# Questions tagged [circular-statistics]

Directional 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 $\mathbb{R}^n$.

167 questions
Filter by
Sorted by
Tagged with
0answers
31 views

### Reference books on uniform spherical distributions in multiple dimensions

QUESTION What is a citation of a book whose scope includes the uniform distribution  that is generalized to an $n$-ball ? Among other things, I'd like to read a book that include such ...
1answer
42 views

### quantifying asymmetry on a sphere

I have a scalar quantity that is distributed on a sphere. I would like to quantify the asymmetry in this scalar field. is there any standard method to do this? Let's say that the function on the ...
1answer
19 views

### How do you test for bias in a circular reference plane?

I've been trying to get my head around how to do hypothesis testing for a circular scale in hypothesis testing, but I am having a lot of trouble. I know well how to test for linear scales, but when it ...
0answers
38 views

### Compare semi-circular data

I have data on angles between vectors and thus the data lies in the range $[0,\pi]$. I have two samples of such data, of different sizes. I want some way of quantifying the difference between these ...
0answers
12 views

### Calculate percentiles of angles/bearings in Python

I have a dataset with a variable that is the angle of the event (record) from a central point (e.g. crime events in relation to a defined city center). I want to calculate percentiles for the variable....
1answer
42 views

### How to interprete the p values of cos and sin terms in periodic regression?

I have camera trap data where for each site and hour I have the abundance of wild herbivores. I want to create a model where I can estimate the effect of predator activity on the activity and behavior ...
0answers
35 views

### Polynomial regression in a circular data set

I'm working on a data set where I have a set of events per time of the day (in a 1h time slot). I made the sum of the events and plotted a bar as show below. In order to define an equation that could ...
1answer
48 views

0answers
119 views

### Regression for looping (circular?) variable [duplicate]

I am trying to calculate a regression curve for a dataset, where my independent variable ranges from 0 to 1, but 0 is equivalent to 1. In other words, my independent variable loops around. Therefore, ...
1answer
80 views

### Semicircular mean

I am running MCMC sampling to determine an angular parameter resulting in several thousand samples. The angle is restricted to $[0,\pi]$ as we cannot distinguish $\alpha$ and $\alpha+\pi$. For ...
1answer
353 views

### Including time of day in a linear regression model

The title may be entirely inappropriate for this question: that depends on whether I am on the right track. I am developing a statistical model to evaluate flower temperature based on air temperature. ...
1answer
26 views

### Statistical method to show a cycling pattern

let's say I have multiple time-series $A_i(x)$ and $B_i(x)$. Here, $i$ stands for a person (person 1, person 2, person 3, ..., person $i$, ..). Is there a method to show that the fluctuations in $A$ ...
1answer
48 views

### Power analysis for circular data

Imagine I have a sample distribution for a circular data set with a mean group direction and known variation. I would like to do a power analysis for a known effect size (e.g. to determine what sample ...
2answers
271 views

### Timestamps in Ridge Regression Scikit Learn

I am trying to transform data for use in regression, most likely the Ridge or Lasso technique implemented in sklearn.linear_model. My training data contains time ...
0answers
54 views

### Distance between angle distributions

I want to quantify the complexity of the street network of different cities. For each city I have the angle distribution of its streets. My hypothesis that the more complex the street network, the ...
1answer
47 views

### Prediction with circular variable

Suppose I have a set of $N$ observations for a circular variable $\theta_i$. Each trial for which an observation of $\theta_i$ is taken can lead to an outcome $x_i \in \{0,1\}$. Next, suppose that the ...
1answer
142 views

### Standard error of circular standard deviation

How to calculate the standard error of circular standard deviation estimated with equation $s = (2(1 − R))^{-\frac{1}{2}}$ or $s_{0} = (−2 \ln{R})^{-\frac{1}{2}}$ where R is the length of the mean ...
1answer
39 views

### Comparison of empirical distributions in ciruclar/polar coordinates

I have 4 sets of 24 measurements of a polar variable (univariate). I want to use a statistical test, like the Kolmogorov-Smirnov test, to test whether said sets differ significantly from each other. ...
1answer
219 views

### Linear model with interation for circular data in R

I have a circular dependant variable (in radians) and a linear independant variable (year) which I would like to model against each other and extract a slope value. I have been trying to use ...
0answers
119 views

### Time series analysis: periodogram peak uncertainty estimate

I'm analysing a time series with a Lomb-Scargle periodogram. Here's what the periodogram looks like: As you can see, there are three peaks very close together (I've tried much finer frequency grids ...
0answers
124 views

