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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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2
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0answers
14 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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12 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
110 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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16 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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14 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
48 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
48 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 ...
2
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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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42 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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15 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
50 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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45 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 ...
2
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1answer
48 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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33 views

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 ...
2
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1answer
36 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 ...
0
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1answer
28 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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35 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 ...
3
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1answer
152 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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20 views

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 ...
3
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1answer
79 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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0answers
13 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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0answers
104 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 ...
2
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0answers
58 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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20 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 ...
2
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0answers
101 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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0answers
139 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
90 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 ...
4
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1answer
435 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. ...
0
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1answer
26 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
56 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
316 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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0answers
60 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 ...
2
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1answer
50 views

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 ...
4
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1answer
164 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 ...
0
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1answer
43 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. ...
1
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1answer
271 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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0answers
130 views

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 ...
6
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125 views

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 ...
0
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1answer
35 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 ...
2
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0answers
231 views

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 ...
3
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0answers
108 views

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 (...
3
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2answers
1k 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://...
2
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1answer
67 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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0answers
38 views

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
595 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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0answers
462 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 ...
2
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1answer
11k views

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 ...
0
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1answer
58 views

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 ...
2
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1answer
83 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
60 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 ...