circmoment¶

astropy.stats.circstats.circmoment(data, p=1.0, centered=False, axis=None, weights=None)[source] [edit on github]

Computes the p-th trigonometric circular moment for an array of circular data.

Parameters: data : numpy.ndarray or Quantity Array of circular (directional) data, which is assumed to be in radians whenever data is numpy.ndarray. p : float, optional Order of the circular moment. centered : Boolean, optional If True, central circular moments are computed. Default value is False. axis : int, optional Axis along which circular moments are computed. The default is to compute the circular moment of the flattened array. weights : numpy.ndarray, optional In case of grouped data, the i-th element of weights represents a weighting factor for each group such that sum(weights, axis) equals the number of observations. See [1], remark 1.4, page 22, for detailed explanation. circmoment : numpy.ndarray or Quantity The first and second elements correspond to the direction and length of the p-th circular moment, respectively.

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.

Examples

>>> import numpy as np
>>> from astropy.stats import circmoment
>>> from astropy import units as u
>>> data = np.array([51, 67, 40, 109, 31, 358])*u.deg
>>> circmoment(data, p=2)
(<Quantity 90.99263082432564 deg>, <Quantity 0.48004283892950717>)