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

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

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.


[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. <>


>>> 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>)