Circular Statistics Tests in Python

This repository contains Python implementations of three important tests for circular (directional) statistics:

1. Kuiper's Test of Uniformity
2. Watson's Two-Sample Test of Homogeneity
3. Rayleigh Test of Uniformity

Original Implementation

The original implementations of these tests were written in R by:

Author: Claudio Agostinelli
E-mail: claudio@unive.it

Python Implementation

This Python port was created by Lucas Kühl.

Installation

To use these tests, you need Python 3.6 or later. The implementation depends on NumPy and SciPy.

1. Clone this repository:

   git clone /~https://github.com/lk96er/circular_statistics.git
   
   

2. Install the required packages:

   pip install -r requirements.txt
   

Usage

Here are some examples of how to use the tests:

import numpy as np
from circular_statistics import KuiperTest, WatsonTwoTest, RayleighTest

# Generate some random circular data
x = np.random.uniform(0, 2*np.pi, 100)
y = np.random.uniform(0, 2*np.pi, 100)

# Kuiper's Test
kuiper_test = KuiperTest(x, alpha=0.05)
kuiper_test.run_test()
kuiper_test.print_results()

# Watson's Two-Sample Test
watson_test = WatsonTwoTest(x, y, alpha=0.05)
watson_test.run_test()
watson_test.print_results()

# Rayleigh Test
rayleigh_test = RayleighTest(x)
rayleigh_test.run_test()
rayleigh_test.print_results()

# Rayleigh Test with specified mean direction
rayleigh_test_mu = RayleighTest(x, mu=np.pi)
rayleigh_test_mu.run_test()
rayleigh_test_mu.print_results()

Tests Description

1. Kuiper's Test: Tests the null hypothesis that a sample of circular data is drawn from a uniform distribution.

2. Watson's Two-Sample Test: Tests the null hypothesis that two samples of circular data come from the same distribution.

3. Rayleigh Test: Tests the null hypothesis that a sample of circular data is uniformly distributed around the circle. It can also test for a specified mean direction.

Contributing

Contributions to improve the code or add new circular statistics tests are welcome. Please feel free to submit a pull request or open an issue.

License

This project is licensed under the GNU General Public License version 2 (GPL-2) - see the LICENSE file for details.

References

Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in Circular Statistics. World Scientific, Singapore.

Acknowledgments

Special thanks to Claudio Agostinelli for the original R implementation of these tests.