Package: Directional 7.0

Michail Tsagris

Directional: A Collection of Functions for Directional Data Analysis

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. (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). <doi:10.48550/arXiv.2302.02468>. g) Tsagris M., Papastamoulis P. and Kato S. (2024). "Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution". <doi:10.48550/arXiv.2409.03292>.

Authors:Michail Tsagris [aut, cre], Giorgos Athineou [aut], Christos Adam [aut], Zehao Yu [aut], Anamul Sajib [ctb], Eli Amson [ctb], Micah J. Waldstein [ctb], Panagiotis Papastamoulis [ctb]

Directional_7.0.tar.gz
Directional_7.0.tar.gz(r-4.5-noble)Directional_7.0.tar.gz(r-4.4-noble)
Directional_7.0.tgz(r-4.4-emscripten)Directional_7.0.tgz(r-4.3-emscripten)
Directional.pdf |Directional.html✨
Directional/json (API)

# Install 'Directional' in R:
install.packages('Directional', repos = c('https://cran.r-universe.dev', 'https://cloud.r-project.org'))

Peer review:

This package does not link to any Github/Gitlab/R-forge repository. No issue tracker or development information is available.

5.14 score 3 stars 3 packages 127 scripts 1.4k downloads 4 mentions 239 exports 93 dependencies

Last updated 19 days agofrom:1694c80196. Checks:OK: 2. Indexed: yes.

TargetResultDate
Doc / VignettesOKDec 05 2024
R-4.5-linuxOKDec 05 2024

Exports:acg.mleafricaArotationasiabic.mixpkbdbic.mixspcauchybic.mixvmfcardio.mlecipc.mlecipc.regcirc.cor1circ.cor2circ.cors1circ.cors2circ.dcorcirc.summarycircbeta.mlecircexp.mlecirclin.corcircpurka.regcolspml.mlecolvm.mlecolwatsonsconc.testcosapcosnndcardiodcipcdcircbetadcircexpdcircpurkadesagdESAGddgcpcdggvmdirdadirda.cvdirknndirknn.tunedkentdmixpkbddmixspcauchydmixvmfdmmvmdpkbddpurkadsespcdspcauchydspmldvmdvmfdwooddwrapcauchyembed.aovembed.bootembed.circaovembed.permembedcirc.bootembedcirc.permesag.contouresag.mleesag.regESAGd.mleetoaeuclideuclid.inveul2roteuropef.rbingfb.saddlefishkentgcpc.mlegcpc.regggvm.mlegroup.gofgroup.vmhabeck.rothaversine.disthcf.aovhcf.boothcf.circaovhcf.permhcfboothcfcirc.boothcfcirc.permhcfcircboothclr.aovhclr.boothclr.circaovhclr.permhclrcirc.boothclrcirc.permhet.aovhet.boothet.circaovhet.permhetboothetcirc.boothetcirc.permhetcircboothspher.regiag.mleiag.regiagdiagesagkent.contourkent.logconkent.mleknn.regknnreg.tunekuiperlambertlambert.invlr.aovlr.bootlr.circaovlr.permlrcirc.bootlrcirc.permmakefoldsmatrixfisher.mlemeandir.testmediandirmediandir_2mixpkbd.mlemixspcauchy.mlemixvmf.contourmixvmf.mlemmvm.mlemultispml.mlemultivm.mlemultivmf.mlenorth.americansmedianoceaniapc.testpcardiopcipcpcircbetapcircexppcircpurkapgcpcpk2pkbd.contourpkbd.mlepkbd.mle2pkbd.regpkbd.reg2pkbd2testpmmvmpspmlptestpurka.contourpurka.mlepvmpwrapcauchyquat2rotracgrayleighrbinghamrcipcrcircbetarcircexprcircpurkaread.fbmresagrESAGdrfbrgcpcriagrkentrmatrixfisherrmixpkbdrmixspcauchyrmixvmfrot.matrixrot2eulrot2quatrotationrpkbdrsespcrsoprspcauchyrspmlrvmfrvonmisesrwrapcauchyscore.cipcscore.spmlsespc.mlesespc.regsipc.mlesipc.regsouth.americasp2spcauchy.contourspcauchy.mlespcauchy.mle2spcauchy.regspcauchy2testspher.corspher.dcorspher.esag.contourspher.kent.contourspher.mixvmf.contourspher.pkbd.contourspher.purka.contourspher.regspher.sespc.contourspher.spcauchy.contourspher.vmf.contourspherconc.testsphereplotspml.fbedspml.mlespml.nbspml.regspml.regsspmlnb.predtang.concvecvisual.checkvm.kdevm.nbvmf.contourvmf.kdevmf.kerncontourvmf.mlevmf.regvmf2vmf2testvmfkde.tunevmfregvmkde.tunevmnb.predwatsonwood.mleworldmapwrapcauchy.mle

