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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3
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0answers
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 ...
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1answer
306 views

Check for significant difference between numbers of sightings per cardinal direction

I have data in a form like this: quantity direction 10 n 5 e 6 ne 12 n 20 nw 5 s 8 n 1 sw 3 se 2 ne 6 nw 8 n 2 se 3 e 4 w 9 nw The information behind these ...
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2answers
983 views

Calculating goodness-of-fit for circular data?

What is the proper way to report the goodness-of-fit for circular data estimates? Is there an equivalent to $R^2$ that can be used. The toolbox I have can calculate the correlation between two sets ...
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526 views

Which statistical tests are reasonable with this time of day data set?

I'm not really sure which statistical test is appropriate for my data. data: I have behavioral data (being active, resting, eating ...) with a time stamp. Data was taken between 6-18 h and is not ...
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1answer
355 views

Circular statistics for showing the directional mean lies outside a specified region of a duty cycle

I'm doing an analysis to examine if my data points are clustered along a polar axis (the cycle of a repeated playback sound followed by silence). I'm interested in: Are the data points clustered ...
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133 views

Is a time frame of time of day circular data?

I have data points with time of day. But I only took data between about 6:00 AM and 18:00 PM. If I want to test these data for distribution do I have to take a circular test? Or should I take a non-...
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1answer
76 views

How to test if the vectors I'm measuring have different directions?

I have a set of N measurements of a p-dimensional vector, and another set of N measurements of a different p-dimensional vector. Each measurement is contaminated with random gaussian noise. How can I ...
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1answer
104 views

How to change variable of distribution from vector to angle from fixed point?

I have a distribution of vector $\textbf{x}=\langle \sin{\phi_x}\cos{\theta_x}, \sin{\phi_x}\sin{\theta_x}, \cos{\phi_x} \rangle$ on the unit sphere (von Mises-Fisher): \begin{align}f(\phi_x,\...
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298 views

Estimating effective degrees of freedom of a time series (of circular data)

I have a $1 \times N$ vector, x of instantaneous phases (in radians). To determine the 'systematicity' or 'non-uniformity' of this set of phases, I use the formula (in MATLAB notation): ...
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1answer
5k views

How do I interpret the standard deviation of a directional dataset?

Lets say I start with a vonMises distribution dataset of compass directions: ...
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2answers
1k views

Normalisation of circular statistics, such as wind direction in degrees, for clustering

I have a set of data points each representing a day and a number of features associated with it: temperature, wind speed, wind direction, humidity... etc. Before the analysis, I am meant to normalise ...
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1answer
746 views

Classification of circular data

I have a multi-class classification problem with circular and linear data. For example a feature vector contains 20 circular ($\theta \in [0,2\pi)$) and two linear ($\in (0,1)$) variables. I plan to ...
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2answers
119 views

Plot angles around $360^\circ$ (North)

I want to plot wind angles. I typically have around 25 observations (the amount is not important here). I want to use a line chart to quickly see the trend (veering or backing) and the amount of ...
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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 ...
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1answer
2k views

Interpreting circular-linear regression coefficient

I'm trying to use the circular package in R to perform regression of a circular response variable and linear predictor, and I do not understand the coefficient ...
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1answer
350 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 ...
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3answers
11k views

Is time of the day (predictor in regression) a categorical or a continuous variable?

I am trying to perform multiple regression. One of the feature variables is time of the day, represented by 0 to 23. I am confused as to whether I need to use dummy coding or not. Is this a ...
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1answer
990 views

Kuiper's Test P Value in R

I am trying to implement a kuiper's test on a set of data and looking for an R package (or other program) that can give a p-value without monte carlo simulation or only a range of p-values. All of the ...
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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 ...
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2answers
256 views

Does Spearman's Rank Correlation Imply Periodicity?

I have collected data from an online survey that asked people to 'rate' a corpus of music track excerpts with 8 emotional adjectives such as 'happy', 'sad', 'angry', etc. They could only select one ...
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1answer
2k views

Statistics in polar coordinates

All statistical methods/approaches/tools that I have encountered so far are always in Cartesian coordinates. Why not polar? Doesn't math "work out" a little different in polar coordinates? (for ...
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1answer
3k views

regression with circular response variable

I am analyzing some data where the variables of interests are circular (angles). I use R and the circular package. In my dataset, every observation consists in a ...
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1answer
7k views

Use of circular predictors in linear regression

I am trying to fit a model using wind data (0, 359) and time of day (0, 23), but I am concerned that they will poorly fit into a linear regression because they are not themselves linear parameters. I ...
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1answer
1k views

sample from a von Mises distribution by transforming a RV?

Is there a distribution $p$ that I can sample from, such that for $\epsilon \sim p$, and for closed-form deterministic function $g_{\mu,\kappa}$, $g_{\mu, \kappa}(\epsilon) \sim \mathrm{vonMises(\mu,...
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108 views

Appropriate test for similarity of four vectors?

