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Toolbox for circular statistics with Matlab.

Philipp Berens

Email:philipp.berens@uni-tuebingen.de

Homepage:www.berenslab.org

Tal Krasovsky & Marc J. Velasco

P. Berens, CircStat: A Matlab Toolbox for Circular Statistics, Journal of Statistical Software, Volume 31, Issue 10, 2009http://www.jstatsoft.org/v31/i10

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

• circ_r Resultant vector length
• circ_mean Mean direction of a sample of circular data
• circ_axialMean direction for axial data
• circ_medianMedian direction of a sample of circular data
• circ_std Dispersion around the mean direction (std, mardia)
• circ_var Circular variance
• circ_skewnessCircular skewness
• circ_kurtosisCircular kurtosis
• circ_momentCircular p-th moment
• circ_distDistances around a circle
• circ_dist2Pairwise distances around a circle
• circ_confmean Confidence intervals for mean direction
• circ_statsSummary statistics

• circ_rtestRayleigh's test for nonuniformity
• circ_otestHodges-Ajne test (omnibus test) for nonuniformity
• circ_raotestRao's spacing test for nonuniformity
• circ_vtestV-Test for nonuniformity with known mean direction
• circ_medtestTest for median angle
• circ_mtestOne-sample test for specified mean direction
• circ_wwtestMulti-sample test for equal means, one-factor ANOVA
• circ_hktest Two-factor ANOVA
• circ_ktest Test for equal concentration parameter
• circ_symtestTest for symmetry around median angle
• circ_kuipertest Test whether two distributions are identical (like KS test)

• circ_corrccCircular-circular correlation coefficient
• circ_corrclCircular-linear correlation coefficient

• circ_kappa Compute concentration parameter of a von Mises distribution
• circ_plotVisualization for circular data
• circ_clust Simple clustering for circular data
• circ_samplecdf Evaluate CDF of a sample of angles

• rad2angConvert radian to angular values
• ang2radConvert angular to radian values

All functions take arguments in radians (expect forang2rad). 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'.

• 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

The implementation follows in most cases 'Biostatistical Analysis' and all referenced equations and tables are taken from this book, if not otherwise noted. In some cases, the other books were preferred for implementation was more straightforward for solutions presented there.

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

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.

Distributed under Open Source BSD License