# circstd¶

astropy.stats.circstd(data, axis=None, weights=None, method='angular')[source]

Computes the circular standard deviation of an array of circular data.

The standard deviation implemented here is based on the definitions given by [1], which is also the same used by the R package ‘CirStat’ [2].

Two methods are implemented: ‘angular’ and ‘circular’. The former is defined as sqrt(2 * (1 - R)) and it is bounded in [0, 2*Pi]. The latter is defined as sqrt(-2 * ln(R)) and it is bounded in [0, inf].

Following ‘CircStat’ the default method used to obtain the standard deviation is ‘angular’.

Parameters
datanumpy.ndarray or dimensionless Quantity

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

axisint, optional

Axis along which circular variances are computed. The default is to compute the variance of the flattened array.

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 [3], remark 1.4, page 22, for detailed explanation.

methodstr, optional

The method used to estimate the standard deviation:

• ‘angular’ : obtains the angular deviation

• ‘circular’ : obtains the circular deviation

Returns
circstdnumpy.ndarray or dimensionless Quantity

Angular or circular standard deviation.

References

1

P. Berens. “CircStat: A MATLAB Toolbox for Circular Statistics”. Journal of Statistical Software, vol 31, issue 10, 2009.

2

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

3

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

Examples

>>> import numpy as np
>>> from astropy.stats import circstd
>>> from astropy import units as u
>>> data = np.array([51, 67, 40, 109, 31, 358])*u.deg
>>> circstd(data)
<Quantity 0.57195022>


Alternatively, using the ‘circular’ method:

>>> import numpy as np
>>> from astropy.stats import circstd
>>> from astropy import units as u
>>> data = np.array([51, 67, 40, 109, 31, 358])*u.deg
>>> circstd(data, method='circular')
<Quantity 0.59766999>