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Module « scipy.stats »

Fonction skew - module scipy.stats

Signature de la fonction skew

def skew(a, axis=0, bias=True, nan_policy='propagate', *, keepdims=False) 

Description

help(scipy.stats.skew)

    


Compute the sample skewness of a data set.

For normally distributed data, the skewness should be about zero. For
unimodal continuous distributions, a skewness value greater than zero means
that there is more weight in the right tail of the distribution. The
function `skewtest` can be used to determine if the skewness value
is close enough to zero, statistically speaking.

Parameters
----------
a : ndarray
    Input array.
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
bias : bool, optional
    If False, then the calculations are corrected for statistical bias.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
skewness : ndarray
    The skewness of values along an axis, returning NaN where all values
    are equal.

Notes
-----
The sample skewness is computed as the Fisher-Pearson coefficient
of skewness, i.e.

.. math::

    g_1=\frac{m_3}{m_2^{3/2}}

where

.. math::

    m_i=\frac{1}{N}\sum_{n=1}^N(x[n]-\bar{x})^i

is the biased sample :math:`i\texttt{th}` central moment, and
:math:`\bar{x}` is
the sample mean.  If ``bias`` is False, the calculations are
corrected for bias and the value computed is the adjusted
Fisher-Pearson standardized moment coefficient, i.e.

.. math::

    G_1=\frac{k_3}{k_2^{3/2}}=
        \frac{\sqrt{N(N-1)}}{N-2}\frac{m_3}{m_2^{3/2}}.

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
   Probability and Statistics Tables and Formulae. Chapman & Hall: New
   York. 2000.
   Section 2.2.24.1

Examples
--------
>>> from scipy.stats import skew
>>> skew([1, 2, 3, 4, 5])
0.0
>>> skew([2, 8, 0, 4, 1, 9, 9, 0])
0.2650554122698573

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