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Module « scipy.stats »

Fonction pmean - module scipy.stats

Signature de la fonction pmean

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

Description

help(scipy.stats.pmean)

    


Calculate the weighted power mean along the specified axis.

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

.. math::

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

and, with equal weights, it gives:

.. math::

    \left( \frac{ 1 }{ n } \sum_{i=1}^n a_i^p \right)^{ 1 / p }  \, .

When ``p=0``, it returns the geometric mean.

This mean is also called generalized mean or Hölder mean, and must not be
confused with the Kolmogorov generalized mean, also called
quasi-arithmetic mean or generalized f-mean [3]_.

Parameters
----------
a : array_like
    Input array, masked array or object that can be converted to an array.
p : int or float
    Exponent.
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 of the returned array and of the accumulator in which the
    elements are summed. If `dtype` is not specified, it defaults to the
    dtype of `a`, unless `a` has an integer `dtype` with a precision less
    than that of the default platform integer. In that case, the default
    platform integer is used.
weights : array_like, optional
    The weights array can either be 1-D (in which case its length must be
    the size of `a` along the given `axis`) or of 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
-------
pmean : ndarray, see `dtype` parameter above.
    Output array containing the power mean values.

See Also
--------

:func:`numpy.average`
    Weighted average
:func:`gmean`
    Geometric mean
:func:`hmean`
    Harmonic mean


Notes
-----
The power mean is computed over a single dimension of the input
array, ``axis=0`` by default, or all values in the array if ``axis=None``.
float64 intermediate and return values are used for integer inputs.

The power mean is only defined if all observations are non-negative;
otherwise, the result is NaN.

.. versionadded:: 1.9

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] "Generalized Mean", *Wikipedia*,
       https://en.wikipedia.org/wiki/Generalized_mean
.. [2] Norris, N., "Convexity properties of generalized mean value
       functions", The Annals of Mathematical Statistics, vol. 8,
       pp. 118-120, 1937
.. [3] Bullen, P.S., Handbook of Means and Their Inequalities, 2003

Examples
--------
>>> from scipy.stats import pmean, hmean, gmean
>>> pmean([1, 4], 1.3)
2.639372938300652
>>> pmean([1, 2, 3, 4, 5, 6, 7], 1.3)
4.157111214492084
>>> pmean([1, 4, 7], -2, weights=[3, 1, 3])
1.4969684896631954

For p=-1, power mean is equal to harmonic mean:

>>> pmean([1, 4, 7], -1, weights=[3, 1, 3])
1.9029126213592233
>>> hmean([1, 4, 7], weights=[3, 1, 3])
1.9029126213592233

For p=0, power mean is defined as the geometric mean:

>>> pmean([1, 4, 7], 0, weights=[3, 1, 3])
2.80668351922014
>>> gmean([1, 4, 7], weights=[3, 1, 3])
2.80668351922014

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