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04 Nov 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Dave

This is a great toolbox. However, I have an issue with circ_corrcl, or perhaps I'm misunderstanding its proper use. When I feed it perfectly correlated data, I do not get rho=1:

circ_corrcl(linspace(-pi,pi,1000),linspace(0,10,1000))
ans = .7785

I noticed this while trying to see if I could get a sign for the rho value (which is always positive by the definition in the function). Unfortunately, I don't have a copy of the Zar text available.

07 Oct 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens W. Owen Brimijoin

indispensable

22 Sep 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Ch. Lat.

you meant "circ_rtest Rayleigh's test for nonuniformity " this is not what you look for ?

22 Sep 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Ch. Lat.

@ Wasim Malik. I believe the toolbox fieldtrip has it, but their implementation is a bit more bothersome.

01 Jun 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Wasim Malik

On a quick look, the Moore-Rayleigh test for uniformity of vector data (B.R. Moore, Biometrika, 1980) does not seem to be available in this toolbox. Philipp, do you have any plans to implement it? Alternatively, does anyone know if a Matlab implementation of that test is available elsewhere? Thanks.

01 Jun 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Wasim Malik

14 May 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Diego

Hi everybody!

I have a question about circ_plot.m; When I execute this code the angles appear from 0 to 360 degrees.

I only want represent values from 0 to 180. How I can do it? Thanks in advance!

09 Feb 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Richard Edmonds

Actually, ignore the inverse_cdf function I have provided. It should generate a vlaue for kappa and it needs adjusting for values of thetahat other than zero.

07 Feb 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Richard Edmonds

Great submission. It would be nice to have cdf and inversion cdf for the vmpdf functions. Here's what I wrote for my needs
function p = circ_vmcdf(alpha, thetahat, kappa)
%integrates the pdf from an angle of -pi to an angle alpha
F = @(x)circ_vmpdf(x, thetahat, kappa);
p = quad(F,-pi(),alpha);
end

function theta = circ_vminv(p, thetahat, kappa)
%computes the inverse of the abovecirc_vmcdf.
fun =@(alpha)(circ_vmcdf(alpha, thetahat, kappa)-p);
theta = fzero(fun,[-pi pi]);
end

05 Feb 2014 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Sepideh

Hi,
Thanks for the great contribution.
Can you please let me know if it is ok to get negative mean or median?
Shall I add 360 to the final angle to make it positive?
Cheers,
Sep

09 Oct 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Pete

Thanks for the toolkit.

Does anybody have a clue how to do multiple-regression with circular data?

26 Jul 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens bbegginnerr

Hi everyone,
Quick question regarding circ_hktest - I quite often get NaNs as an output in the 'Interaction' row. Any idea what am I doing wrong?
Thanks in advance for help.

13 Jun 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Philipp Berens

Mear - could you be more specific regarding your doubts about the wwtest?

The negative values for circ_mean are a result of the way circ_mean is implemented. If you prefer them to be between 0 and 2pi, just edit the function to provide the data in that format.

I'll update the von Mises function in a future release.

10 Jun 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Mear

Just a quick question concerning the circ_mean function: I usually get the results in negative values, despite all the input angles being in positive degrees (conv. to rads). It's hardly a big deal to translate this to [0,360] degrees, but it is a bit annoying and seems unneccesary. Is this how it should be? I'm also getting some results for the wwtest which seem very wrong to me (but make sense in light of the negative mean values), and it's making me question the accuracy of this toolbox.

21 May 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens sergio

Marc, thanks, you are right.
I generated a von mises distribution with the mu and kappa estimated from my angles, say x, i.e.:
[mu kappa] = circ_vmpar(x)
and then
vonmis = circ_randvm(mu,kappa,length(x))

Then I use the kuiper test to see whether the two distribution x and vonmis differ significantly (the difference can be in any property, such as mean, location and dispersion):
[H,pValue] = circ_kuipertest(x, vonmis)

However I was wondering if it is possible to have more accurate p-value estimates in the Kuiper test, as already asked by another user before.

18 May 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens sergio

Dear Mark,
thanks for your tip, however I'm not really convinced.
Both the circ_ktest and the circ_kuipertest are not described in the pdf:
http://www.jstatsoft.org/v31/i10/paper

Anyway, circ_ktest is a parametric two-sample test to determine whether two concentration parameters are different.
The circ_kuipertest is a two-sample test which allow to test whether two input samples differ significantly. The difference can be in any property, such as mean location and dispersion. It is a circular analogue of the Kolmogorov-Smirnov test.

I do not understand how these tests could help me with a goodness-of-fit test for the Von Mises-Fisher distribution, but probably is my limit.

Could anyone being of any help?

Regards,

Sergio

14 May 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Marc

sergio - did you see the pdf with descriptions? (http://www.jstatsoft.org/v31/i10/paper)

You probably want either the ktest of the kuipertest.

