MLE of some circular distributions with multiple samples
Normalised spatial median for directional data
maps of the world and the continents
Hypothesis test for SIPC distribution over the SESPC distribution
Projections based test of uniformity
MLE of the Purkayashta distribution
Cumulative distribution function of circular distributions
Converting an unsigned unit quaternion to rotation matrix on SO(3)
Angular central Gaussian random values simulation
Rayleigh's test of uniformity
Simulation from a Bingham distribution using any symmetric matrix A
Read a file as a Filebacked Big Matrix
Simulation of random values from the ESAG distribution
Simulation of random values from a spherical Fisher-Bingham distributi...
Simulation of random values from a spherical Kent distribution
Simulation from a Matrix Fisher distribution on SO(3)
Simulation of random values from a mixture of rotationally symmetric d...
Rotation matrix from a rotation axis and angle of rotation
Compute the Euler angles from a rotation matrix on SO(3).
Converting a rotation matrix on SO(3) to an unsigned unit quaternion
Rotation matrix to rotate a spherical vector along the direction of an...
Simulation of random values from the SESPC distribution
Random sample of matrices in SO(p)
Simulation of random values from rotationally symmetric distributions
Simulation of random values from some circular distributions
Score test for many simple CIPC and SPML regressions
MLE of the SESPC distribution
Spherical regression using the SESPC distribution
Two sample location test for (hyper-)spherical data
Spherical-spherical correlation
Spherical and hyper-spherical distance correlation
Contour plot (on the sphere) of the ESAG and Kent distributions
Contour plot (on the sphere) of a mixture of von Mises-Fisher distribu...
Spherical-Spherical regression
Contour plot (on the sphere) of the SESPC distribution
Contour plot (on the sphere) of some spherical rotationally symmetric ...
Test for equality of concentration parameters for spherical data
Interactive 3D plot of spherical data
Forward Backward Early Dropping selection for circular data using the ...
MLE of some circular distributions
Circular or angular regression
Many simple circular or angular regressions
A test for testing the equality of the concentration parameter among g...
Generation of unit vector(s) with a given angle
Check visually whether matrix Fisher samples is correctly generated or...
Kernel density estimation of circular data with a von Mises kernel
Naive Bayes classifiers for directional data
Contour plots of some rotationally symmetric distributions
Kernel density estimation for (hyper-)spherical data using a von Mises...
Contour plot of spherical data using a von Mises-Fisher kernel density...
MLE of (hyper-)spherical rotationally symmetric distributions
Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (...
(Hyper-)spherical regression using the rotational symmetric distributi...
Tuning of the bandwidth parameter in the von Mises kernel for circular...
Prediction with some naive Bayes classifiers for circular data
MLE of the Wood bimodal distribution on the sphere
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. <doi:10.1007/s11222-017-9756-4>. 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. <doi:10.1080/23737484.2019.1684854>. 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. <doi:10.1007/s11222-019-09872-2>. 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. <doi:10.1080/03610918.2022.2045499>. 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. <doi:10.1214/23-EJS2210>. f) Tsagris M. and Alzeley O. (2025). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". Australian & New Zealand Journal of Statistics, 67(1): 77--103. <doi:10.1111/anzs.12434>. g) Tsagris M., Papastamoulis P. and Kato S. (2025). "Directional data analysis: spherical Cauchy or Poisson kernel-based distribution". Statistics and Computing, 35:51. <doi:10.1007/s11222-025-10583-0>.