Dependencies:askpassbase64encbigassertrbigparallelrbigstatsrbitbslibcachemclassclassIntclicodetoolscolorspacecowplotcurlDBIdigestdoParallele1071evaluatefansifarverfastmapffflockfontawesomeforeachfsggplot2gluegtablehighrhtmltoolshtmlwidgetshttrisobanditeratorsjquerylibjsonliteKernSmoothknitrlabelinglatticelifecyclemagrittrMASSMatrixmemoisemgcvmimemunsellnlmeopensslparallellypillarpkgconfigproxypsR6rappdirsRColorBrewerRcppRcppArmadilloRcppEigenRcppGSLRcppParallelRcppZigguratRfastRfast2rglRhpcBLASctlrlangrmarkdownrmioRnanoflannrnaturalearthRSpectras2sassscalessfsysterratibbletinytexunitsutf8vctrsviridisLitewithrwkxfunyaml

Readme and manuals

Help Manual

Help pageTopics
This is an R package that provides methods for the statistical analysis of directional data, including massive (very large scale) directional data.Directional-package
(Hyper-)spherical regression using the rotational symmetric distributionspkbd.reg pkbd.reg2 spcauchy.reg vmfreg
A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar datatang.conc
Angular central Gaussian random values simulationracg
Analysis of variance for (hyper-)spherical dataembed.aov hcf.aov hclr.aov het.aov lr.aov
Analysis of variance for circular dataembed.circaov hcf.circaov hclr.circaov het.circaov lr.circaov
BIC to choose the number of components in a model based clustering using mixtures of rotationally symmetric distributionsbic.mixpkbd bic.mixspcauchy bic.mixvmf
Bootstrap 2-sample mean test for (hyper-)spherical dataembed.boot hcf.boot hclr.boot het.boot lr.boot
Bootstrap 2-sample mean test for circular dataembedcirc.boot hcfcirc.boot hclrcirc.boot hetcirc.boot lrcirc.boot
Bootstrap ANOVA for (hyper-)spherical datahcfboot hetboot
Bootstrap ANOVA for circular datahcfcircboot hetcircboot
Check visually whether matrix Fisher samples is correctly generated or not.visual.check
Circular correlations between two circular variablescirc.cors1 circ.cors2
Circular correlations between two circular variablescirc.cor1 circ.cor2
Circular distance correlation between two circular variablescirc.dcor
Circular or angular regressioncipc.reg circpurka.reg gcpc.reg spml.reg
Circular-linear correlationcirclin.cor
Column-wise MLE of the angular Gaussian and the von Mises Fisher distributionscolspml.mle colvm.mle
Column-wise uniformity tests for circular datacolwatsons
Contour plot (on the plane) of the ESAG and Kent and ESAG distributions without any dataesag.contour kent.contour
Contour plot (on the sphere) of a mixture of von Mises-Fisher distributionsspher.mixvmf.contour
Contour plot (on the sphere) of some spherical rotationally symmetric distributionsspher.pkbd.contour spher.purka.contour spher.spcauchy.contour spher.vmf.contour
Contour plot (on the sphere) of the ESAG and Kent distributionsspher.esag.contour spher.kent.contour
Contour plot (on the sphere) of the SESPC distributionspher.sespc.contour
Contour plot of a mixture of von Mises-Fisher distributions model for spherical data only.mixvmf.contour
Contour plot of spherical data using a von Mises-Fisher kernel density estimatevmf.kerncontour
Contour plots of some rotationally symmetric distributionspkbd.contour purka.contour spcauchy.contour vmf.contour
Conversion of cosines to azimuth and plungecosap
Converting a rotation matrix on SO(3) to an unsigned unit quaternionrot2quat
Converting an unsigned unit quaternion to rotation matrix on SO(3)quat2rot
Cross validation for estimating the classification ratedirda.cv
Cumulative distribution function of circular distributionspcardio pcipc pcircbeta pcircexp pcircpurka pgcpc pmmvm pspml pvm pwrapcauchy
Density of a mixture of rotationally symmetric distributionsdmixpkbd dmixspcauchy dmixvmf
Density of some (hyper-)spherical distributionsdpkbd dpurka dspcauchy dvmf iagd
Density of some circular distributionsdcardio dcipc dcircbeta dcircexp dcircpurka dgcpc dggvm dmmvm dspml dvm dwrapcauchy
Density of the SESPC distributiondsespc
Density of the spherical ESAG and Kent distributionsdesag dESAGd dkent
Density of the Wood bimodal distribution on the spheredwood
Euclidean transformationeuclid
Compute the Euler angles from a rotation matrix on SO(3).rot2eul
Forward Backward Early Dropping selection for circular data using the SPML regressionspml.fbed
Generate random folds for cross-validationmakefolds
Generation of unit vector(s) with a given anglevec
Goodness of fit test for grouped datagroup.gof
Generation of three-dimensional random rotations using Habeck's algorithm.habeck.rot
Harvesine distance matrixhaversine.dist
Hyper spherical-spherical regressionhspher.reg
Hypothesis test for IAG distribution over the ESAG distributioniagesag
Hypothesis test for SIPC distribution over the SESPC distributionpc.test
Hypothesis test for von Mises-Fisher distribution over Kent distributionfishkent
