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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14 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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28 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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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 ...
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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 ...
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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. ...
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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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12 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
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 ...
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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 ...
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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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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
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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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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 ...
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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 ...
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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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8 views

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: ...
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1answer
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 ...
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3answers
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 ...
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2answers
146 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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29 views

Generating points from generalized Fisher distribution on sphere and rotating this bunch of points

I have a bunch of points ($x_1, x_2, \dots, x_k$) around north pole ($n = (0,0,1)^T$) distributed according to generalized Fisher distribution with $\mu = (1,0,0)$. How can I rotate all these points ...
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1answer
61 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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37 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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22 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
37 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
29 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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1answer
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 ...
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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 ...
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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 ...
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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 $\sigma^2$ ...
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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 ...
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1answer
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 ...
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1answer
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: ...
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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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17 views

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 ...
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1answer
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 ...
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42 views

How can I determine differences between two circular distributions?

I have circular datasets. I am using this MATLAB package to perform tests on my data. https://au.mathworks.com/matlabcentral/fileexchange/10676-circular-statistics-toolbox-directional-statistics . I ...
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19 views

Variance of Random Vector in the Circular Orthogonal Ensemble

Let $x$ be a (uniformly) randomly chosen column of a random orthogonal matrix (of size $K$ x $K$) distributed according to Haar measure. What is $\mathbb{E}[x]$, $\mathbb{E}[x x^T]$, $Cov(x, x)$, and $...
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1answer
53 views

Reference books on uniform spherical distributions in multiple dimensions [duplicate]

QUESTION What is a citation of a book whose scope includes the uniform distribution [1] that is generalized to an $n$-ball [2]? Among other things, I'd like to read a book that include such ...
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1answer
50 views

quantifying asymmetry on a sphere

I have a scalar quantity that is distributed on a sphere. I would like to quantify the asymmetry in this scalar field. is there any standard method to do this? Let's say that the function on the ...
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1answer
20 views

How do you test for bias in a circular reference plane?

I've been trying to get my head around how to do hypothesis testing for a circular scale in hypothesis testing, but I am having a lot of trouble. I know well how to test for linear scales, but when it ...
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56 views

Compare semi-circular data

I have data on angles between vectors and thus the data lies in the range $[0,\pi]$. I have two samples of such data, of different sizes. I want some way of quantifying the difference between these ...
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43 views

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....
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1answer
335 views

What is a correct loss for a model predicting angles from images?

Backgrounds I am working with a dataset, where compass-like images are labeled with their corresponding angles from horizontal line ($0$ degrees). I am trying to make a CNN model to predict the ...
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1answer
134 views

How to interprete the p values of cos and sin terms in periodic regression?

I have camera trap data where for each site and hour I have the abundance of wild herbivores. I want to create a model where I can estimate the effect of predator activity on the activity and behavior ...
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91 views

Polynomial regression in a circular data set

I'm working on a data set where I have a set of events per time of the day (in a 1h time slot). I made the sum of the events and plotted a bar as show below. In order to define an equation that could ...
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1answer
111 views

How to interpret coefficients of angular terms in a regression model?

Given the model $$Y = a + \beta_1 x_1 + \beta_2 x_2 + \beta_3 \cos(\angle) + \beta_4 \sin(\angle) + \text{ errors}$$ resulting from a negative binomial regression, how can I explain the $\beta_3 \cos((...

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