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Module « scipy.stats.mstats »

Fonction gmean - module scipy.stats.mstats

Signature de la fonction gmean

def gmean(a, axis=0, dtype=None, weights=None, *, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.mstats.gmean)

    


Compute the weighted geometric mean along the specified axis.

The weighted geometric mean of the array :math:`a_i` associated to weights
:math:`w_i` is:

.. math::

    \exp \left( \frac{ \sum_{i=1}^n w_i \ln a_i }{ \sum_{i=1}^n w_i }
               \right) \, ,

and, with equal weights, it gives:

.. math::

    \sqrt[n]{ \prod_{i=1}^n a_i } \, .

Parameters
----------
a : array_like
    Input array or object that can be converted to an 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.
dtype : dtype, optional
    Type to which the input arrays are cast before the calculation is
    performed.
weights : array_like, optional
    The `weights` array must be broadcastable to the same shape as `a`.
    Default is None, which gives each value a weight of 1.0.
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
-------
gmean : ndarray
    See `dtype` parameter above.

See Also
--------

:func:`numpy.mean`
    Arithmetic average
:func:`numpy.average`
    Weighted average
:func:`hmean`
    Harmonic mean


Notes
-----
The sample geometric mean is the exponential of the mean of the natural
logarithms of the observations.
Negative observations will produce NaNs in the output because the *natural*
logarithm (as opposed to the *complex* logarithm) is defined only for
non-negative reals.

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] "Weighted Geometric Mean", *Wikipedia*,
       https://en.wikipedia.org/wiki/Weighted_geometric_mean.
.. [2] Grossman, J., Grossman, M., Katz, R., "Averages: A New Approach",
       Archimedes Foundation, 1983

Examples
--------
>>> from scipy.stats import gmean
>>> gmean([1, 4])
2.0
>>> gmean([1, 2, 3, 4, 5, 6, 7])
3.3800151591412964
>>> gmean([1, 4, 7], weights=[3, 1, 3])
2.80668351922014

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