mad_std

astropy.stats.mad_std(data, axis=None, func=None, ignore_nan=False)

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.

Returns:

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.

See also

biweight_midvariance, biweight_midcovariance, median_absolute_deviation

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)))
>>> print(madstd)    # doctest: +FLOAT_CMP
2.0232764659422626