scipy.stats.

gzscore#

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

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:

aarray_like: Sample data.
axisint or None, optional: Axis along which to operate. Default is 0. If None, compute over the whole array a.
ddofint, 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:

gzscorearray_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.

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	✓	✓

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()

../../_images/scipy-stats-gzscore-1_00_00.png

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()

../../_images/scipy-stats-gzscore-1_01_00.png

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

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

../../_images/scipy-stats-gzscore-1_02_00.png