Compute the biweight midvariance for an array
Returns the biweight midvariance for the array elements. The biweight midvariance is a robust statistic for determining the midvariance (ie. the standard deviation) of a distribution.
The biweight location is given by the follow equation
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:
.. math::
u_{i} = frac{(x_i-M)}{cMAD}
where MAD is the median absolute deviation. For the midvariance parameter, c is typically uses a value of 9.0.
For more details, see Beers, Flynn, and Gebhardt, 1990, AJ, 100, 32B
Parameters : | a : array_like
c : float
M : float, optional
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Returns : | biweight_midvariance: float :
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See also
median, biweight_location
Examples
This will generate random variates from a Gaussian distribution and return the median absolute deviation for that distribution:
>>> from astropy.stats.funcs import biweight_midvariance
>>> from numpy.random import randn
>>> randvar = randn(10000)
>>> scl = biweight_midvariance(randvar)