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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Modeling repeated measures analysis with circular variables

(question cross-posted to stack overflow here:https://stackoverflow.com/questions/72189932/circular-analysis-repeated-measures-design-model-building-evaluation-and-inte?noredirect=1#...
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How to calculate the value (wind direction) of "maximal effect" in a linear-circular correlation?

I am trying to evaluate the effect of wind direction (circular variable) on a dependent linear variable. I have used circular-linear regression to find the correlation coefficient between the two ...
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Which statistical test should I use to see if the month of onset of a disease is random or clusters in the winter?

I have data showing which month a disease started for 119 subjects. The months are represented by 1-12 (Jan - December). We hypothesize the disease more often onsets during winter months. What test ...
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Loss Function for Polar Coordinates Target Variables?

Suppose I want to do regression on targets that are polar coordinates. What loss functions are appropriate? I know I could always use mean squared error, but I'm not sure that's the most appropriate.
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How can I quantify this non-linear relationship where y-values peak within a narrow range of x-values?

I have plotted this data, and to me there appears to be a clear relationship between the variables (sediment accumulates when wind direction is between 150 and 250 degrees). Is there a appropriate ...
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Multiple regression for circular (periodic) target [duplicate]

Please kindly provide some advice on maximizing regression accuracy with a circular target, in this case, angles between 0 and 2pi. The training set has the shape (14585110, 6). The angle information ...
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Why doesn't mean square error work in case of angular data?

Suppose, the following are the first few lines from a dataset for solving a regression problem: ...
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2 votes
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Machine learning regressor for cyclic values

I have a question regarding training a Machine Learning regressor for cyclic values. For instance, consider phase values. We cannot use conventional regression methods for this as for example the ...
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4 votes
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Why does the von Mises-Fisher distribution need two parameters?

The von Mises-Fisher distribution has two parameters: the mean $\mu \in \mathbb{R}^p$ and concentration $\kappa \geq 0$, where $\mu$ is constrained to have unit norm. Why not instead define the ...
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Variance of von Mises-Fisher Distribution

As a follow up to this previous question on the expectation of the von Mises-Fisher distribution, what is the variance of a von-Mises Fisher distribution as a function of the mean direction $\mu$ and ...
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Best practice for cyclical feature encoding for tree-based methods

Right now I'm facing a dataset of professional road cyclists which contains training data of the athletes at different dates over two years. For some tree-based methods I'm still looking for a 'best ...
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Fitting sine wave with lm in R for circadian activity- frequencies?

I'm trying to fit a sine wave over some activity data, just like this post. I've managed to get a reasonable looking graph for one condition: However, when I plot the other condition the wave looks ...
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Best distance measure for cluster analysis of time series data with a circular variable

I'm doing hierarchical clustering on a set of time series (say 21 time series of 400 time points), however the variable I want to cluster is a circular variable, i.e. a directional vector between 0 ...
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2 votes
2 answers
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How to define distance for vector of angles?

I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
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5 votes
3 answers
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Measure of similarity between two distributions - with variable starting point (wrap-around)

I would like to compute the (dis)similarity between two distributions. The first represents tones sung by an experimental subject during a recording. There are different numbers of tones, each with ...
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Different methods for evaluating skewness of circular data

I am trying to find skewness of circular data. As far as I understood, there are different methods for this. For example these methods: Pewsey, Metrika, 2004 (link) Statistical analysis of circular ...
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use GAMM models for full circular wind direction data

using a GAM modeling approach enables to include circular data as fixed effects. I wish to analyze the effect of wind on the flight behaviour of birds. In order to do so I want to add wind speed and ...
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Skewness of Von mises distribution using two different methods

I want to use skewness of circular data using circ_skewness code in MATLAB. I know there are two methods for this: Pewsey, Metrika, 2004 Statistical analysis of circular data, Fisher, p. 34 However,...
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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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6 votes
3 answers
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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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2 votes
1 answer
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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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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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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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16 votes
2 answers
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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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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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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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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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1 vote
1 answer
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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 ...
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6 votes
2 answers
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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 ...
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4 votes
3 answers
194 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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1 vote
1 answer
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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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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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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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4 votes
1 answer
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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 ...
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2 votes
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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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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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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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1 answer
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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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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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3 votes
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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 ...
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4 votes
2 answers
132 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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1 vote
1 answer
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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 ...
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2 votes
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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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3 votes
1 answer
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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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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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1 vote
1 answer
237 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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1 vote
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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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16 votes
3 answers
3k 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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