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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15 views

Appropriate to rescale kernel densities to radians and use watson's two sample test of homogeneity?

I'm looking at activity budgets of animals derived from camera traps and gps collars. I'm pooling multiple cameras or gps collars within each group before comparing the activity of two groups against ...
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158 views

Converting a circular outcome variable to a linear one

I have a problem where I want to measure deviations from zero degrees. This outcome variable is a circular measure, since a deviation of -180 degrees is equivalent to 180 degrees. However, I don't ...
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25 views

Skewness and kurtosis of VonMises distribution

I could not find a reference that has mentioned the skewness and kurtosis of a circular data that has Von Mises distribution. What are the values? and it is great if someone can introduce some ...
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18 views

Covariate analysis comparing distributions / means of circular data

Are there publicly available software packages to run an analysis comparing the means or distributions of two samples of circular data with the presence of a covariate? If not, are there ways to ...
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40 views

Two sample Kuiper test for checking normality of circular data

I have circular data and want to check whether it is a normal (Von Mises) distribution or not. I do the following steps: Create a Von Mises distribution with the same mean and kappa as my main data. ...
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324 views

Expected ratio of x'Ax and x'AAx on a unit sphere?

Suppose $A$ is symmetric positive definite matrix. Is there a nice expression for the first moment of the following quantity? $$\frac{x^TAx}{x^TA^2 x}$$ Where $x$ is distributed as $\text{Normal}(0,...
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32 views

Testing for circular uniformity of headings (Rayleigh, v-test)

I have two-dimensional recordings of animal trajectories. The animals exit their nest and I am trying to test whether their headings over a period of time have a distribution different than uniform. ...
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16 views

Simulate from Circular - Linear Data in R

I would like to simulate, using R, data from the Johnson-Wehrly distribution that is governed by the following pdf: \begin{eqnarray*} f_{X,Y}(x,y) = 2\pi g[2\pi(F_X(x) - F_Y(y))]f_X(x)f_Y(y), \end{...
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98 views

Distribution of $\langle x^2,a\rangle$ where $x$ is is a random direction?

Suppose $x\in R^n$ follows the uniform distribution on the surface of a unit sphere centered at 0 and $a$ is a vector in $R^n$. What can we say about the distribution of the following quantity? $$\...
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52 views

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 ...
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86 views

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 ...
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132 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 ...
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1answer
65 views

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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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 ...
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16 views

What is the correct distance metric for hour?

I want to cluster points using time and spatial coordinates. My time dimension is only containing hour of day. In order to have a correct representation of time I transform my hour using ...
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124 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 ...
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78 views

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 ...
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61 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-...
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17 views

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 ...
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30 views

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 ...
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1answer
104 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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26 views

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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61 views

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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55 views

How to use Principal Components Analysis (PCA) to find overall orientation of polygons collectively?

I was advised to use the Principal Component Analysis (PCA) to find first eigenvector which gives the direction of the first principal direction. Principal Component Analysis (PCA) is a new concept to ...
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48 views

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 ...
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93 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 ...
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45 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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37 views

Loss function for multidimensional regression on tree different angles

I am looking for a loss function for a deep learning model which is able to predict 3 angles. The first angle is in the range of [-10,10] degrees, the second angle is in the range of [50, 60] degrees ...
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67 views

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 ...
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41 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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1answer
104 views

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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15 views

Perfomance comparison of circular mean estimators with long-tailed noise

I am trying to compare the performance of two estimators of the mean of a circular random variable. One of these estimators gives estimates with lower absolute error but only for samples that are ...
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1answer
95 views

Calculating the trend of an angle when it crosses 360 -> 0

I have a variable that measures an angle describing the relative position of two objects (i.e., can range from 0-359), and I would like to quantify how this has changed through time. For example, here ...
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85 views

Circular variance of a mixture of Von Mises distributions

Does anyone know if there is an analytical solution for the (circular) variance of a mixture of Von Mises distributions that all have equal (circular) mean? Simulation results suggest that the ...
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3answers
2k views

Linear regression with "hour of the day"

I am trying to fit a linear model using "hour of the day" as parameter. What I'm struggling with, is, that I've found two possible solutions on how to handle this: Dummy encoding for every ...
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33 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 ...
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1answer
124 views

Interpretation of coefficients in mixed-effects model with circular response?

