Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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 $\mathbb{R}^n$.

280 questions
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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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Converting a circular outcome variable to a linear one

I have a problem where I want to measure deviations from zero degrees. This outcome variable is a circular measure, since a deviation of -180 degrees is equivalent to 180 degrees. However, I don't want to complicate my model (using a linear mixed…
Abundance
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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 example drawing a spline is easy $r = \theta…
Anton
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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 circular package there is lm.circular which allows doing regression using…
Marius
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Measuring Circularity of a set of Co-planar points

I am trying to find a way to quantify how circular or symmetric a shape is. What is a good way to measure the circularity of these set of points? I already have the coordinates of the points along the perimeter of the shape. The image below shows…
Oliver Moore
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Circular/directional data analysis within a narrow arc

I am studying the presence of an anatomical variation to the structure of a long bone in healthy and diseased individuals. I have two separate groups of individuals. The anatomical variation is torsion of long bone which sounds simple enough but not…
petvet72
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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 would like to do is the equivalent of linear…
Mutewinter
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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 corresponding tests?
user13449
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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 the data was not uniformly distributed around a circle but can we make any predictions on whether the distribution was…
AvadaMouse
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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 analysis) for the watson's two sample test with ties…
nathmar
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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 parameters that represent a single variable. My…
Fein
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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 directional variance, we noticed that there are…
Tyrion
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Is there two-sample test for wrapped normal circular data?

I have two sets of randomly generated data with the wrapped normal circular distribution. I would like to test for homogeneity of means between these two samples. I was considering using Watson-Williams test but which requires that the samples are…
Zhao Jiayan
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How to compute the mean of three or more location coordinates

I have basically three location coordinates viz. (lat1, long1), (lat2, long2) and (lat3, long3). How to calculate the mean of these three points? It`s not like arithmetic mean for euclidean points since these are points on a sphere. Regards, Lesnar
Lesnar
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In circular statistics, is the difference between the means of two samples equivalent to the mean of their differences?

I'm comparing wind direction distributions using Python's scipy.stats.circmean and scipy.stats.circstd, and I encountered some unexpected results. As illustrated for example in this answer, for 'normal' (non-circular) data, the mean of the…
Peter9192
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