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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Characterize conditions in which Taylor moment approximation is good

I am working with the Projected Gaussian, or Angular Gaussian distribution, which is given by $z = \frac{x}{||x||}$, where $x \sim \mathcal{N}(\mu, \Sigma)$. This is a distribution on the sphere in $\...
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Predicted circular regression curve from a bpnr regression

I'm trying to understant how to interpretresults from the bpnreg package to do glm on a circular response variable (flight directions). I understood from the paper that the interpretation can be done ...
Tanuki's user avatar
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Modelling the effect of a continuous (linear) predictor on a non-von Mises circular data

I am working with circular data (n=800+) representing the time of animal activity in radians, scaled between 0 and 2π. My objective is to determine the influence of a linear predictor, specifically ...
MountJ's user avatar
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Analytically estimate joint Von Mises distribution parameters from multiple underlying distributions with arbitrary weights

Given a set of n one dimensional (circular) Von Mises distributions, it is possible to randomly sample each distribution (with a different weight, ...
Matt Summersgill's user avatar
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Maximum Entropy distribution of a ticking clock

Say I have a clock that emits "ticks". An ideal clock looks like a dirac comb. It has: perfect periodicity of ticks (there is a precise fixed time interval between any two consecutive ticks)...
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I am looking for a regression formula to calculate a polar curve that goes through a set of points analogous to linear regression, how do I do this? [closed]

Suppose you have an arbitrary set of points in a two dimensional space, what is the "curve of best fit" not line of best fit that can be used to model the data?
Nathan's user avatar
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Conclusions on modality from Rayleigh's Uniformity Test

Rayleigh's Uniformity Test (RUT), when run on a circular distribution C, returns p ~= 0. Then, we can confidently assert that ...
AvadaMouse's user avatar
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Formulas, approximations, or bounds for $\mathbb{E}\left( \frac{X}{\lVert X \rVert} \right)$, $X\sim N(\mu, \Sigma)$?

In another question, I asked for $\mathbb{E}\left( \frac{X}{\lVert X \rVert} \right)$, in the case where $X \in \mathbb{R}^d \sim N(\mu, I_{d})$. Somebody posted an exact formula based on the symmetry ...
dherrera's user avatar
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Distribution of intersection of $n$-sphere and hyperplane projected onto $c$

Suppose $x$ is uniformly sampled from an n-sphere of radius $1$ restricted to points with $\langle a, x\rangle=b$ for a given unit vector $a$ and a constant $b$ Given a unit vector $c$, what is the ...
Yaroslav Bulatov's user avatar
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Significance test of the amplitude of sinusoidal regression

I am working on a multi-level logistic regression model with a binary outcome and a circular predictor. Thanks to this post, I know that I have to add sine and cosine of the circular variable as a ...
Dominik Rolph's user avatar
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Overlapping circular bearing distributions on a plane

I have some directional hydrophones capable of recognizing transient signals/sound and estimating the circular probability density function of the bearing, or direction, that the sound came from. I ...
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Distribution of Data Within Hypersphere That Maximizes the Nuclear Norm?

Suppose I have $N$ points in $\mathbb{R}^D$ such that for each point $x_n$, its L2 norm is at most 1: $$||x_n||_2^2 = x_n^T x_n \leq 1$$ Assuming $N > D >> 0$, if I construct a matrix $X \in \...
Rylan Schaeffer's user avatar
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What concentration $\kappa \in [0, \infty)$ maximizes the entropy of the von Mises-Fisher distribution?

I'd like to prove what concentration parameter $\kappa \in [0, \infty)$ maximizes the (differential) entropy of a von-Mises Fisher Distribution. The differential entropy of of a von Mises-Fisher ...
Rylan Schaeffer's user avatar
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Cubic spline with circular predictor [duplicate]

I have a set of observations $y_i$ for a set of values of the independent variable $x_i$. $x_i$ takes values of angles, so it is a circular variable. Is there some method to perform cubic splines or ...
dherrera's user avatar
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Calculating summary statistics on a distribution of "day of year" data [R]

Say I have a dataset that consists of 1,000 integers between 1 and 365 that represent days of the year a certain event happened. I am trying to figure out how I could calculate summary statistics of ...
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Non-Uniform Spherical Distributions

Suppose $X_i\overset{\text{iid}}{\sim} N(0,1)$, and define the random vector $\mathbf{X}=(X_1,\ldots,X_n)$. Then the normalized vector $\mathbf{Z}:=\frac{\mathbf{X}}{\|\mathbf{X}\|_2}$ is uniformly ...
youngtableaux's user avatar
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How to plot angular time series?