I have a dataset from an experiment where wild ants were surveyed continuously for 24 hours under a number of temperature treatments (chambers). Whenever an ant was observed, the species of the ant ...
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25 views

Decomposition of the second moment of a circular distribution

When we have a "usual" random variable $X$ on the real line, we can break down the second moment. $$ \mathbb{E}[X^2] = (\mathbb{E}[X])^2 + var(X) $$ Is there an equivalent for a circular ...
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1answer
224 views

calculating correlation for angles (and other kinds of circular data)

I have two sequences of angles in radians. I can compute the Pearson correlation coefficient between them. It turns out to be very low since the angles are sort of bimodal distributions with the two ...
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1answer
56 views

Measuring Similarity between 2 Angular Distributions

For a project I'm working on, I have two sets of samples, where each set has N x length 7 vectors. For context, each vector represents the joint parameter setting for a robot (the angle each joint of ...
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48 views

Distributions on an ellipsoid?

This is my first question. I hope somebody can help me with this. I am after the name of a distribution and references would be incredibly useful. I am looking for a generalisation of the von-Mises ...
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67 views

Statistical tests for periodicity in a histogram

I am trying to analyse the distribution of pairwise distances between data points distributed on a circle. In particular, I am interested in determining whether there is any periodicity in these data....
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1answer
156 views

Earth mover's distance implementation for circular distributions?

I am interested in finding an implementation (preferably in R but not necessary) to calculate earth mover's distance between two empirical distributions of circular data. My data are time points on a ...
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3answers
174 views

Shouldn't we take absolute values when + or - sign indicates only direction, not higher or lower values?

What I am trying to do? I want to explore the relationship between Magnetic Field and Blood Pressure in case of diabetic patients. In short, I will create a heavy magnetic field and will collect ...
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2answers
161 views

Where is the error in my computation of the wrapped normal distribution density?

Let $\sigma\in(0,1)$ $$\phi(x):=\frac1{\sqrt{2\pi\sigma^2}}e^{-\frac{x^2}{2\sigma^2}}\;\;\;\text{for }x\in\mathbb R$$ and $$\psi(x):=\sum_{k\in\mathbb Z}\phi(x+k)\;\;\;\text{for }x\in\mathbb R$$ $\...
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1answer
197 views

Circular Statistics in Python Help

I'm trying to perform some circular statistics in Python and, having never done circular statistics before and being mostly self taught in python, thought I'd turn to this place for some help because ...
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43 views

circular ranked lists

I have two lists which are circular, in that given list ['A','B','C','D','E'] 'A' and 'E' are the same distance apart as 'A' and 'B' and so on. Given I have rankings R1=['A','B','C','D','E'] R2=['...
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25 views

Hypothesis testing and von Misher-Fisher distribution

I have set of random unit vectors $x_i$, $i=10...30$. How to correctly test hypothesis that all of them from von Mises-Fisher distribution with unknown $\mu_d$ and $\kappa$ parameters, $d=128$?
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1answer
60 views

Understanding the Rejection Sampling for a vector

I am thinking about this classical problem in statistical simulations. We want to apply the Rejection sampling to simulate a random vector $Y=(Y_1, Y_2)$ of a uniform distribution from a unit disc $D =...
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1answer
36 views

Using direction of motion as a variable: What do do with undefined/infinite slopes?

I have a list of x,y coordinates representing an object's motion through 2d space. I need to do statistics where I use the direction of motion (slope) as a covariate to my variable of interest. ...

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