# 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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### Good choices of PRNG for uniform circular (directional) data?

I'm planning to simulate iid one-dim variates with continuous uniform distribution on a normalized circle (which circumference is $1$ instead of $2\pi$). Namely, a sample consists of $n$ points ...
627 views

### How can I do a t-test on 2D data?

How can I do a t-test on 2D data with latitude and longitude attributes? I have 2 clusters of similar coordinates but in different time, I want to do a t-test to see if they are statistically ...
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 ...
32 views

### How to do statistics on different geometries?

The original motivation: Let's say, we have two particles, doing random one motion on an infinite 1-D lattice $\mathbb{Z}$, and we are interested in the autocorrelation of the trajectory of each ...
165 views

### Haar prior for von Mises distribution

Ok, Let me tell you that this is the very first time that I have no idea with the question below. I can not find a solution or anything that will lead me to it. I say this to prevent comments "what ...
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### How to find variance of a complicated expression?

I have an equation given by $$\phi(k)=\sqrt{1-\rho^{2}}\sum_{j=1}^{k-1}\rho^{k-j-1}e(j)$$ where $\rho$ has value between 0 to 1 and $e$ is modeled as $\mathcal{C}\mathcal{N}(0,\sigma^{2})$, i.e. ...
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### non-parametric circular statistics

I am working on a research question of color preference (which can be represented in a circular space). I have divided the circular space into 16 equally spaced bins and done a pairwise comparison ...
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### Calculate percentiles of angles/bearings in Python

I have a dataset with a variable that is the angle of the event (record) from a central point (e.g. crime events in relation to a defined city center). I want to calculate percentiles for the variable....
133 views

### calculating orientation anisotropy of a set of 3D vectors

I have a set of unit-length 3D vectors (represented as cartesian 3-tuples) with 180$^\circ$ equivalence (rotated through any plane passing through the origin i.e. $v=-v$), all situated at the origin (...
658 views

### How can I fit a normal (von Mises) distribution to discrete angular data?

This bears some explaining: I have a set of data from a psychophysics experiment where participants selected a response from a discrete set of 8 possible responses. These responses were actually ...
234 views

### Transform non-normal circular data

I have a set of time-series data showing event times for two different groups. Let's call them Site 1 and Site 2. My analysis shows one group is circular normal around a 24 hr clock (von Mises ...
2k views

### Circular variance

I'm attempting to replicate a particular analysis of circular data. The author of this analysis writes I calculated . . . variance . . . for the observed recall errors, defining variance as the ...
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### A question concerning distribution of $\mathbf{Y}/\|\mathbf{Y}\|_2$ where $\mathbf{Y}\sim \mathcal{N}(\boldsymbol{\mu},\mathbf{I})$

I know that when $\mathbf{Y}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$, $\mathbf{Y}/\|\mathbf{Y}\|_2$ is distributed uniformly on the unit sphere. But to my surprise, I failed to find a simple closed ...
208 views

### Von Mises distribution to detect outliers

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, ...
52 views

### Equivalent of a one-tailed paired t-test for circular data?

I have a set of paired circular measurements representing the timing (in phase) of two different events. I would like to determine whether one event occurs earlier (smallest difference in a counter-...
35 views

### Circular linear regression to estimate missing values in circular data

I have a data set of wind direction and wind speed data but some of the wind direction data are missing. There are many good candidates for predictors of wind direction. I want to use the R package ...
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### Limitations to using the principle of least squares to fit an ellipse to experimental data?

I have used the method described below many times without issue to determine the major and minor axes of the "data ellipse". However, for this set of data (Fig. A) the method described below is ...
427 views

### pca on polar coordinates?

I have a dataset composed of 123 rows (time bins) and 20 columns (variables) The question I have is the following. each row,column pair has a radian value and a radius value. If I convert these pairs ...
78 views

### Adding an hour feature to data

I need to add an hour feature to my data. Assigning "dummy variables" (which is what I usually do) does not work in this case, apparently (wouldn't elaborate - but believe me this is so). At first,...
146 views

### Correlation for circular / angular variables

Is there a commonly accepted practice for calculating (and/or visualizing) correlation between angular variables? (I.e. 359° is pretty close to 1°.) I'm sure I could concoct a suitable trigonometric ...
54 views

### two samples comparison with cyclic variables

How to check if two samples are from the same distribution, when the variable is cyclic? A simple answer for non-cyclic variable is the Kolmogorov-Smirnov test. What is the equivalent for cyclic ...
137 views

### Find the most frequent timespan of event occurrence

I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery. Most of time, the robbery does not occur when the owner is watching => the declared ...
160 views

### Angles expressed in degrees of arc as regression variables

I have binary count data as a response variable in my logistic regression. The independent variables include, among others, two variables of inclination and orientation measurements, annotated in ...
355 views

### Scale and normalization of dates

It's common to normalize the different vars before applying some kind of supervised/unsupervised learning. Which algorithm do you use with the dates? You use the day of year (1, 200, 300) and perform ...
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### what is the name of distribution similar to von mises distribution

I am wondering whether the following PDF is a named distribution. Over the interval $0< \theta < \pi$, the PDF of the distribution is written as  P(\theta) = \frac{2^{-n/2} k^{n/2} e^{k \cos (\...
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### 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 ...