# 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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### 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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### 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 ...
37 views

### Circular-linear regression error-in-variables model? [closed]

I have a dataset from a calibration certificate in which: The measured voltage is the independent variable X and goes approximately from 0 [V] to 10 [V]. I know the resolution of this variable which ...
25 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 ...
52 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. ...
18 views

### Circular variable in spatial GLM / SVM modeling using R [duplicate]

I am modeling spatial data using multiple rasters with the variables shown below. ...
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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 ...
28 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 ...
55 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 ...
1k 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 ...
28 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 ...
67 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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### 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 ...
11 views

### How to calculate Moore Rayleigh test?

I am trying to code a function which computes Moore's modified version of the Rayleigh test. I am doing ok with the second half of the calculation but I am unsure how to "number the vectors ...
35 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 ...
34 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 ...
13 views

### Circular regression with two circular regressors

I would like to test how well two circular regressors explain the variance of a circular response variable. One of the regressors consists of only two angles (either 0 or 180). Can anyone help me in ...
42 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 ...
17 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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### What is the best way to generate fake noncircular data? [duplicate]

How can I generate fake data that resembles this real data from a youtube video: The following is my attempt to do so: ...
52 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 ...
102 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 ...
146 views

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### 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. ...
96 views

### How to calculate the standard error of the mean for circular data?

I followed the suggestions here to calculate the SD from circular data in the R circular package: How to calculate standard deviation of circular data However, I need the SE of the mean for a number ...
23 views

### What is Directional Quantile Regression?

I am coming from a computer science background and I am reading this research paper https://www.sciencedirect.com/science/article/pii/S0047259X10001636 There are so many math equations that I don't ...
55 views

### Hierarchical modelling for a circular distribution

Suppose we want to estimate the distribution of a random variable defined over time of day and day of the week given a sample. In addition: We cannot assume that the distribution is the product of ...
55 views

### Can we sample from the wrapped normal distribution and evaluate the density of the sample simultaneously?

In a computer program (written in C++), given $x\in[0,1)$ and $\sigma>0$, I need to sample $y$ from the wrapped normal distribution $\mathcal W_{x,\:\sigma^2}$ with mean $x$ and variance $\sigma^2$ ...
151 views

### Sum of two Von Mises random variables

I know that the sum of two independent normally distributed random variables is also a normal random variable, but is this true of other distributions? For example, what probability distribution does ...
234 views

### compute standard deviation of wind direction angle

How would one compute the standard deviation of wind direction that can assume values between 0 and 360°? I have the wind information in u and v components and corresponding angle. Getting the average ...
146 views

### interpretation of Rayleigh test results

I have a group of bearings that appear to be clustered toward the SW. I wanted to compare this to a uniform distribution, so I selected a Rayleigh test. Here is my code in R: ...
34 views

### 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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### Harmonic vs circular regression

Is there a difference between harmonic and circular regression? I've been working with more longitudinal data recently and trying to model circadian patterns that involve transforming the time ...
853 views

### Loss function (and encoding?) for angles

I'm training a network to predict the angle of arrival of a signal. Labels are single values in the [-180, 180) interval. I'm seeing a discontinuity in predictions around ±180 degrees, which makes ...