# 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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### GLMM with interaction terms between two circular predictor variables?

I am running a GLMM to see if several weather and nest box covariates influence occupancy (binary linear response). I would like to include two circular predictors (wind direction and box entrance ...
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### Use of circular predictor in GLMM

I am developing a mixed-effects binomial logistic regression (using glmmTMB, family = binomial) where the response is presence-absence. One of my potential predictors is hour of day, which takes ...
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### Reference for Directional Statistics of Plane Orientation

I've got a project I'm working on where I've got the orientation (normal) vectors of planes. These vectors are all within a unit hemisphere where the $z$-coordinate is strictly positive. The ...
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### is there a closed form of the CF (characteristic function) of a bivariate von Mises distribution?

is there a closed form of the CF (characteristic function) of a bivariate von Mises distribution? And if I have two parameters that follow von Mises distribution, but my two parameters will be mixed ...
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### How to cluster time-of-day event data?

Suppose I have data about patient sneezes, e.g.,: Name Time Loudness Alex 07:59 10 Bob 08:03 12 Charlie 17:06 9 Alex 08:09 13 ... You can see ...
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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 ...
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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 ...
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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 ...
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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 ...
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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?
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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 ...
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### 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 ...
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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 ...
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