# Tagged Questions

Directional statistics deals with distributions of angles (on a circle, on a sphere, or another kind of hypersphere appropriate for dimension at hand)

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### What is the name for this distribution defined on a circle

One can define the probability distribution: $$p(\theta; \alpha, \theta_0) = \frac{ e^{ \alpha \cos( \theta-\theta_0) }}{ 2 \pi I_0(\alpha)}$$ over an angular variable $\theta \in [0,2 \pi]$. By ...
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### Computing a circular-linear partial correlation

The CircStats toolbox for MATLAB (http://bit.ly/18C1SCF) implements a procedure to compute a correlation between a linear and a circular variable. Specifically, the ...
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### What does the abbreviation “p.e.” mean?

I came across a paper that uses the abbreviation "p.e.": Khatri and Madria, The Von Mises-Fisher Matrix Distribution in Orientation Statistics. 1976. It's in Section 7 on page 105. I'm including a ...
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### Estimating covariance of the difference of directional distributions derived from Gaussian mixtures

Given Gaussian mixtures $X_1, X_2 \in \mathbb{R}^p$ defined as $$P(X_i = x) = \sum_s \omega^{(s)}_i \mathcal{N}(x; \mu^{(s)}_i, \Sigma_i)$$ where the superscript $(s)$ indexes the $s$-th component of ...
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### Circular statistics and bidirectional data

I am curious if tests such as Rayleigh's test, Kuiper's test, and Watson's test are valid for bidirectional data (i.e. 180 degrees) as well as unidirectional data. If not, what are the appropriate ...
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### How to test equality of variances with circular data

I am interested in comparing the amount of variability within 8 different samples (each from a different population). I am aware that this can be done by several methods with ratio data: F-test ...
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### How can I produce a plot showing the directional angles of my points? [closed]

I want to be able to compare the angles of neighbours in a herd of hippos. I have data for the x and y coordinates and the angles that they are facing (using imageJ, angles are between -180 and 180 ...
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### How do I specify priors for angle parameters in BUGS/JAGS?

I am writing a hierarchical BUGS model that involves both linear and angle variables. I want the hyper-parameters to be normally distributed, which is straight-forward for the linear variables, but ...
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### Estimating kappa of von Mises distribution

Is there a way to calculate an estimate of $\kappa$ from data for the von Mises distribution? It seems very easy to do in R, http://rgm2.lab.nig.ac.jp/RGM2/func.php?rd_id=CircStats:A1inv, but python ...
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### Circular/elliptical tests for datasets with magnitude and direction

I am trying to analyse (using R) a set of r(theta) data to see if the magnitude (r) is dependent on direction (theta). I have looked at circular statistics but these only seem to deal with the ...
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### Repeated measures ANOVA for circular / angular / directional data

I am looking for a test for circular data that is equivalent to linear repeated measures ANOVA (I have an experiment using human participants where the same sample of participants perform multiple ...
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### Logistic regression with directional data as IV

I am looking for good references on using directional data (measure of direction in degrees) as an independent variable in regression; ideally, it would also be useful for hierarchical nonlinear ...
Context I have two sets of data that I want to compare. Each data element in both sets is a vector containing 22 angles (all between $-\pi$ and $\pi$). The angles relate to a given human pose ...
In circular statistics, the expectation value of a random variable $Z$ with values on the circle $S$ is defined as $$m_1(Z)=\int_S z P^Z(\theta)\textrm{d}\theta$$ (see wikipedia). This is a very ...