Questions tagged [circular-statistics]

Directional 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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6 views

Finding an appropriate distribution for a constant offset to angle in a weighted sum of different sine waves

I am working on implementing Stan estimation of biomathematical models of sleep. Bio-mathematical models of sleep assume a "circadian" process (C), which measures the degree of sleepiness associated ...
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12 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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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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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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31 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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82 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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139 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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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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38 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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31 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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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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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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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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54 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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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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52 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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43 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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97 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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141 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
65 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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31 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 ...
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545 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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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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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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51 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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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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51 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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32 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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234 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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118 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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72 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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86 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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42 views

Variables measured on two different scales

I am dealing with three continuous predictor variables (corolla tube width, corolla tubedepth, corolla inclination) and a discontinuous response variable (counts of bee visits). I am confused on how ...
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49 views

Is there two-sample test for wrapped normal circular data?

I have two sets of randomly generated data with the wrapped normal circular distribution. I would like to test for homogeneity of means between these two samples. I was considering using Watson-...
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56 views

In circular statistics, is the difference between the means of two samples equivalent to the mean of their differences?

I'm comparing wind direction distributions using Python's scipy.stats.circmean and scipy.stats.circstd, and I encountered some ...
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331 views

How to generate a data sample along a annulus (between fixed radii)? [duplicate]

I would like to create a random data sample to test a clustering algorithm using python. One specific data sample I would like to generate consists of two non-overlapping annuluses (annuli?); however, ...
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1answer
157 views

Extracting the linear equation for a circular-circular regression

I am trying to create a predictive model using a relationship found by the lm.circular function from the circular package. The ...
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67 views

Limitations to using the principle of least squares to fit an ellipse to experimental data?

I have used the method described below many times without issue to determine the major and minor axes of the "data ellipse". However, for this set of data (Fig. A) the method described below is ...
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22 views

Is there a MANOVA test on circular variables?

I have a population 4 individuals moving in different directions in 9 different compartments. The movement is not coherent between the different compartments, but I suspect that it is coherent between ...
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133 views

Is the product of two Wrapped Normal Variables a Wrapped Normal Variable? [closed]

I know that the sum of two Wrapped Normal Variables is a Wrapped Normal Variable. In particular, if $\theta_1 \sim WN(\mu_1, \rho_1)$ and $\theta_2 \sim WN(\mu_2, \rho_2)$, then $\theta_1 + \theta_2 \...
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185 views

Regression for looping (circular?) variable [duplicate]

I am trying to calculate a regression curve for a dataset, where my independent variable ranges from 0 to 1, but 0 is equivalent to 1. In other words, my independent variable loops around. Therefore, ...
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1answer
105 views

Semicircular mean

I am running MCMC sampling to determine an angular parameter resulting in several thousand samples. The angle is restricted to $[0,\pi]$ as we cannot distinguish $\alpha$ and $\alpha+\pi$. For ...
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1answer
846 views

Including time of day in a linear regression model

The title may be entirely inappropriate for this question: that depends on whether I am on the right track. I am developing a statistical model to evaluate flower temperature based on air temperature. ...
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1answer
27 views

Statistical method to show a cycling pattern

let's say I have multiple time-series $A_i(x)$ and $B_i(x)$. Here, $i$ stands for a person (person 1, person 2, person 3, ..., person $i$, ..). Is there a method to show that the fluctuations in $A$ ...
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79 views

Power analysis for circular data

Imagine I have a sample distribution for a circular data set with a mean group direction and known variation. I would like to do a power analysis for a known effect size (e.g. to determine what sample ...
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440 views

Timestamps in Ridge Regression Scikit Learn

I am trying to transform data for use in regression, most likely the Ridge or Lasso technique implemented in sklearn.linear_model. My training data contains time ...
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77 views

Distance between angle distributions

I want to quantify the complexity of the street network of different cities. For each city I have the angle distribution of its streets. My hypothesis that the more complex the street network, the ...