Circular Statistics Toolbox (Directional Statistics)

Compute descriptive and inferential statistics for circular or directional data.
Aktualisiert 8. Jun 2012

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CircStat for Matlab

Toolbox for circular statistics with Matlab.

Authors: Philipp Berens

Marc Velasco, Tal Krasovsky

P. Berens, CircStat: A Matlab Toolbox for Circular Statistics, Journal of Statistical Software, Volume 31, Issue 10, 2009

Please cite this paper when the provided code is used (not the technical report!). See licensing terms for details.

circ_r Resultant vector length
circ_mean Mean direction of a sample of circular data
circ_axial Mean direction for axial data
circ_median Median direction of a sample of circular data
circ_std Dispersion around the mean direction (std, mardia)
circ_var Circular variance
circ_skewness Circular skewness
circ_kurtosis Circular kurtosis
circ_moment Circular p-th moment
circ_dist Distances around a circle
circ_dist2 Pairwise distances around a circle
circ_confmean Confidence intervals for mean direction
circ_stats Summary statistics

circ_rtest Rayleigh's test for nonuniformity
circ_otest Hodges-Ajne test (omnibus test) for nonuniformity
circ_raotest Rao's spacing test for nonuniformity
circ_vtest V-Test for nonuniformity with known mean direction
circ_medtest Test for median angle
circ_mtest One-sample test for specified mean direction
circ_wwtest Multi-sample test for equal means, one-factor ANOVA
circ_hktest Two-factor ANOVA
circ_ktest Test for equal concentration parameter
circ_symtest Test for symmetry around median angle
circ_kuipertest Test whether two distributions are identical (like KS test)

circ_corrcc Circular-circular correlation coefficient
circ_corrcl Circular-linear correlation coefficient

circ_kappa Compute concentration parameter of a vm distribution

circ_plot Visualization for circular data
circ_clust Simple clustering for circular data
circ_samplecdf Evaluate CDF of a sample of angles

rad2ang Convert radian to angular values
ang2rad Convert angular to radian values

All functions take arguments in radians (expect for ang2rad). For a detailed description of arguments and outputs consult the help text in the files.

Since 2010, most functions for descriptive statistics can be used in Matlab style matrix computations. As a last argument, add the dimension along which you want to average. This changes the behavior slightly from previous relaeses, in that input is not reshaped anymore into vector format. Per default, all computations are performed columnwise (along dimension 1).

- E. Batschelet, Circular Statistics in Biology, Academic Press, 1981
- N.I. Fisher, Statistical analysis of circular data, Cambridge University Press, 1996
- S.R. Jammalamadaka et al., Topics in circular statistics, World Scientific, 2001
- J.H. Zar, Biostatistical Analysis, Prentice Hall, 1999

If you have suggestions, bugs or feature requests or want to contribute code, please email me.

Zitieren als

Philipp Berens (2024). Circular Statistics Toolbox (Directional Statistics) (, MATLAB Central File Exchange. Abgerufen .

Kompatibilität der MATLAB-Version
Erstellt mit R2012a
Kompatibel mit allen Versionen
Windows macOS Linux

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Version Veröffentlicht Versionshinweise

Update on median, wwtest, hktest, kuiper. Also added examples from paper.

Bugfixes in wwtest, kuiper, median, hktest and added example files from paper.

Updates fixing the bugs reported in the last few months.

Touched files:
kuipertest, plot, kurtosis, clust, axialmean, vmrnd, skewness, moment, median

Bugfixes and updates

Bug in circ_clust fixed.

Bugfix in circ_hktest: lines 159 and 163 were switched.

Small bugfixes, mainly in the help sections

Various bugfixes. Added Matlab-style computations.

Bug fix in circ_stats.

Bug fix in circ_skewness and circ_kurtosis. Thanks to Shiquan Wang.

Bug fix in circ_dist and circ_clust.

Bug fix.

Two new tests

Updated reference for paper

Added reference.

Removed some bugs.

Added new, more complicated tests (ANOVA like testing).

A number of small bug fixes.

Changed licensing