# Questions tagged [circular-statistics]

Directional statistics (also called circular or spherical statistics) is the discipline of statistics that deals with directions (unit vectors in $\mathbb{R}^n$), axes (lines through the origin in $\mathbb{R}^n$) or rotations in $\mathbb{R}^n$.

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### Multiple regression in directional / circular statistics?

I'm trying to develop a predictive model for an angular dependent variable (on $[0,2\pi])$ using several independent measurements – also angular variables, on $[0,2\pi]$ – as predictors. Each ...
1k views

### Cosine similarity between a clean signal and its noisy version

Given a $D$-dimensional datum that is an iid sample from a spherical Gaussian distribution, and the noise-corrupted version of that datum generated by adding spherical Gaussian noise, is there a ...
1k views

### How to derive the Projected normal distribution

Suppose we have a bivariate normal variable $\mathbf{x}= (x_1, x_2)$ with mean $\mu_1$ and $\mu_2$ and variances $\sigma_1^2$ and $\sigma_2^2$ and correlation $\rho$. I need to obtain the pdf of the ...
601 views

### Sum of random vectors with fixed amplitudes

Is there a simple way to evaluate the pdf of the amplitude of a sum of vectors with fixed amplitudes and random phases? Explicitly, let $Ae^{i\phi}=\sum_{n=1}^NA_ne^{i\phi_n}$, where $N$ is a fixed ...
143 views

### 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 ...
850 views

### 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 ...
3k views

### What does the abbreviation “p.e.” mean?

I came across a paper that uses the abbreviation "p.e.": Khatri and Mardia, 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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### Nearest Neighbor Algorithm for Circular dimensions

Is there an algorithm for fast nearest neighbor search of circular dimensions? e.g., For a dimension based on "hour of day", a KD-tree would place 00:01 and 23:59 far apart. But the proper distance ...
213 views

### 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 ...
497 views

### 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 ...
136 views

### Test for difference of distributions on a torus

I have two circular dependent variables and would like to test for a difference in the distributions (presumably circular means) between multiple treatment groups. There are a number of multivariate ...
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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 ...
839 views

### How do I specify priors for angle parameters in BUGS/JAGS? [closed]

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 I'...
4k views

### Estimating kappa of von Mises distribution

Is there a way to calculate an estimate of the parameter $\kappa$ 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,...
676 views

### 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 ...