I am trying to inspect a circular time series (a long time series of angular measures in 0-360°). The main aim would be to identify abrupt changes in the time series, but as a start I would like to ...
Calcifer's user avatar
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Is there an "antipodal" conditional disintegration of the von Mises Fisher distribution?

For more on conditional disintegration, cf. e.g. the references [1] [2], or these questions [a] [b] on math stackexchange. Question: For the von-Mises Fisher distribution, is there a conditional ...
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Large data sets with heavy tails - best fitting strategy

I have relatively large data sets with about 20000 to 25000 data. The data are the orientation angles (0 - 180°) of fibers in a composite material. You can see two example histograms showing the most ...
DasK's user avatar
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What is the entropy of a mixture of von Mises-Fisher distributions?

What results exist for computing (or approximating) the entropy of a mixture of von Mises-Fisher distributions?
Rylan Schaeffer's user avatar
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What is the value of $\sum_i x_i^2 v_i$ for isotropic $x$?

Suppose $x$ is an isotropic random variable in $\mathbb{R}^d$ with $E[\|x\|^2]=d$ and $v$ is some vector. It appears that $\sum_i x_i^2 v_i \approx \sum_i v_i$ when $d \approx \infty$. What is an easy ...
Yaroslav Bulatov's user avatar
7 votes
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231 views

Donut-like Distribution in Cartesian Coordinates

I have a set of points $P_i$ which are described by an angle $\theta_i$ and a magnitude $r_i$. $\theta_i$ follows a Uniform distribution $(\theta_i \sim U(0, 2\pi))$ and $r_i$ follows a chi-k ...
Liam F-A's user avatar
8 votes
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Radial axis transformation in polar kernel density estimate

Consider a kernel density estimate of a continuous, non-negative random variable defined over the unit circle with no discontinuity between 360 and 0 degrees. Unlike in the most common KDE ...
Reinderien's user avatar
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How to choose priors for bounds on circular truncated distributions?

I am considering choices of priors for truncated distributions on a circle. Let's take the truncated normal distribution on the unit circle as an example. It has parameters $\mu \in [-\pi, \pi]$ and $\...
Galen's user avatar
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4 votes
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Possibility priors in Bayesian analysis?

A couple of trains of thought have come together for a model I am designing. Let's start with the first part: Bayesian inference doesn't update strongly enough. One of the parameters $\theta$ is an ...
Galen's user avatar
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watson's two sample test with ties - does it exist on R?

I would like to compare two samples with the watson's two sample test in R (circular data). As I have a lot of ties in my samples, I followed the example given in the book from Zar (Biostatistical ...
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How to calculate confidence intervals for circular data?

I managed to convert my data i circular/polar data (angle, r). Now I would like to compare two treatments to see if they are statistically different. I thought to use the Watson's U2 test but ...
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Does it make sense to transform a feature containing hours (24h) into two features with xy-coordinates of each hour in the space? [duplicate]

I have a clustering problem that I might solve with an algorithm based on Euclidean distance (e.g. K-Means). One potential feature is the "hour" at which each user began an interaction. As ...
rusiano's user avatar
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How do I interpret the sine and cosine terms in a linear-circular regression?

When using a circular variable as a predictor (X) in a linear regression, the consensus seems to be to split the variable into sine and cosine terms. e.g. Y ~ cos(X) + sin(X) + etc This creates two ...
Fein's user avatar
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1 answer
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Python / R package for multivariate gaussian process regression for circular data?

I have two circular predictor features (two angles between 0 and 360 degrees) and a circular outcome (another angle, between 0 and 360 degrees). I'd like to be able to fit a model and get predictions ...
ach's user avatar
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3 votes
1 answer
467 views

Regression of circular variable with scikit-learn

I am trying to use Support Vector Regression on a (neurophysiological) dataset where the position of points on a circular manifold in N dimensions is correlated with a circular variable (phase of an ...
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Clustering and grouping of rhythmic data (acrophases)

I am looking for suggestions towards a clustering method for rhythmic/oscillation data. We performed cosinor regression (sin(2*pi*time/period)+cos(2*pi*time/period))...
ATpoint's user avatar
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Calculating the parameters of von Mises distribution

I would like to calculate the values of the concentration ($\kappa$) and mean direction ($\mu$) for a von Mises mixture model from the theta values given by the movMF() function in R. At the bottom of ...
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Within a circle, Find a probability distribution to model a random variable with distance to center and angle information

Within a circle with radius R, a random variable with two types of information as below: Distance to the circle center. The distance should satisfy uniform distribution~U[a R], where 0<=a<R is ...
daxia's user avatar
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3 answers
356 views

Measuring dispersion in circular data

stats noob here. I have a (circular) dataset with values in [0, 2pi]. I need some kind of a measure of how disperse or diverse the dataset is. I have looked a bit into non circular (regular) data, and ...
Ajinkya Kulkarni's user avatar
2 votes
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72 views

Is circular correlation maximized by points laying on a square grid on the plane?

