# 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 $\mathbb{R}^n$.

223 questions
Filter by
Sorted by
Tagged with
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 ...
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 ...
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 ...
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 ...
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 ...
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-...
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 ...
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,\...
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): ...
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: ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1k views

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 ...