### Good choices of PRNG for uniform circular (directional) data?

I'm planning to simulate iid one-dim variates with continuous uniform distribution on a normalized circle (which circumference is $1$ instead of $2\pi$). Namely, a sample consists of $n$ points ...
1answer
34 views

### P-Value from Watson.test

I am using the circular package to evaluate if my circular data is uniform or not. The package PDF can be found here -> https://cran.r-project.org/web/packages/circular/circular.pdf The p-value ...
0answers
203 views

### pca on polar coordinates?

I have a dataset composed of 123 rows (time bins) and 20 columns (variables) The question I have is the following. each row,column pair has a radian value and a radius value. If I convert these pairs ...
0answers
107 views

### calculating orientation anisotropy of a set of 3D vectors

I have a set of unit-length 3D vectors (represented as cartesian 3-tuples) with 180$^\circ$ equivalence (rotated through any plane passing through the origin i.e. $v=-v$), all situated at the origin (...
2answers
874 views

### Regression using circular variable (hour from 0~23) as predictor

My question originally arises from reading this post Use of circular predictors in linear regression. Right now, I'm trying construct linear regression using "Bike Sharing dataset" from https://...
1answer
65 views

### Integer predictors in Poisson regression

I am trying to fit a model of total rental bike with ten predictors using Poisson Regression. Four of them are integer : Season : 1-4 Month : 1-12 Day : 0-6 Hour : 0-23 I usually treat integer ...
0answers
38 views

### Identifying two distributions from a circular scan and then finding their centre points

I’ve got three clusters of points. These are 315 readings taken from a circular scan, i.e. the reading at x = 315 is actually next to x =0. There are two clusters in the data - zero and non-zero (but ...
1answer
556 views

### Maximum Likelihood Estimation to fit Von Mises to grouped (interval) circular data

EDIT: see below- I used the pdf instead of the cdf for my likelihood. Fixed, but with a fun new problem! This is a follow-up to a question I asked here. For reasons explained earlier, I'm attempting ...
0answers
431 views

### How can I fit a normal (von Mises) distribution to discrete angular data?

This bears some explaining: I have a set of data from a psychophysics experiment where participants selected a response from a discrete set of 8 possible responses. These responses were actually ...
1answer
9k views

### Is the month ordinal or nominal variable?

I read in some article that the month of the year was being considered as qualitative nominal variable, but for me the month of the year has a clearly ordered structure and should therefore be ...
1answer
58 views

### Estimate parameter using MLE method [closed]

$$L=-2n\log(2 \pi)-n \log I_0(\lambda p)+\sum_{i=1}^{n} [\lambda p\cos(x_i-X_i)]-\sum_{i=1}^{n}log[c-m_1\cos(y_i-BX_i)-m_2\sin(y_i-BX_i)]$$ where $\lambda, X_i, m_1, m_2 , p$ are parameter i reach ...
1answer
82 views

### 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 ...
2answers
59 views

### Assessing correlation with a variable in degrees [duplicate]

This is probably a fairly simple question but it occurred to me, when trying to go through some data, that I wasn't sure how. Say you have some numeric variable vs. arc degrees-- like the price of ...
0answers
35 views

### Curve fitting with a polar input variable

Imagine we have a set of data, with two variables, the first of which can be represented in polar co-ordinates (for example hour or day, or day of week). The second variable is a real valued and has ...
1answer
130 views

### Variance of angle to $(X,Y)$ where both $X-\mu_X$ and $Y-\mu_Y \sim N(0,\sigma^2)$ independently

$X$ and $Y$ arise from observations contaminated by i.i.d. additive Gaussian noise $\sigma$. I seek the approximate variance of the angle from the origin to $(X,Y)$. What I've tried: The answer (...
0answers
314 views

### How can I do a t-test on 2D data?

How can I do a t-test on 2D data with latitude and longitude attributes? I have 2 clusters of similar coordinates but in different time, I want to do a t-test to see if they are statistically ...
0answers
232 views

### “Parametric bootstrap” or “Monte Carlo test”

I have a data set on counts of amphibians in buckets around a pond, which I have detailed in a previous post: Circular statistics for discrete, irregular sector data To conduct a test of circular ...
1answer
57 views

### How can I apply interpolation to angle data?

My data is in angles (degrees) and I intend to write a code that is trying to understand if there is a systematic (biased) behaviour in data. For example, if my data set is (10, 20, 30, 40) then a ...