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Module « scipy.stats »

Fonction median_abs_deviation - module scipy.stats

Signature de la fonction median_abs_deviation

def median_abs_deviation(x, axis=0, center=<function median at 0x0000020DE8B2F2B0>, scale=1.0, nan_policy='propagate') 

Description

help(scipy.stats.median_abs_deviation)

Compute the median absolute deviation of the data along the given axis.

The median absolute deviation (MAD, [1]_) computes the median over the
absolute deviations from the median. It is a measure of dispersion
similar to the standard deviation but more robust to outliers [2]_.

The MAD of an empty array is ``np.nan``.

.. versionadded:: 1.5.0

Parameters
----------
x : array_like
    Input array or object that can be converted to an array.
axis : int or None, optional
    Axis along which the range is computed. Default is 0. If None, compute
    the MAD over the entire array.
center : callable, optional
    A function that will return the central value. The default is to use
    np.median. Any user defined function used will need to have the
    function signature ``func(arr, axis)``.
scale : scalar or str, optional
    The numerical value of scale will be divided out of the final
    result. The default is 1.0. The string "normal" is also accepted,
    and results in `scale` being the inverse of the standard normal
    quantile function at 0.75, which is approximately 0.67449.
    Array-like scale is also allowed, as long as it broadcasts correctly
    to the output such that ``out / scale`` is a valid operation. The
    output dimensions depend on the input array, `x`, and the `axis`
    argument.
nan_policy : {'propagate', 'raise', 'omit'}, optional
    Defines how to handle when input contains nan.
    The following options are available (default is 'propagate'):

    * 'propagate': returns nan
    * 'raise': throws an error
    * 'omit': performs the calculations ignoring nan values

Returns
-------
mad : scalar or ndarray
    If ``axis=None``, a scalar is returned. If the input contains
    integers or floats of smaller precision than ``np.float64``, then the
    output data-type is ``np.float64``. Otherwise, the output data-type is
    the same as that of the input.

See Also
--------
numpy.std, numpy.var, numpy.median, scipy.stats.iqr, scipy.stats.tmean,
scipy.stats.tstd, scipy.stats.tvar

Notes
-----
The `center` argument only affects the calculation of the central value
around which the MAD is calculated. That is, passing in ``center=np.mean``
will calculate the MAD around the mean - it will not calculate the *mean*
absolute deviation.

The input array may contain `inf`, but if `center` returns `inf`, the
corresponding MAD for that data will be `nan`.

References
----------
.. [1] "Median absolute deviation",
       https://en.wikipedia.org/wiki/Median_absolute_deviation
.. [2] "Robust measures of scale",
       https://en.wikipedia.org/wiki/Robust_measures_of_scale

Examples
--------
When comparing the behavior of `median_abs_deviation` with ``np.std``,
the latter is affected when we change a single value of an array to have an
outlier value while the MAD hardly changes:

>>> import numpy as np
>>> from scipy import stats
>>> x = stats.norm.rvs(size=100, scale=1, random_state=123456)
>>> x.std()
0.9973906394005013
>>> stats.median_abs_deviation(x)
0.82832610097857
>>> x[0] = 345.6
>>> x.std()
34.42304872314415
>>> stats.median_abs_deviation(x)
0.8323442311590675

Axis handling example:

>>> x = np.array([[10, 7, 4], [3, 2, 1]])
>>> x
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> stats.median_abs_deviation(x)
array([3.5, 2.5, 1.5])
>>> stats.median_abs_deviation(x, axis=None)
2.0

Scale normal example:

>>> x = stats.norm.rvs(size=1000000, scale=2, random_state=123456)
>>> stats.median_abs_deviation(x)
1.3487398527041636
>>> stats.median_abs_deviation(x, scale='normal')
1.9996446978061115

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