Interactive 3D plot of spherical datasphereplot
Inverse of Lambert's equal area projectionlambert.inv
Inverse of the Euclidean transformationeuclid.inv
k-NN algorithm using the arc cosinus distancedirknn
k-NN regression with Euclidean or (hyper-)spherical response and or predictor variablesknn.reg
Lambert's equal area projectionlambert
Logarithm of the Kent distribution normalizing constantkent.logcon
Many simple circular or angular regressionsspml.regs
maps of the world and the continentsafrica asia europe north.america oceania south.america worldmap
Mixtures of rotationally symmetric distributionsmixpkbd.mle mixspcauchy.mle mixvmf.mle
MLE of (hyper-)spherical rotationally symmetric distributionsacg.mle iag.mle multivmf.mle pkbd.mle pkbd.mle2 sipc.mle spcauchy.mle spcauchy.mle2 vmf.mle
MLE of some circular distributionscardio.mle cipc.mle circbeta.mle circexp.mle gcpc.mle ggvm.mle mmvm.mle spml.mle wrapcauchy.mle
MLE of some circular distributions with multiple samplesmultispml.mle multivm.mle
MLE of the ESAG distributionesag.mle ESAGd.mle
MLe of the Kent distributionkent.mle
MLE of the Matrix Fisher distribution on SO(3)matrixfisher.mle
MLE of the Purkayashta distributionpurka.mle
MLE of the SESPC distributionsespc.mle
MLE of the Wood bimodal distribution on the spherewood.mle
Naive Bayes classifiers for directional dataspml.nb vm.nb
Normalised spatial median for directional datansmedian
Permutation based 2-sample mean test for (hyper-)spherical dataembed.perm hcf.perm hclr.perm het.perm lr.perm
Permutation based 2-sample mean test for circular dataembedcirc.perm hcfcirc.perm hclrcirc.perm hetcirc.perm lrcirc.perm
Prediction of a new observation using discriminant analysis based on some distributionsdirda
Prediction with some naive Bayes classifiers for circular dataspmlnb.pred vmnb.pred
Projections based test of uniformityptest
Random sample of matrices in SO(p)rsop
Rayleigh's test of uniformityrayleigh
Read a file as a Filebacked Big Matrixread.fbm
Rotation axis and angle of rotation given a rotation matrixArotation
Rotation matrix from a rotation axis and angle of rotationrot.matrix
Construct a rotation matrix on SO(3) from the Euler angles.eul2rot
Rotation matrix to rotate a spherical vector along the direction of anotherrotation
Saddlepoint approximations of the Fisher-Bingham distributionsfb.saddle
Score test for many simple CIPC and SPML regressionsscore.cipc score.spml
Simulation from a Bingham distribution using any symmetric matrix Arbingham
Simulation from a Matrix Fisher distribution on SO(3)rmatrixfisher
Simulating from a Bingham distributionf.rbing
Simulation of random values from a mixture of rotationally symmetric distributionsrmixpkbd rmixspcauchy rmixvmf
Simulation of random values from a spherical Fisher-Bingham distributionrfb
Simulation of random values from a spherical Kent distributionrkent
Simulation of random values from rotationally symmetric distributionsriag rpkbd rspcauchy rvmf
Simulation of random values from some circular distributionsrcipc rcircbeta rcircexp rcircpurka rgcpc rspml rvonmises rwrapcauchy
Simulation of random values from the ESAG distributionresag rESAGd
Simulation of random values from the SESPC distributionrsespc
Spherical and hyper-spherical distance correlationspher.dcor
Fast calculation of the spherical and hyperspherical medianmediandir mediandir_2
Spherical regression using rotationally symmetric distributionsiag.reg sipc.reg vmf.reg
Spherical regression using the ESAG distributionesag.reg
Spherical regression using the SESPC distributionsespc.reg
Spherical-spherical correlationspher.cor
Spherical-Spherical regressionspher.reg
Summary statistics for circular datacirc.summary
Summary statistics for grouped circular datagroup.vm
Test for a given mean directionmeandir.test
Test for equality of concentration parameters for spherical dataspherconc.test
A test for testing the equality of the concentration parameter among g samples, where g >= 2 for ciruclar dataconc.test
The k-nearest neighbours using the cosinus distancecosnn
Transform unit vectors to angular dataetoa
Tuning of the bandwidth parameter in the von Mises kernel for circular datavmkde.tune
Tuning of the bandwidth parameter in the von Mises-Fisher kernel for (hyper-)spherical datavmfkde.tune
k-NN algorithm using the arc cosinus distance. Tuning the k neigboursdirknn.tune
Tuning of the k-NN regression with Euclidean or (hyper-)spherical response and or predictor variablesknnreg.tune
Two sample location test for (hyper-)spherical datapk2 pkbd2test sp2 spcauchy2test vmf2 vmf2test
Uniformity tests for circular data.kuiper watson
Kernel density estimation of circular data with a von Mises kernelvm.kde
Kernel density estimation for (hyper-)spherical data using a von Mises-Fisher kernelvmf.kde