CircStat for Matlab

Toolbox for circular statistics with Matlab.

Authors:

Philipp Berens

Email: philipp.berens@uni-tuebingen.de

Homepage: www.berenslab.org

Contributors:

Tal Krasovsky & Marc J. Velasco

Reference:

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

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

Contents:

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. By default, all computations are performed along the first non-singular dimension. For example circ_mean([0 pi]) and circ_mean([0; pi]) both return pi/2. This changes the behavior slightly from previous releases, but acts more like built-in Matlab functions (e.g., sum. Many functions also take a dim argument indicating the dimension along which data should be processed.

Descriptive Statistics

• 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

Statistical Tests

• 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)

Correlations

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

Misc.

• circ_kappa Compute concentration parameter of a von Mises 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

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

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.

Disclaimer:

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