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 $\mathbb{R}^n$.
Questions tagged [circular-statistics]
242 questions
32
votes
3 answers
Is hour of day a categorical variable?
Is "hour of the day" where the value can be 0, 1, 2, ..., 23 a categorical variable? I would be tempted to say no, since 5, for example, is 'closer' to 4 or 6 than it is to 3 or 7.
On the other hand, there is the discontinuity between 23 and 0.
So…
Paul Reiners
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30
votes
4 answers
Encoding Angle Data for Neural Network
I am training a neural network (details not important) where the target data is a vector of angles (between 0 and 2*pi). I am looking for advice on how to encode this data. Here is what I am currently trying (with limited success):
1) 1-of-C…
Ari Herman
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30
votes
4 answers
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 distribution to follow a Poisson distribution if I…
Jonjilla
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25
votes
1 answer
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 would like to transform them using Python. I have…
compguy24
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23
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2 answers
How to test equality of variances with circular data
I am interested in comparing the amount of variability within 8 different samples (each from a different population). I am aware that this can be done by several methods with ratio data: F-test equality of variance, Levene test, etc.
However, my…
Alex Williams
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16
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2 answers
Expected ratio of x'Ax and x'AAx on a unit sphere?
Suppose $A$ is symmetric positive definite matrix. Is there a nice expression for the first moment of the following quantity?
$$\frac{x^TAx}{x^TA^2 x}$$
Where $x$ is distributed as $\text{Normal}(0,I_n)$. This is the ratio of two quadratic forms…
Yaroslav Bulatov
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16
votes
3 answers
Linear regression with "hour of the day"
I am trying to fit a linear model using "hour of the day" as parameter. What I'm struggling with, is, that I've found two possible solutions on how to handle this:
Dummy encoding for every hour of the day
Transform hours into cyclic variable
I…
NclsK
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15
votes
5 answers
Best distance measure to use to compare vectors of angles
Context
I have two sets of data that I want to compare. Each data element in both sets is a vector containing 22 angles (all between $-\pi$ and $\pi$). The angles relate to a given human pose configuration, so a pose is defined by 22 joint…
Josh
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15
votes
2 answers
Trigonometric operations on standard deviations
Addition, subtraction, multiplication and division of normal random variables are well defined, but what about trigonometric operations?
For instance, let us suppose that I'm trying to find the angle of a triangular wedge (modelled as a right-angle…
Bossykena
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15
votes
1 answer
Time series modeling of circular data
I'm building ARIMA models for some wind/waves data. I'm building a separate model for each variable.
Two of the variables that I need to model are wave and wind direction. The values are in degrees (0-360°). Is it possible to model this type of data…
krsnik93
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14
votes
1 answer
Logistic regression with directional data as IV
I am looking for good references on using directional data (measure of direction in degrees) as an independent variable in regression; ideally, it would also be useful for hierarchical nonlinear models (the data are nested). I am also interested in…
Peter Flom
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14
votes
1 answer
Intuition for higher moments in circular statistics
In circular statistics, the expectation value of a random variable $Z$ with values on the circle $S$ is defined as
$$
m_1(Z)=\int_S z P^Z(\theta)\textrm{d}\theta
$$
(see wikipedia).
This is a very natural definition, as is the definition of the…
Rasmus
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13
votes
2 answers
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 incredibly weird and not what it should look like…
Jessica Harvey-Carroll
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13
votes
1 answer
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 coordinates doesn't feels right, since I am trying…
rep_ho
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10
votes
3 answers
Test of association for a normally-distributed DV by directional independent variables?
Is there an hypothesis test of whether a normally-distributed dependent variable is associated with a directionally-distributed variable?
For example, if time of day is the explanatory variable (and assuming things like day of week, month of year,…
Alexis
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