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Module « scipy.stats »

Fonction gstd - module scipy.stats

Signature de la fonction gstd

def gstd(a, axis=0, ddof=1) 

Description

help(scipy.stats.gstd)

Calculate the geometric standard deviation of an array.

The geometric standard deviation describes the spread of a set of numbers
where the geometric mean is preferred. It is a multiplicative factor, and
so a dimensionless quantity.

It is defined as the exponential of the standard deviation of the
natural logarithms of the observations.

Parameters
----------
a : array_like
    An array containing finite, strictly positive, real numbers.

    .. deprecated:: 1.14.0
        Support for masked array input was deprecated in
        SciPy 1.14.0 and will be removed in version 1.16.0.

axis : int, tuple or None, optional
    Axis along which to operate. Default is 0. If None, compute over
    the whole array `a`.
ddof : int, optional
    Degree of freedom correction in the calculation of the
    geometric standard deviation. Default is 1.

Returns
-------
gstd : ndarray or float
    An array of the geometric standard deviation. If `axis` is None or `a`
    is a 1d array a float is returned.

See Also
--------
gmean : Geometric mean
numpy.std : Standard deviation
gzscore : Geometric standard score

Notes
-----
Mathematically, the sample geometric standard deviation :math:`s_G` can be
defined in terms of the natural logarithms of the observations
:math:`y_i = \log(x_i)`:

.. math::

    s_G = \exp(s), \quad s = \sqrt{\frac{1}{n - d} \sum_{i=1}^n (y_i - \bar y)^2}

where :math:`n` is the number of observations, :math:`d` is the adjustment `ddof`
to the degrees of freedom, and :math:`\bar y` denotes the mean of the natural
logarithms of the observations. Note that the default ``ddof=1`` is different from
the default value used by similar functions, such as `numpy.std` and `numpy.var`.

When an observation is infinite, the geometric standard deviation is
NaN (undefined). Non-positive observations will also produce NaNs in the
output because the *natural* logarithm (as opposed to the *complex*
logarithm) is defined and finite only for positive reals.
The geometric standard deviation is sometimes confused with the exponential
of the standard deviation, ``exp(std(a))``. Instead, the geometric standard
deviation is ``exp(std(log(a)))``.

References
----------
.. [1] "Geometric standard deviation", *Wikipedia*,
       https://en.wikipedia.org/wiki/Geometric_standard_deviation.
.. [2] Kirkwood, T. B., "Geometric means and measures of dispersion",
       Biometrics, vol. 35, pp. 908-909, 1979

Examples
--------
Find the geometric standard deviation of a log-normally distributed sample.
Note that the standard deviation of the distribution is one; on a
log scale this evaluates to approximately ``exp(1)``.

>>> import numpy as np
>>> from scipy.stats import gstd
>>> rng = np.random.default_rng()
>>> sample = rng.lognormal(mean=0, sigma=1, size=1000)
>>> gstd(sample)
2.810010162475324

Compute the geometric standard deviation of a multidimensional array and
of a given axis.

>>> a = np.arange(1, 25).reshape(2, 3, 4)
>>> gstd(a, axis=None)
2.2944076136018947
>>> gstd(a, axis=2)
array([[1.82424757, 1.22436866, 1.13183117],
       [1.09348306, 1.07244798, 1.05914985]])
>>> gstd(a, axis=(1,2))
array([2.12939215, 1.22120169])

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