astropy.stats.mad_std(data, axis=None, func=None, ignore_nan=False)[source] [edit on github]

Calculate a robust standard deviation using the median absolute deviation (MAD).

The standard deviation estimator is given by:

$\sigma \approx \frac{\textrm{MAD}}{\Phi^{-1}(3/4)} \approx 1.4826 \ \textrm{MAD}$

where $$\Phi^{-1}(P)$$ is the normal inverse cumulative distribution function evaluated at probability $$P = 3/4$$.

Parameters: data : array-like Data array or object that can be converted to an array. axis : {int, sequence of int, None}, optional Axis along which the robust standard deviations are computed. The default (None) is to compute the robust standard deviation of the flattened array. func : callable, optional The function used to compute the median. Defaults to numpy.ma.median for masked arrays, otherwise to numpy.median. ignore_nan : bool Ignore NaN values (treat them as if they are not in the array) when computing the median. This will use numpy.ma.median if axis is specified, or numpy.nanmedian if axis=None and numpy’s version is >1.10 because nanmedian is slightly faster in this case. mad_std : float or ndarray The robust standard deviation of the input data. If axis is None then a scalar will be returned, otherwise a ndarray will be returned.

Examples

>>> import numpy as np
>>> from astropy.stats import mad_std
>>> rand = np.random.RandomState(12345)
>>> madstd = mad_std(rand.normal(5, 2, (100, 100)))