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Von Mises distribution to detect outliers

Cross Validated Asked by velvetshelter on December 13, 2021

I am working out the difference between two angles from a circle, and I work out the mean difference across 96 trials in 10 separate samples.

In order to detect outliers for statistical analysis, Barnett & Lewis (Outliers in Statistical Data, 1984) suggest the use of a von Mises basic model (at section 7.1).

  1. Is a von Mises distribution appropriate in my case? I’m not interested in the raw angle values per se, but the difference between them.

  2. I understand how outliers are calculated from z-scores, standard deviations from the mean, etc., but I don’t understand how how they are calculated from von Mises – can anybody offer simple clarification?

One Answer

I don't quite understand what you're doing, and I had to look at Wikipedia to remind myself about von Mises, so take my answers with a grain of salt. If you could create an analogous problem with just real numbers instead of angles on a circle, would it make sense to you? von Mises is like a Gaussian on the circle. Are the angle differences all actually small enough to approximate the distribution as a Gaussian?

  1. Angle differences also live within 0 to $2pi$, so von Mises could be appropriate. But only if it is! Just like points on the real axis may or may not be described by a Gaussian.

  2. You could calculate the "circular variance" and then set the $kappa$ parameter to match using $<cos delta theta> = I_1(kappa)/I_0(kappa)$. Then detect outliers that have small values of the von Mises distribution, recalculate $kappa$, and repeat. Assuming zero mean here. Basically do the analogue of what you'd do with a sample drawn from the real numbers.

Answered by mfardal on December 13, 2021

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