rayleightest¶

astropy.stats.circstats.
rayleightest
(data, axis=None, weights=None)[source]¶ Performs the Rayleigh test of uniformity.
This test is used to identify a nonuniform 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 pvalues suggest to reject the null hypothesis.
 Parameters
 datanumpy.ndarray or Quantity
Array of circular (directional) data, which is assumed to be in radians whenever
data
isnumpy.ndarray
. axisint, optional
Axis along which the Rayleigh test will be performed.
 weightsnumpy.ndarray, optional
In case of grouped data, the ith 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.
 Returns
 pvaluefloat or dimensionless Quantity
pvalue.
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.rproject.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://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.4762>
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>