astropy.stats.vonmisesmle(data, axis=None, weights=None)[source]#

Computes the Maximum Likelihood Estimator (MLE) for the parameters of the von Mises distribution.

datandarray or Quantity

Array of circular (directional) data, which is assumed to be in radians whenever data is numpy.ndarray.

axisint, optional

Axis along which the mle will be computed.

weightsnumpy.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.

mufloat or Quantity

The mean (aka location parameter).

kappafloat or Quantity [:ref: ‘dimensionless’]

The concentration parameter.



S. R. Jammalamadaka, A. SenGupta. “Topics in Circular Statistics”. Series on Multivariate Analysis, Vol. 5, 2001.


C. Agostinelli, U. Lund. “Circular Statistics from ‘Topics in Circular Statistics (2001)’”. 2015. <https://cran.r-project.org/web/packages/CircStats/CircStats.pdf>


>>> import numpy as np
>>> from astropy.stats import vonmisesmle
>>> from astropy import units as u
>>> data = np.array([130, 90, 0, 145])*u.deg
>>> vonmisesmle(data) 
(<Quantity 101.16894320013179 deg>, <Quantity 1.49358958737054>)