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biweight_location

astropy.stats.biweight_location(a, c=6.0, M=None)[source] [edit on github]

Compute the biweight location for an array.

Returns the biweight location for the array elements. The biweight is a robust statistic for determining the central location of a distribution.

The biweight location is given by the following equation

C_{bl}= M+\frac{\Sigma_{\|u_i\|<1} (x_i-M)(1-u_i^2)^2} {\Sigma_{\|u_i\|<1} (1-u_i^2)^2}

where M is the sample mean or if run iterative the initial guess, and u_i is given by

u_{i} = \frac{(x_i-M)}{cMAD}

where MAD is the median absolute deviation.

For more details, see Beers, Flynn, and Gebhardt, 1990, AJ, 100, 32B

Parameters:

a : array-like

Input array or object that can be converted to an array.

c : float

Tuning constant for the biweight estimator. Default value is 6.0.

M : float, optional

Initial guess for the biweight location.
Returns:

biweight_location : float

Returns the biweight location for the array elements.

See also

median_absolute_deviation, biweight_midvariance

Examples

This will generate random variates from a Gaussian distribution and return the biweight location of the distribution:

>>> from astropy.stats.funcs import biweight_location
>>> from numpy.random import randn
>>> randvar = randn(10000)
>>> cbl = biweight_location(randvar)

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