Background Circular correlation is given by: $$R_{\operatorname{circular}} \triangleq \frac{\sum_{i=1}^m \sin (x_i - \bar x) \sin (y_i - \bar y)}{\sqrt{\sum_{i=1}^m \sin (x_i - \bar x)^2} \sqrt{\sum_{...
Galen's user avatar
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Definition of directional variance

We are currently adding some basic functionality for directional statistics to SciPy. Directional statistics refer to data whose magnitude does not matter such as unit vectors. While implementing the ...
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Running a poisson GLM with cyclical explanatory variable?

Im running a few poisson GLMs looking at count data of bats sightings in relation to lunar cycle. We specifically want to look at how species are affected leading up to and away from new moon/full ...
Dillon Jones's user avatar
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35 views

How best to model day time dependet activity?

I aquired the median activity data of animals per hour and wanted to model them dependent on time. Now I have tried different models and came up with the following. (This only includes a small portion ...
paschep's user avatar
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1 answer
321 views

How to calculate the value (wind direction) of "maximal effect" in a linear-circular correlation?

I am trying to evaluate the effect of wind direction (circular variable) on a dependent linear variable. I have used circular-linear regression to find the correlation coefficient between the two ...
L_Horner's user avatar
3 votes
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290 views

Which statistical test should I use to see if the month of onset of a disease is random or clusters in the winter?

I have data showing which month a disease started for 119 subjects. The months are represented by 1-12 (Jan - December). We hypothesize the disease more often onsets during winter months. What test ...
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How can I quantify this non-linear relationship where y-values peak within a narrow range of x-values?

I have plotted this data, and to me there appears to be a clear relationship between the variables (sediment accumulates when wind direction is between 150 and 250 degrees). Is there a appropriate ...
L_Horner's user avatar
11 votes
1 answer
2k views

Why doesn't mean square error work in case of angular data?

Suppose, the following are the first few lines from a dataset for solving a regression problem: ...
user366312's user avatar
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2 votes
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Machine learning regressor for cyclic values

I have a question regarding training a Machine Learning regressor for cyclic values. For instance, consider phase values. We cannot use conventional regression methods for this as for example the ...
Aep's user avatar
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6 votes
3 answers
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Why does the von Mises-Fisher distribution need two parameters?

The von Mises-Fisher distribution has two parameters: the mean $\mu \in \mathbb{R}^p$ and concentration $\kappa \geq 0$, where $\mu$ is constrained to have unit norm. Why not instead define the ...
Rylan Schaeffer's user avatar
2 votes
0 answers
284 views

Variance of von Mises-Fisher Distribution

As a follow up to this previous question on the expectation of the von Mises-Fisher distribution, what is the variance of a von-Mises Fisher distribution as a function of the mean direction $\mu$ and ...
Rylan Schaeffer's user avatar
13 votes
2 answers
1k views

Fitting sine wave with lm in R for circadian activity- frequencies?

I'm trying to fit a sine wave over some activity data, just like this post. I've managed to get a reasonable looking graph for one condition: However, when I plot the other condition the wave looks ...
Jessica Harvey-Carroll's user avatar
1 vote
1 answer
107 views

Best distance measure for cluster analysis of time series data with a circular variable

I'm doing hierarchical clustering on a set of time series (say 21 time series of 400 time points), however the variable I want to cluster is a circular variable, i.e. a directional vector between 0 ...
Bingo Bango's user avatar
2 votes
2 answers
730 views

How to define distance for vector of angles?

I have a vector of angles and I am looking for a method to compute the distance of my vector with any other vector of angles? I am looking for something similar to Euclidean distance but I know that ...
Aep's user avatar
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6 votes
3 answers
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Measure of similarity between two distributions - with variable starting point (wrap-around)

I would like to compute the (dis)similarity between two distributions. The first represents tones sung by an experimental subject during a recording. There are different numbers of tones, each with ...
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