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scipy.stats.

# gzscore

scipy.stats.gzscore(a, *, axis=0, ddof=0, nan_policy='propagate')

  Compute the geometric standard score.

  Compute the geometric z score of each strictly positive value in the sample, relative to the geometric mean and standard deviation. Mathematically the geometric z score can be evaluated as:

      gzscore = log(a/gmu) / log(gsigma)

  where `gmu` (resp. `gsigma`) is the geometric mean (resp. standard deviation).

  Parameters:
    a array_like

      Sample data.

    axis int or None, optional

      Axis along which to operate. Default is 0. If None, compute over the whole array a.

    ddof int, optional

      Degrees of freedom correction in the calculation of the standard deviation. Default is 0.

    nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

      Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’. Note that when the value is ‘omit’, nans in the input also propagate to the output, but they do not affect the geometric z scores computed for the non-nan values.

  Returns:
    gzscore array_like

      The geometric z scores, standardized by geometric mean and geometric standard deviation of input array a.

  See also

  `gmean`

    Geometric mean

  `gstd`

    Geometric standard deviation

  `zscore`

    Standard score

  Notes

  This function preserves ndarray subclasses, and works also with matrices and masked arrays (it uses `asanyarray` instead of `asarray` for parameters).

  Added in version 1.8.

  Array API Standard Support

  `gzscore` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  > See Support for the array API standard for more information.

  References

  [1]

  “Geometric standard score”, Wikipedia, https://en.wikipedia.org/wiki/Geometric_standard_deviation#Geometric_standard_score.

  Examples

  Draw samples from a log-normal distribution:

      >>> import numpy as np
      >>> from scipy.stats import zscore, gzscore
      >>> import matplotlib.pyplot as plt

      >>> rng = np.random.default_rng()
      >>> mu, sigma = 3., 1.  # mean and standard deviation
      >>> x = rng.lognormal(mu, sigma, size=500)

  Display the histogram of the samples:

      >>> fig, ax = plt.subplots()
      >>> ax.hist(x, 50)
      >>> plt.show()

  Display the histogram of the samples standardized by the classical zscore. Distribution is rescaled but its shape is unchanged.

      >>> fig, ax = plt.subplots()
      >>> ax.hist(zscore(x), 50)
      >>> plt.show()

  Demonstrate that the distribution of geometric zscores is rescaled and quasinormal:

      >>> fig, ax = plt.subplots()
      >>> ax.hist(gzscore(x), 50)
      >>> plt.show()