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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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The Sine and Cosine transformations for circular predictor variables [duplicate]

I have read the answer to how one can deal with circular predictor variables suggested by NicK Cox. It suggests using the sine and cosine as a solution. I am I supposed to either use one of them or ...
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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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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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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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1answer
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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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Phase marginal for a multivariate complex Gaussian density

Suppose $z$ is a random variable taking values in $\mathbb{C}^n$ and admitting the complex Gaussian density $p(z;W) \propto \exp{(-\frac{1}{2}z^*Wz)}$, where $W$ is Hermitian. Let $r$ be the vector of ...
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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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10 views

Error in lm.circlular.cl

I have a dataframe where I have information on the departure bearing when individuals are leaving a certain site, the departure date, and the distance they travelled. I'm interested in modelling the ...
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44 views

Help with circular-circular regression

I am looking for assistance in using the lm.circular function of the circular package. I am unsure of A) why the package authors ...
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Limitations to using the principal 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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18 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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62 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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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
68 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
246 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
25 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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1answer
34 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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2answers
204 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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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 ...
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1answer
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Prediction with circular variable

Suppose I have a set of $N$ observations for a circular variable $\theta_i$. Each trial for which an observation of $\theta_i$ is taken can lead to an outcome $x_i \in \{0,1\}$. Next, suppose that the ...
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1answer
108 views

Standard error of circular standard deviation

How to calculate the standard error of circular standard deviation estimated with equation $s = (2(1 − R))^{-\frac{1}{2}}$ or $s_{0} = (−2 \ln{R})^{-\frac{1}{2}}$ where R is the length of the mean ...
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Circular datasets: homolog genes [closed]

I am looking for a homolog genes circular datasets, how can I find those kinds of datasets?
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1answer
36 views

Comparison of empirical distributions in ciruclar/polar coordinates

I have 4 sets of 24 measurements of a polar variable (univariate). I want to use a statistical test, like the Kolmogorov-Smirnov test, to test whether said sets differ significantly from each other. ...
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1answer
153 views

Linear model with interation for circular data in R

I have a circular dependant variable (in radians) and a linear independant variable (year) which I would like to model against each other and extract a slope value. I have been trying to use ...
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Time series analysis: periodogram peak uncertainty estimate

I'm analysing a time series with a Lomb-Scargle periodogram. Here's what the periodogram looks like: As you can see, there are three peaks very close together (I've tried much finer frequency grids ...
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Good choices of PRNG for uniform circular (directional) data?

I'm planning to simulate iid one-dim variates with continuous uniform distribution on a normalized circle (which circumference is $1$ instead of $2\pi$). Namely, a sample consists of $n$ points ...
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1answer
30 views

P-Value from Watson.test

I am using the circular package to evaluate if my circular data is uniform or not. The package PDF can be found here -> https://cran.r-project.org/web/packages/circular/circular.pdf The p-value ...
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pca on polar coordinates?

I have a dataset composed of 123 rows (time bins) and 20 columns (variables) The question I have is the following. each row,column pair has a radian value and a radius value. If I convert these pairs ...
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calculating orientation anisotropy of a set of 3D vectors

I have a set of unit-length 3D vectors (represented as cartesian 3-tuples) with 180$^\circ$ equivalence (rotated through any plane passing through the origin i.e. $v=-v$), all situated at the origin (...
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2answers
677 views

Regression using circular variable (hour from 0~23) as predictor

My question originally arises from reading this post Use of circular predictors in linear regression. Right now, I'm trying construct linear regression using "Bike Sharing dataset" from https://...
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1answer
64 views

Integer predictors in Poisson regression

I am trying to fit a model of total rental bike with ten predictors using Poisson Regression. Four of them are integer : Season : 1-4 Month : 1-12 Day : 0-6 Hour : 0-23 I usually treat integer ...
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Identifying two distributions from a circular scan and then finding their centre points

I’ve got three clusters of points. These are 315 readings taken from a circular scan, i.e. the reading at x = 315 is actually next to x =0. There are two clusters in the data - zero and non-zero (but ...
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1answer
499 views

Maximum Likelihood Estimation to fit Von Mises to grouped (interval) circular data

EDIT: see below- I used the pdf instead of the cdf for my likelihood. Fixed, but with a fun new problem! This is a follow-up to a question I asked here. For reasons explained earlier, I'm attempting ...
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373 views

How can I fit a normal (von Mises) distribution to discrete angular data?

