# rayleightest#

astropy.stats.circstats.rayleightest(data, axis=None, weights=None)[source]#

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.

Parameters:
data

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 [1], remark 1.4, page 22, for detailed explanation.

Returns:
p-value

References

[1]

S. R. Jammalamadaka, A. SenGupta. “Topics in Circular Statistics”. Series on Multivariate Analysis, Vol. 5, 2001.

[2]

C. Agostinelli, U. Lund. “Circular Statistics from ‘Topics in Circular Statistics (2001)’”. 2015. <https://cran.r-project.org/web/packages/CircStats/CircStats.pdf>

[3]

M. Chirstman., C. Miller. “Testing a Sample of Directions for Uniformity.” Lecture Notes, STA 6934/5805. University of Florida, 2007.

[4]

D. Wilkie. “Rayleigh Test for Randomness of Circular Data”. Applied Statistics. 1983. <http://wexler.free.fr/library/files/wilkie%20(1983)%20rayleigh%20test%20for%20randomness%20of%20circular%20data.pdf>

Examples

```>>> 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>
```