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 0x7f5076a88f70>, scale=1.0, nan_policy='propagate') 

Description

median_abs_deviation.__doc__

    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:

    >>> 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