I have four samples under four treatment conditions, and I want to test the hypothesis that they increase in such a way that the relative differences between them stay the same. Pearson correlation ...
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1answer
339 views

Estimating von Mises Parameters for Angular Data

I want to model some angular data. Any input on how to incorporate the von Mises distribution and suggestions on appropriate priors in RJAGS for von Mises mean and concentration would be greatly ...
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27 views

min ChiSquare to fit dipole axis

I am trying to fit a dipole. As I am not sure about some aspects (and not sure whether I understand it at all) I would like to ask this question here. Basically I have a distribution of $n$ sample ...
6
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1answer
884 views

How to create a QQ plot of azimuths to test rotational symmetry of a spherical point dataset?

I am trying to do some Q-Q plots and the Kuiper test for rotational symmetry about the mean direction. These are unit vector, spherical data. What I am struggling to understand is the rotation from ...
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1answer
3k views

Regression and Correlation of Wind Direction (circular) Data

I'm currently facing a problem which I thought simpler in the beginning. Basically I have outputs of wind direction from a model and observed wind direction from my sensors (both in degrees). What I ...
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0answers
81 views

Hypothesis test for lower circular distance in angular datasets

I need to know how I can test in directional statistics whether there is significant evidence of the circular distance between the mean of one dataset and certain angle being smaller than the distance ...
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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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1answer
51 views

Tests of equal variances- am I doing this right?

In my experiment, I want to test whether dogs are more likely to head directly to a goal. The data is in the form so that $0$ (degrees) is a heading to the goal, $-90^\circ$ is a heading to the left ...
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1answer
708 views

understanding U-statistics calculation in directional statistics

I'm trying to work with U-statistics as described in Mardia and Jupp's 2000 book Directional Statistics (2). Specifically pages 220-2 there is a test for the equality of concentration parameters. The ...
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1answer
86 views

Statistical model for axis angle rotations

I would like to describe a large number of measurements of rotations $\textbf{x}_i$. Each rotation is described by its rotation axis $\textbf{v} =\frac{\textbf{x}}{|\textbf{x}|}$ and the rotation ...
2
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1answer
199 views

Goodness of fit test for bivariate circular distributions

I'm trying to implement a goodness-of-fit test for a bivariate distribution on the torus. In the univariate case, i use the distribution function to transform the data so it presents a uniform ...
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2answers
2k views

Predict magnitude from angle in linear regression

I have some data where I want to see if the magnitude of an effect depends on the direction. (Analogous to asking if wind speed depends on wind direction, for example.) In the ...
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4answers
16k views

Simulate a uniform distribution on a disc

I was attempting to simulate injection of random points within a circle, such that any part of the circle has the same probability of having a defect. I expected the count per area of the resulting ...
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2answers
1k views

Expectation of von Mises Fisher Distribution

The von Mises- Fisher distribution is defined as $$ \frac{\kappa^{p/2-1}}{2\pi I_{p/2-1}(\kappa)}\exp(\kappa \mu^Tx) $$ It is defined over the unit sphere i.e. $||x||_2^2=1$. My question is what is ...
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2answers
2k views

Average and standard deviation of timestamps (time wraps around at midnight)

I have lots of sensor data with timestamps like "2014-09-09 16:10:45" and accompanying sensor readings. To get some insight into these I want to find "unusual" events by looking at the average and ...
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1answer
304 views

Do you know of any public circular/angular dataset? [closed]

I've been trying to locate and access circular/angular datasets for my research. I'm particularly interested in datasets that distribute according to a mean centered circular distribution with ...
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1answer
276 views

Prior on a non identifiable parameter-MCMC integration

To introduce the problem I will explain the Projected normal distribution. Let $\mathbf{z}_i=(z_{i1},z_{i2})$ be a bivariate vector distributed as a bivariate normal with vector mean $\boldsymbol{\...
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0answers
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 ...
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1answer
5k views

regression for angular/circular data

I have supervised learning problem where targets are angles. If I would do simple regression then numbers 360 and 1 would be far away for my model, but actually they are close and predicting x and y ...
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2answers
677 views

Detecting outliers in circular data?

I've a day of the year data about number of event occurence in different sites: A day of the year is circular data. I know that a usual detecting of outliers, for example by boxplot is no use here: ...
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2answers
236 views

visualizing orientation (zenith and azimuth) data (e.g. with a circular or spherical histogram)?

I want to understand the distribution of orientation angles in a 3D image (represented as a triangular mesh). For each triangle in the image I have zenith ($\Theta$) and azimuth ($\phi$) And I can ...
5
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2answers
512 views

Data on a circle - testing if points are close to another given point

I have a set of points that lie on a circle, and I know their angles. Is there a way that I can test whether they are closer to another point x on the circle than ...
5
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1answer
350 views

What transformations preserve the von Mises distribution?

The von Mises distribution is entirely defined on the circle with a density given by $$f(x) = (2\,\pi\, I_0(\kappa))^{-1} \exp(\kappa \cos(x-\mu))\ ,$$ where $x$ is in an arbitrary real interval of ...
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2answers
432 views

Best transformation for sinuous data sets?

I am analysing annual behavioural patterns and am currently scratching my head over how to best transform data to test for correlation where my independent variable is the moon phase (given as ...
2
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1answer
598 views

Comparing Multivariate Means

Apologies in advance if this is very basic; I am quite new to statistics. I have a large set of 7 dimensional data, for two groups. In my example, they are express relative preferences over a ...
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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, ...