13 May 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens sergio

Hi guys, I'm new to circular statistics and I've downloaded this package.

Given some vectors, I'd like to test if they are distributed following a Von Mises-Fisher distribution.
Do you know what instructions of the package I should use?
Can you help?

02 Apr 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Aviram Gelblum

After some testing I figured the previous bug has to do with recurrence of unique values in the data. I took care of it by using
alpha=alpha+0.00001*(1:numel(alpha)), but this is obviously a workaround which isn't satisfactory for a self-respecting algorithm.

At any rate, I forgot to mention how great this toolbox is. It has been of great help, and saved me a lot of time and work.

02 Apr 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Aviram Gelblum

Hi, I'm getting wrong clustering using circ_clust.
for example, if I give as an input circ_clust([1 1 1 1 3.5 4 5.5 0.5],2)

I get
ans =
1
2
1
1
1
1
1
1

sometimes the clustering does work, but I don't know why it does/doesn't...

I'm using Matlab 2012b...

14 Feb 2013 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Dylan Muir

Great toolbox. I was wondering if it is possible to have more accurate p-value estimates in the Kuiper test?

11 Dec 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Francesco Montorsi

Hi,
great toolbox, thanks.
By the way, I agree with Allan's comment (see below) that regarding the Von Mises distribution, it may be useful to have an implementation with higher numerical stability. In particular, I added this trivial function, which returns the log-pdf of the Von Mises distrib:

function [p alpha] = circ_vm_logpdf(alpha, thetahat, kappa)

% if no angles are supplied, 100 evenly spaced points around the circle are
% chosen
if nargin < 1 || isempty(alpha)
alpha = linspace(0, 2*pi, 101)';
alpha = alpha(1:end-1);
end
if nargin < 3
kappa = 1;
end
if nargin < 2
thetahat = 0;
end

alpha = alpha(:);

% evaluate pdf
C = -log( 2*pi*besseli(0,kappa) );
p = C + kappa*cos(alpha-thetahat);

Thanks to the greater numerical stability log-pdfs are often used in place of pdfs, so this little function may be of help to others...

06 Nov 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Allan

Hi there, great toolbox. I propose a change to avoid numerical instability in circ_vmpdf.m.
Current code to evaluate the pdf:

C = 1/(2*pi*besseli(0,kappa));
p = C * exp(kappa*cos(alpha-thetahat));

Proposed replacement code:
C = log(1)-log(2*pi*besseli(0,kappa,1))+(kappa*cos(alpha-thetahat))-kappa;
p = exp(C);

Examples:

circ_vmpdf(0,0,1000)

Old code result: NaN
New code result: 12.6141

18 Sep 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Philipp Berens

Ryan, the average is in the dot product w'*exp(...) which in the simplest case is a vector of ones - so this is the sum operation. exp(i*angle) decomposes the angle into its sine and cosine components. Finally, angle is atan2. Compare the results of your and my code - they should be identical with my code likely running a bit fast due to matrix style computations.

Bst
Philipp

16 Aug 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Ryan

I haven't run through this toolbox yet, so I apologize if I am missing something with this question (I just glanced through the source code because I am interested in directional stats).

When you calculate the mean, the formula you use is:

% compute weighted sum of cos and sin of angles
r = w'*exp(1i*alpha);

% obtain mean by
mu = angle(r);

Now, correct me if I'm wrong, but this doesn't seem to calculate the average at all? It seems to me that here we are inputting a data array into the angle command, which will output the phase angle of each element of that array, not a singular mean.

Wouldn't a better way of calculating the average be to use atan2? Something like:

for i = 1:w
S(i) = sin(alpha(i));
C(i) = cos(alpha(i));
end

X = sum(S)*(1/w);
Y = sum(C)*(1/w);

mu = atan2(X,Y);

15 Aug 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Marnix Maas

Thanks for the great toolbox! I have a question: I have a set of directional stochastic variables that are mutually correlated. I have used circ_corrcc to construct a correlation matrix for these variables, but I’m also interested in their covariance matrix. There does not appear to be a function for this in the current toolbox.

Not having any previous experience with circular statistics, I’m wondering if it makes sense to construct a covariance matrix by de-normalizing the correlation matrix, multiplying each element by the two corresponding circular standard deviations? Perhaps a covariance matrix could be a useful addition to the toolbox.

Thanks,
Marnix

21 Jul 2012 Sampling from multivariate correlated binary and poisson random variables These Matlab functions can be used to generate multivariate correlated binary variables, and correl Author: Philipp Berens Kozlov Sacha

OK, I see, it's a problem of Win64 MatLab: C compiler is not included, so you have to download it first (see "mex -setup") and then compile your bivnor.c for this plateform ("mex bivnor.c").