This bears some explaining: I have a set of data from a psychophysics experiment where participants selected a response from a discrete set of 8 possible responses. These responses were actually ...
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1answer
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Is the month ordinal or nominal variable?

I read in some article that the month of the year was being considered as qualitative nominal variable, but for me the month of the year has a clearly ordered structure and should therefore be ...
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1answer
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Estimate parameter using MLE method [closed]

$$L=-2n\log(2 \pi)-n \log I_0(\lambda p)+\sum_{i=1}^{n} [\lambda p\cos(x_i-X_i)]-\sum_{i=1}^{n}log[c-m_1\cos(y_i-BX_i)-m_2\sin(y_i-BX_i)]$$ where $\lambda, X_i, m_1, m_2 , p$ are parameter i reach ...
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1answer
78 views

Circular/directional data analysis within a narrow arc

I am studying the presence of an anatomical variation to the structure of a long bone in healthy and diseased individuals. I have two separate groups of individuals. The anatomical variation is ...
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2answers
57 views

Assessing correlation with a variable in degrees [duplicate]

This is probably a fairly simple question but it occurred to me, when trying to go through some data, that I wasn't sure how. Say you have some numeric variable vs. arc degrees-- like the price of ...
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34 views

Curve fitting with a polar input variable

Imagine we have a set of data, with two variables, the first of which can be represented in polar co-ordinates (for example hour or day, or day of week). The second variable is a real valued and has ...
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1answer
118 views

Variance of angle to $(X,Y)$ where both $X-\mu_X$ and $Y-\mu_Y \sim N(0,\sigma^2)$ independently

$X$ and $Y$ arise from observations contaminated by i.i.d. additive Gaussian noise $\sigma$. I seek the approximate variance of the angle from the origin to $(X,Y)$. What I've tried: The answer (...
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282 views

How can I do a t-test on 2D data?

How can I do a t-test on 2D data with latitude and longitude attributes? I have 2 clusters of similar coordinates but in different time, I want to do a t-test to see if they are statistically ...
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206 views

“Parametric bootstrap” or “Monte Carlo test”

I have a data set on counts of amphibians in buckets around a pond, which I have detailed in a previous post: Circular statistics for discrete, irregular sector data To conduct a test of circular ...
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1answer
54 views

How can I apply interpolation to angle data?

My data is in angles (degrees) and I intend to write a code that is trying to understand if there is a systematic (biased) behaviour in data. For example, if my data set is (10, 20, 30, 40) then a ...
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1answer
161 views

Find correlation between different wind direction with aerosol

I have wind direction and aerosol data. I want to find correlation between different wind direction (like: corr between N-E/aerosol, E-S/aerosol, S-W/aerosol and W-N/aerosol). wind direction data are ...
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2answers
74 views

Adding an hour feature to data

I need to add an hour feature to my data. Assigning "dummy variables" (which is what I usually do) does not work in this case, apparently (wouldn't elaborate - but believe me this is so). At first,...
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1answer
360 views

How to perform PCA on angular data in R?

I've been looking for a way to perform PCA on angular data in R and haven't succeeded yet. I have a set of monitoring data for each of multiple plant species on the number of flowers opened at every ...
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Change of variables for a PDF of angles (circular/wrapped data)

I have a PDF with angle $\theta$ as the independent variable: $R(\theta)$. $\theta$ is defined up to mod $\pi$ -- accordingly, $R(\theta) = R(\theta + \pi)$. I need to express this PDF as a function ...
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2answers
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How to test if turtles are dying mostly at a particular time of year?

I have citizen science records of turtle sightings (alive/dead, and if dead what caused its death e.g. car/predator/etc), and the date they were spotted. What would be the most appropriate test to ...
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2answers
198 views

Von Mises mixtures: What is the maximum kappa value?

I have an R script that is estimating the concentration parameters (kappa) for Von Mises mixtures. This script is giving me values of kappa that are 60, 100 e.c.t. I was expecting kappa to be less ...
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2answers
814 views

Comparisons of circular means

First, I have to say my mathematical understanding of circular statistics is rather limited. I need to carry out a statistical comparison of means of circular data, i.e. two groups of data (phase ...