Code covered by the BSD License

# Circular Statistics Toolbox (Directional Statistics)

### Philipp Berens (view profile)

08 Apr 2006 (Updated )

Compute descriptive and inferential statistics for circular or directional data.

### Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

circ_stats(alpha, w, d)
```function stats = circ_stats(alpha, w, d)
%
% stats = circ_stats(alpha, w)
%   Computes descriptive statistics for circular data.
%
%   Input:
%     alpha   sample of angles in radians
%     [w      weightings in case of binned angle data]
%     [d    spacing of bin centers for binned data, if supplied
%           correction factor is used to correct for bias in
%           estimation of r]
%
%   Output:
%     stats   structure containing descriptive statistics
%
% References:
%   Statistical analysis of circular data, N. I. Fisher
%   Topics in circular statistics, S. R. Jammalamadaka et al.
%   Biostatistical Analysis, J. H. Zar
%
% Circular Statistics Toolbox for Matlab

% By Philipp Berens, 2009
% berens@tuebingen.mpg.de

alpha = alpha(:);
if nargin<2
w = ones(size(alpha));
end

if nargin < 3
d = 0;
end

% mean
stats.mean = circ_mean(alpha,w);

% median
if sum(w)==length(alpha)
if numel(alpha) > 1000
idx = randperm(numel(alpha));
idx = idx(1:1000);
else
idx = 1:numel(alpha);
end
stats.median = circ_median(alpha(idx));
else
stats.median = NaN;
end

% variance
stats.var = circ_var(alpha,w,d);

% standard deviation
[stats.std stats.std0] = circ_std(alpha,w,d);

% skewness
[stats.skewness stats.skewness0] = circ_skewness(alpha,w);

% kurtosis
[stats.kurtosis stats.kurtosis0] = circ_kurtosis(alpha,w);

```