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Module « scipy.stats »

Fonction moment - module scipy.stats

Signature de la fonction moment

def moment(a, order=1, axis=0, nan_policy='propagate', *, center=None, keepdims=False) 

Description

help(scipy.stats.moment)

    


Calculate the nth moment about the mean for a sample.

A moment is a specific quantitative measure of the shape of a set of
points. It is often used to calculate coefficients of skewness and kurtosis
due to its close relationship with them.

Parameters
----------
a : array_like
    Input array.
order : int or 1-D array_like of ints, optional
    Order of central moment that is returned. Default is 1.
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.
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.
center : float or None, optional
    The point about which moments are taken. This can be the sample mean,
    the origin, or any other be point. If `None` (default) compute the
    center as the sample mean.
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
-------
n-th moment about the `center` : ndarray or float
    The appropriate moment along the given axis or over all values if axis
    is None. The denominator for the moment calculation is the number of
    observations, no degrees of freedom correction is done.

See Also
--------

:func:`kurtosis`, :func:`skew`, :func:`describe`
    ..

Notes
-----
The k-th moment of a data sample is:

.. math::

    m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - c)^k

Where `n` is the number of samples, and `c` is the center around which the
moment is calculated. This function uses exponentiation by squares [1]_ for
efficiency.

Note that, if `a` is an empty array (``a.size == 0``), array `moment` with
one element (`moment.size == 1`) is treated the same as scalar `moment`
(``np.isscalar(moment)``). This might produce arrays of unexpected shape.

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] https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms

Examples
--------
>>> from scipy.stats import moment
>>> moment([1, 2, 3, 4, 5], order=1)
0.0
>>> moment([1, 2, 3, 4, 5], order=2)
2.0

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