https://github.com/cnuahs/hermans-rasson
The Hermans-Rasson test for non-uniformity of circular data.
https://github.com/cnuahs/hermans-rasson
circular-statistics hermans-rasson matlab rayleigh-test statistics
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The Hermans-Rasson test for non-uniformity of circular data.
- Host: GitHub
- URL: https://github.com/cnuahs/hermans-rasson
- Owner: cnuahs
- License: mit
- Created: 2019-02-03T09:02:48.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2020-11-23T10:43:16.000Z (over 5 years ago)
- Last Synced: 2025-01-03T07:48:50.352Z (over 1 year ago)
- Topics: circular-statistics, hermans-rasson, matlab, rayleigh-test, statistics
- Language: MATLAB
- Homepage:
- Size: 25.4 KB
- Stars: 3
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
[](https://au.mathworks.com/matlabcentral/fileexchange/70185-a-matlab-implementation-of-the-hermans-rasson-test)
# hermans-rasson
A Matlab implementation of the Hermans-Rasson test for non-uniformity of circular data. The test is described in:
Hermans M, Rasson J. (1985). A new Sobolev test for uniformity on the circle. Biometrika. 72:698–702. doi: 10.1093/biomet/72.3.698.
The Hermans-Rasson test can provide additional power (c.f. the Rayleigh test, for example) to reject the hypothesis of uniformity in cases where the distribution is multi-modal with unknown symmetry.
Example usage:
```
% multi-modal circular distribution, sum of von Mises distributions
kappa = [3 6];
xbar = [0 5*pi/6];
nsamp = round(logspace(1,3,10)); % number of samples
N = 1e3; % number of bootstrap samples
x = linspace(-pi,pi,361);
n = numel(kappa);
for ii = 1:n
pdf(:,ii) = (2*pi/360)*circ_vmpdf(x(:), xbar(ii), kappa(ii))./n;
end
% plot pdfs
figure
subplot(1,2,1);
plot(x,pdf,'k-'); hold on
pdf = sum(pdf,2);
plot(x,pdf,'k-','LineWidth',1.5);
xlim(pi*[-1,1]);
% sample from the distribution
p = NaN([N,length(nsamp)]);
prayleigh = NaN([N,length(nsamp)]);
for ii = 1:length(nsamp)
xhat = NaN([nsamp(ii),N]);
for jj = 1:N
xhat(:,jj) = randsample(x,nsamp(ii),true,pdf);
prayleigh(jj,ii) = circ_rtest(xhat(:,jj));
end
p(:,ii) = hrtest(xhat);
end
% plot p(H0) vs nsamp
subplot(1,2,2);
semilogx(nsamp,mean(p),'ko-','LineWidth',1.5,'MarkerFaceColor','k'); hold on
semilogx(nsamp,mean(prayleigh),'k.-');
```
The example above uses `circ_vmpdf()` and `circ_rtest()` from Philipp Berens Circular Statstics Toolbox for Matlab, available from https://github.com/circstat/circstat-matlab.git. The output should look something like:
For a comparison of several tests for non-uniformity and some recommendations on their relative merits, see:
Landler L, Ruxton GD, Malkemper EP. (2018). Circular data in biology: advice for effectively implementing statistical procedures. Behavioral ecology and sociobiology. 72(8) 128. doi: 10.1007/s00265-018-2538-y.