rayleightest¶
- astropy.stats.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
ndarray
orQuantity
Array of circular (directional) data, which is assumed to be in radians whenever
data
isnumpy.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 thatnp.sum(weights, axis)
equals the number of observations. See [1], remark 1.4, page 22, for detailed explanation.
- data
- Returns:
- p-value
float
orQuantity
[:ref: ‘dimensionless’]
- 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>