# rayleightest¶

astropy.stats.circstats.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.

Parameters: 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 [1], remark 1.4, page 22, for detailed explanation. p-value : float or dimensionless Quantity p-value.

References

 [1] (1, 2) 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.
 [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.

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>