biweight_midvariance¶
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astropy.stats.
biweight_midvariance
(a, c=9.0, M=None, axis=None)[source] [edit on github]¶ Compute the biweight midvariance.
The biweight midvariance is a robust statistic for determining the midvariance (i.e. the standard deviation) of a distribution. It is given by:
C_{bl}= (n')^{1/2} \frac{[\Sigma_{|u_i|<1} (x_i-M)^2(1-u_i^2)^4]^{0.5}} {|\Sigma_{|u_i|<1} (1-u_i^2)(1-5u_i^2)|}
where u_i is given by
u_{i} = \frac{(x_i-M)}{c MAD}
where c is the tuning constant and MAD is the median absolute deviation. The midvariance tuning constant
c
is typically 9.0.n' is the number of points for which |u_i| < 1 holds, while the summations are over all i up to n:
n' = \Sigma_{|u_i|<1}^n 1
This is slightly different than given in the reference below, but results in a value closer to the true midvariance.
For more details, see Beers, Flynn, and Gebhardt (1990); AJ 100, 32.
Parameters: a : array-like
Input array or object that can be converted to an array.
c : float, optional
Tuning constant for the biweight estimator. Default value is 9.0.
M : float or array-like, optional
Initial guess for the biweight location. An array can be input when using the
axis
keyword.axis : int, optional
Axis along which the biweight midvariances are computed. The default (
None
) is to compute the biweight midvariance of the flattened array.Returns: biweight_midvariance : float or
ndarray
The biweight midvariance of the input data. If
axis
isNone
then a scalar will be returned, otherwise andarray
will be returned.See also
Examples
Generate random variates from a Gaussian distribution and return the biweight midvariance of the distribution:
>>> import numpy as np >>> from astropy.stats import biweight_midvariance >>> rand = np.random.RandomState(12345) >>> from numpy.random import randn >>> bmv = biweight_midvariance(rand.randn(1000)) >>> print(bmv) 0.986726249291