I am trying to analyse the distribution of pairwise distances between data points distributed on a circle. In particular, I am interested in determining whether there is any periodicity in these data.

For example, in the histogram shown below I would like to test whether there is an increase in the frequency of data at pairwise distances that are multiples of 60 degrees (or alternatively at multiples of 90 degrees or 45 degrees etc). Are there any established ways of testing this?

I thought of fitting a simple linear model with sinusoidal regressors and then cross-validating fit quality. However the only way I can think of leaving out data is by leaving out bins and this entire approach seems intuitively unappealing.

Obviously this analysis is further complicated by the fact that pairwise distances tend to be small.

enter image description here

  • 1
    $\begingroup$ Plot the magnitude of the Fourier transform of the data. See stats.stackexchange.com/questions/16117 and search our site for threads about "seasonality." $\endgroup$
    – whuber
    May 18, 2020 at 12:47
  • $\begingroup$ that works thank you! :) $\endgroup$ May 19, 2020 at 8:43


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