CircStat for Matlab
=======================


Toolbox for circular statistics with Matlab. 


Authors: Philipp Berens & Marc J. Velasco

Email: berens@tuebingen.mpg.de

Homepage: http://www.kyb.tuebingen.mpg.de/~berens/circStat.html


Contributors:
Tal Krasovsky


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:

circ_r 				Resultant vector 
length
circ_mean 		Mean direction of a sample of circular 
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
cir
c_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



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.


By Philipp Berens and Marc J. Velasco, 2009
berens@tuebingen.mpg.de , velasco@ccs.fau.edu - www.kyb.mpg.de/~berens/circStat.html
Distributed under Open Source BSD License




