# CircStat

## Description

CircStat is a Matlab toolbox containing a variety of functions for performing circular or directional statistics with MATLAB. The toolbox was MATLAB central's pick of the week. A detailed description can be found in:
P. Berens

#circular statistics, #directional statistics, #software, #matlab

Code, URL, PDF, BibTex

**CircStat: A Matlab Toolbox for Circular Statistics***Journal of Statistical Software, 2009*#circular statistics, #directional statistics, #software, #matlab

Code, URL, PDF, BibTex

Please cite this paper when the provided code is used. See licensing terms for details.

**Contents:**

`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). If you prefer to use the old functions, for now they are contained in the subdirectory 'old'.

**References:**

- 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

**Contact:**

If you have suggestions, bugs or feature requests or want to contribute code, please email me (berens@tuebingen.mpg.de).

All functions in this toolbox were implemented with care and tested on the examples presented in 'Biostatistical Analysis' were possible. Nevertheless, they may contain errors or bugs, which may affect the outcome of your analysis. We do not take responsibility for any harm coming from using this toolbox, neither if it is caused by errors in the software nor if it is caused by its improper application. Please email us any bugs you find.