astropy.stats.rayleightest(data, axis=None, weights=None)[source] [edit on github]

Performs the Rayleigh test of uniformity.

This test is used to identify a non-uniform distribution, i.e. it is designed for detecting an unimodal deviation from uniformity. More precisely, it assumes the following hypotheses: - H0 (null hypothesis): The population is distributed uniformly around the circle. - H1 (alternative hypothesis): The population is not distributed uniformly around the circle. Small p-values suggest to reject the null hypothesis.


data : numpy.ndarray or Quantity

Array of circular (directional) data, which is assumed to be in radians whenever data is numpy.ndarray.

axis : int, optional

Axis along which the Rayleigh test will be performed.

weights : numpy.ndarray, optional

In case of grouped data, the i-th element of weights represents a weighting factor for each group such that np.sum(weights, axis) equals the number of observations. See [R95], remark 1.4, page 22, for detailed explanation.


p-value : float or dimensionless Quantity



[R95](1, 2) S. R. Jammalamadaka, A. SenGupta. “Topics in Circular Statistics”. Series on Multivariate Analysis, Vol. 5, 2001.
[R96]C. Agostinelli, U. Lund. “Circular Statistics from ‘Topics in Circular Statistics (2001)’”. 2015. <https://cran.r-project.org/web/packages/CircStats/CircStats.pdf>
[R97]M. Chirstman., C. Miller. “Testing a Sample of Directions for Uniformity.” Lecture Notes, STA 6934/5805. University of Florida, 2007.
[R98]D. Wilkie. “Rayleigh Test for Randomness of Circular Data”. Applied Statistics. 1983. <http://citeseerx.ist.psu.edu/viewdoc/summary?doi=>


>>> import numpy as np
>>> from astropy.stats import rayleightest
>>> from astropy import units as u
>>> data = np.array([130, 90, 0, 145])*u.deg
>>> rayleightest(data) 
<Quantity 0.2563487733797317>