# 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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### Calculate uncertainty of surface normal based on points uncertainty

How to calculate angular variation of fitted plane from points that has positional uncertainty with normal probability distribution? For example, I have 4 points P1 = 102.0000 84.0000 139.5443 P2 = ...
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1 vote
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### Normality test for circular data

I have some angles and I am wondering how can I test whether the distribution of my data is normal or not. In fact, I want something similar to KS test. Howver, I want to use it for circular data to ...
• 151
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### What would be a good objective function for a computer vision model that predicts rotation?

Let's say I have to correct images of scenes which can be rotated in the range $[0, 2\pi)$. For my particular application I already know a CNN makes sense. I'd use this to detect the orientation, then ...
289 views

### Coefficient of variation of circular data

The definition of coefficient of variation is as follows: coefficient of variation= standard deviation/mean. I am using circular (directional) statistics to find the mean and standard deviation. My ...
• 151
1 vote
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### Interpreting multiple circular-circular regression output

I'm new to circular stats and have been playing with circglmbayes and bpnreg. I'm not sure how to interpret the output. I have consulted the CrossValidated database, and the papers/tutorials ...
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1 vote
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### Is the difference between directional means from two populations significant? (circular data)

I am comparing the orientation of two data sets with geographical lines and have used the processing tool "Linear Directional Mean" (ArcGIS Pro, Spatial Analyst) to calculate the mean of ...
• 11
1 vote
239 views

### Circular statistics polar coordinates data in R

I am very much new to dealing with this type of data (polar coordinates!) and it would be great if someone could help me out. My data come from an experiment in which I had 66 different pairs of ...
• 11
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### When are circular statistics needed (reference)?

I have a set of data of measurements for the lateral angle of the internal acoustic meatus (it's an angle between the canal of our inner ear and another bone structure in our skull). The measurements ...
• 105
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### 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-...
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1 vote
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### How to handle nondifferentiable points of the objective function in the geometric circle fit?

We a given measured points in $(x_i,y_i) \in \mathbb{R}^2$, $i=1,..,n$. The geometric circle fit is the circle with center (a,b) and radius $r$ that minimizes the squared Euclidean distances between ...
1 vote
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### Statistical test for comparing directional data

I have a dataset with number of bats flying out in 8 directions from their home site (i.e) I studied a bat colony with N individuals and I have counted the number of bats (from that colony) that flew ...
236 views

### Hierarchical circular-circular regression in R

I have two circular variables and I want to see if they're correlated. The data comes from a hierarchical and unbalanced experimental design: each participant provided multiple responses and there's ...
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1 vote
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### Signed circular-linear correlation or covariance?

In my recent project, I am implementing an adaptive MCMC procedure for a set of variables, some of which are linear (e.g., temperature in Celsius), some of which are circular (e.g., direction in ...
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### Predict an angle between 0-360, how do I deal with the discontinuity at 0/360? [duplicate]

The title might be a bit convoluted. I have an image recognition problem where I have to detect a direction. If I represent the direction as an angle it has a discontinuity at 0-360. This is not ...
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### Can one uniformly generate complex numbers of absolute value less than a given constant $R \neq 1$? [duplicate]

Can one uniformly generate complex numbers of absolute value less than a given constant R? This would appear to be equivalent to picking points $(x,y)$ uniformly in a disk of radius R, where $x$ is ...
160 views

### Measuring Circularity of a set of Co-planar points

I am trying to find a way to quantify how circular or symmetric a shape is. What is a good way to measure the circularity of these set of points? I already have the coordinates of the points along the ...
1 vote
93 views

### Test if multiple circular distributions have the same mean. i.e. a Watson-Williams-like test for for heterogeneity of means?

I have four sampled unimodal circular distributions - one from each experimental subject. I want to test if the distributions have the same mean phase, rather than a difference. That is, my null ...
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### Variance and CDF for non-directional wrapped gaussian distribution (bounded angles [0, pi])

How can we calculate the standard error sigma and the chance of a sample being within N sigma (CDF) for values bound to ...
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. ...