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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151 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 ...
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627 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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136 views

Test for difference of distributions on a torus

I have two circular dependent variables and would like to test for a difference in the distributions (presumably circular means) between multiple treatment groups. There are a number of multivariate ...
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32 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 ...
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165 views

Haar prior for von Mises distribution

Ok, Let me tell you that this is the very first time that I have no idea with the question below. I can not find a solution or anything that will lead me to it. I say this to prevent comments "what ...
3
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1answer
96 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. ...
3
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41 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 ...
3
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65 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....
3
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133 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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0answers
658 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 ...
3
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234 views

Transform non-normal circular data

I have a set of time-series data showing event times for two different groups. Let's call them Site 1 and Site 2. My analysis shows one group is circular normal around a 24 hr clock (von Mises ...
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2k views

Circular variance

I'm attempting to replicate a particular analysis of circular data. The author of this analysis writes I calculated . . . variance . . . for the observed recall errors, defining variance as the ...
3
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90 views

A question concerning distribution of $\mathbf{Y}/\|\mathbf{Y}\|_2$ where $\mathbf{Y}\sim \mathcal{N}(\boldsymbol{\mu},\mathbf{I})$

I know that when $\mathbf{Y}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$, $\mathbf{Y}/\|\mathbf{Y}\|_2$ is distributed uniformly on the unit sphere. But to my surprise, I failed to find a simple closed ...
3
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1answer
208 views

Von Mises distribution to detect outliers

I am working out the difference between two angles from a circle, and I work out the mean difference across 96 trials in 10 separate samples. In order to detect outliers for statistical analysis, ...
2
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0answers
52 views

Equivalent of a one-tailed paired t-test for circular data?

I have a set of paired circular measurements representing the timing (in phase) of two different events. I would like to determine whether one event occurs earlier (smallest difference in a counter-...
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35 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 ...
2
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1answer
52 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 =...
2
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58 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 ...
2
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0answers
22 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 $...
2
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87 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 ...
2
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427 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 ...
2
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2answers
78 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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146 views

Correlation for circular / angular variables

Is there a commonly accepted practice for calculating (and/or visualizing) correlation between angular variables? (I.e. 359° is pretty close to 1°.) I'm sure I could concoct a suitable trigonometric ...
2
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0answers
54 views

two samples comparison with cyclic variables

How to check if two samples are from the same distribution, when the variable is cyclic? A simple answer for non-cyclic variable is the Kolmogorov-Smirnov test. What is the equivalent for cyclic ...
2
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0answers
137 views

Find the most frequent timespan of event occurrence

I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery. Most of time, the robbery does not occur when the owner is watching => the declared ...
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160 views

Angles expressed in degrees of arc as regression variables

I have binary count data as a response variable in my logistic regression. The independent variables include, among others, two variables of inclination and orientation measurements, annotated in ...
2
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1answer
355 views

Scale and normalization of dates

It's common to normalize the different vars before applying some kind of supervised/unsupervised learning. Which algorithm do you use with the dates? You use the day of year (1, 200, 300) and perform ...
2
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0answers
92 views

what is the name of distribution similar to von mises distribution

I am wondering whether the following PDF is a named distribution. Over the interval $0< \theta < \pi$, the PDF of the distribution is written as $$ P(\theta) = \frac{2^{-n/2} k^{n/2} e^{k \cos (\...
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601 views

Sum of random vectors with fixed amplitudes

Is there a simple way to evaluate the pdf of the amplitude of a sum of vectors with fixed amplitudes and random phases? Explicitly, let $Ae^{i\phi}=\sum_{n=1}^NA_ne^{i\phi_n}$, where $N$ is a fixed ...
2
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497 views

Circular statistics and bidirectional data

I am curious if tests such as Rayleigh's test, Kuiper's test, and Watson's test are valid for bidirectional data (i.e. 180 degrees) as well as unidirectional data. If not, what are the appropriate ...
2
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0answers
126 views

Regression in projective space?

Is there a method for (nonlinear? kernelized?) regression of functions with output in projective space? That is, given a series of examples $x_i\in\mathbb{R}^n$ (or $x_i\in\mathbb{P}^n$) and $y_i\in\...
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6 views

Is the difference between directional means from two populations significant? (circular data)

I am comparing the orientation of two data sets with geographical lines and have used the processing tool "Linear Directional Mean" (ArcGIS Pro, Spatial Analyst) to calculate the mean of ...
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13 views

How to handle nondifferentiable points of the objective function in the geometric circle fit?

We a given measured points in $(x_i,y_i) \in \mathbb{R}^2$, $i=1,..,n$. The geometric circle fit is the circle with center (a,b) and radius $r$ that minimizes the squared Euclidean distances between ...
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23 views

Statistical test for comparing directional data

I have a dataset with number of bats flying out in 8 directions from their home site (i.e) I studied a bat colony with N individuals and I have counted the number of bats (from that colony) that flew ...
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14 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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0answers
73 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 ...
1
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1answer
39 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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0answers
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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21 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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0answers
66 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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0answers
62 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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0answers
130 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
108 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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0answers
84 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 ...
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0answers
200 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 ...
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0answers
40 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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40 views

Symmetry of circular distribution

I wanted to ask somebody for an opinion about one thing I found in the statistical book (Mardia, Jupp - Directional statistic). They were defining circular symmetric distribution in following sense: ...
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71 views

definition of circular/directional random variable

I wanted to ask you to check my definition of circular random variable since i have never seen any. So based on the assumption, that difference between linear and circular variables, is that c.r.v. ...
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0answers
406 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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0answers
137 views

Circular Statistics from Spherical to Cartesian Coordinates

For spherical coordinates with angles $\Theta$ (polar) following truncated normal distribution and $\Phi$ (azimuth) following circular uniform distribution, is there any closed form distribution for ...