18 Jul 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Philipp Berens

Hi Francesco, if you have orientations, multiply all orientations by 2 to obtain directions. If you want to obtain the mean resultant vector, devide its orientation by 2 again.

14 Jul 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Francesco

excuse my previous post! I just realize what p-axial truly meant.

For further reference this will solve the previously cited problem

%% uniform distribution test
% in the interval [0, 180)
y180 = circ_axial(circ_ang2rad(0 + 179*rand(4000,1)),2);
p180 = circ_otest(y180)
% in the interval [0 360)
y360 = deg2rad(0 + 359*rand(4000,1));
p360 = circ_otest(y360)

14 Jul 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Francesco

excuse my previous post! I just realize what p-axial truly meant.

For further reference this will solve the previously cited problem

%% uniform distribution test
% in the interval [0, 180)
y180 = circ_axial(circ_ang2rad(0 + 179*rand(4000,1)),2);
p180 = circ_otest(y180)
% in the interval [0 360)
y360 = deg2rad(0 + 359*rand(4000,1));
p360 = circ_otest(y360)

14 Jul 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Francesco

I am testing the toolbox out with not much of a prior knowledge on the subject. It seems a really good piece of software and it's helping me out grasping some of the theory.

I have a question: if I am dealing with orientations [0, 180) degrees more than directions [0 360), is there a proper way to transform may data prior to using the function in the toolbox?

For example, if I am trying to test for circular uniformity with a population that is uniformly distributed in [0 180) - which I'd like to have a p>0.05 - I obtained a very small value, which is consistent with the test looking over the full interval.

Suggestions? Thanks
Francesco

---Example code ----
y180 = circ_ang2rad(0 + 179*rand(4000,1));
p180 = circ_otest(y180)
% in the interval [0 360)
y360 = deg2rad(0 + 359*rand(4000,1));
p360 = circ_otest(y360)

27 Jun 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Jer Walley

Great toolbox! Exactly what I needed. However, my data has many NaN's - do you have a way to work around data with gaps?

30 May 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Matt Davis

This is a great toolbox - very helpful. A few bug reports:

1. formatSubPlot calls "parseVarArgs" that's not standard matlab, or part of this toolbox. Could you add a pointer to where to download this.

2. In Example 2 the descriptive stats cell needs updating to respect the matrix style computations. So, line 67 should read:

stats(i,1) = circ_mean(ori,spk,2);

and similar for all the other lines of code.

Thanks for supporting this toolbox.

16 May 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Natalia

I confirm Dillon's report on circ_wwtest bug.

26 Apr 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Dillon

Great toolbox but I think there is an error in the logic used at circ_wwtest.m -> checkAssumption() lines 107-115.

The code currently reads:
if n > 10 && rw<.45
warning('Test not applicable. Average resultant vector length < 0.45.') %#ok<WNTAG>
elseif n > 6 && rw<.5
warning('Test not applicable. Average number of samples per population < 11 and average resultant vector length < 0.5.') %#ok<WNTAG>
elseif n >=5 && rw<.55
warning('Test not applicable. Average number of samples per population < 7 and average resultant vector length < 0.55.') %#ok<WNTAG>
elseif n < 5
warning('Test not applicable. Average number of samples per population < 5.') %#ok<WNTAG>
end

Notice that the if/else statements do not match the warning text. Particularly when n>5 the user will always be warned when the resultant vector, rw<0.55 which is not captured by the warning. The corrected if/else statements are as follows:
if n >= 11 && rw<.45
warning('Test not applicable. Average resultant vector length < 0.45.') %#ok<WNTAG>
elseif n<11 && n >= 7 && rw<.5
warning('Test not applicable. Average number of samples per population < 11 and average resultant vector length < 0.5.') %#ok<WNTAG>
elseif n<7 && n >=5 && rw<.55
warning('Test not applicable. Average number of samples per population < 7 and average resultant vector length < 0.55.') %#ok<WNTAG>
elseif n < 5
warning('Test not applicable. Average number of samples per population < 5.') %#ok<WNTAG>
end

I've assumed that the warning statements are correct but if the if/else statements are correct it would be more compact to warn the user under only 2 conditions: n<5 and rw<0.55.

Thanks again for the very useful toolbox.

24 Apr 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Philipp Berens

Thanks for the recent feedback and bugreports. I was away for a while and will start taking care of them soon.

30 Mar 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Omar Mian

Suggestion for addition:
Parametric and nonparametric paired sample tests, Zar (2010) Biostatistical Analysis, sections 27.13 and 27.14

16 Mar 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Pablo Martinez

Sorry wrong line number. The error is at line 169!
in the function circ_hktest.m
pI = 1 - chi2pdf(chiI, df_i);
It should be
pI = 1 - chi2cdf(chiI, df_i);

Great toolbox.

