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# scipy.stats.gstd

scipy.stats.gstd(a, axis=0, ddof=1)

  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 exponent of the standard deviation of `log(a)`. Mathematically the population geometric standard deviation can be evaluated as:

      gstd = exp(std(log(a)))

  New in version 1.3.0.

  Parameters:
    a array_like

      An array like object containing the sample data.

    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

  As the calculation requires the use of logarithms the geometric standard deviation only supports strictly positive values. Any non-positive or infinite values will raise a ValueError. The geometric standard deviation is sometimes confused with the exponent of the standard deviation, `exp(std(a))`. Instead the geometric standard deviation is `exp(std(log(a)))`. The default value for ddof is different to the default value (0) used by other ddof containing functions, such as `np.std` and `np.nanstd`.

  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])

  The geometric standard deviation further handles masked arrays.

      >>> a = np.arange(1, 25).reshape(2, 3, 4)
      >>> ma = np.ma.masked_where(a > 16, a)
      >>> ma
      masked_array(
        data=[[[1, 2, 3, 4],
               [5, 6, 7, 8],
               [9, 10, 11, 12]],
              [[13, 14, 15, 16],
               [--, --, --, --],
               [--, --, --, --]]],
        mask=[[[False, False, False, False],
               [False, False, False, False],
               [False, False, False, False]],
              [[False, False, False, False],
               [ True,  True,  True,  True],
               [ True,  True,  True,  True]]],
        fill_value=999999)
      >>> gstd(ma, axis=2)
      masked_array(
        data=[[1.8242475707663655, 1.2243686572447428, 1.1318311657788478],
              [1.0934830582350938, --, --]],
        mask=[[False, False, False],
              [False,  True,  True]],
        fill_value=999999)