15 Mar 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Pablo Martinez

Great toolbox!

15 Mar 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Pablo Martinez

I found an error in the function circ_hktest.m at line 160
pI = 1 - chi2pdf(chiI, df_i);
It should be
pI = 1 - chi2cdf(chiI, df_i);

01 Mar 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Natalia

Thank you very much for such a useful toolbox. Now, I have a question related to circ_ktest (two-smple test to compare concentration). The F statistic is defined only in case of rbar>.7, Mardia (pag 133, 1999) compute F in the case where resultant vector length is <0.45 :
n1 = length(alpha1);
n2 = length(alpha2);

R1avg=circ_r(alpha1);
R2avg = circ_r(alpha2);

R1 = n1*circ_r(alpha1);
R2 = n2*circ_r(alpha2);

%make sure that rbar > .7
rbar = (R1+R2)/(n1+n2);

if rbar > .7

f = ((n2-1)*(n1-R1))/((n1-1)*(n2-R2));

elseif rbar< .45 %taken from Mardia 1999 p.133 (Baschelet report: Mardia 1972 pag 161)

g11= asin(2*sqrt(3/8)*(R1avg));
g12= asin(2*sqrt(3/8)*(R2avg));

f= (2/sqrt(3))*((g11-g12)/(1/(n1-4)+ 1/(n2-4)).^(1/2));

But here Sample 1 and Sample 2 define the sign of F... and so S1 and S2 will be defined depending on Ravg value being S1>S2 for computation of F. Is this right?
Thank you!
natalia

11 Jan 2012 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Luke

Great tool.
I do have to say that circ_mtest is a bit weird.
The input is [pval, z] but output is set as [h,mu,ul,ll]

08 Dec 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Balazs Barkoczi

Thanks for this excellent toolbox!
I have only some problems with the example files, that I downloaded from http://www.jstatsoft.org/v31/i10
example1:
??? Undefined function or method 'parseVarArgs', therefore the figure 2 isn't complete, and it hasn't axis labels.

example2:
??? Error using ==> mtimes
Inner matrix dimensions must agree.

Error in ==> example2 at 42
zm = r*exp(i*phi);
Perhaps a dot is absent, but after this modification zm = r.*exp(i*phi); the same error occurs:
??? Undefined function or method 'parseVarArgs'
Can somebody help me to fix this problems?
Thank you very much!

11 Nov 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Fuh-Cherng

@Christopher: Thank you so much for your kindness and help. I really appreciate it.

09 Nov 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Christopher

@Fuh: indeed it should and when I step carefully through the function, sometimes the result comes out correct and sometimes it doesn't, somewhat dependent on the numbers in alpha. To fix the problem go to lines 45 and 46 of circ_median (ver 2011f). You see two inequalities, dd>=0 and dd<0. The two inequalities should be identical for consistency and the correct result. Edit line 46 to read:
m2 = sum(dd<=0,1);
Now the function seems to behave as expected.

09 Nov 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Fuh-Cherng

I am new in circular statistics, so don't laugh at me... But I do have a question about the circ_median() function.

Say I have a data set that contains six angles [0.1 0.2 0.3 0.4 0.5 0.6]. when I feed these data into circ_median(), the function returns a median = 0.4

I thought that, when a data set contains an even number of observations, the median would be calculated as the average of the middle two numbers (i.e., (0.3+0.4)/2 = 0.35).

My code is listed below.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
alpha = [0.1 0.2 0.3 0.4 0.5 0.6]';
med = circ_median(alpha)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Can anyone help me with this?

Sincerely,
Fuh

28 Sep 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Philipp Berens

Thanks for the comments.

@Christopher: The ~ has been introduced as a placeholder in the latest MATLAB versions for output arguments that are not needed. I will go back to some dummy variable with the next upload.

@Heida: I don't see an easy way of doing what you suggest with the functions implemented.

@Omzaz: The multi-sample tests assume independent samples. I don't know about repeated-measures ANOVA etc. for circular data. If you find anything let me know.

The option to ignore NaNs... I think this is a tricky thing, because you always make a specific choice how NaNs are treated and each user might have different preferences. I will think about it though.

20 Sep 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Omar Mian

Can any of the multi-sample tests in this toolbox be used with repeated measures data or do they all assume independent samples?

30 Aug 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Omar Mian

Very useful toolbox. Option to ignore NaNs in the calculations would make it even better.

22 Aug 2011 Circular Statistics Toolbox (Directional Statistics) Compute descriptive and inferential statistics for circular or directional data. Author: Philipp Berens Vlad Atanasiu

Good toolbox! I added a function for kernel smoothing density estimate for circular data here: http://www.mathworks.com/matlabcentral/fileexchange/32614-kernel-smoothing-density-estimate-for-circular-data .

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