scipy.stats.gstd¶
- scipy.stats.gstd(a, axis=0, ddof=1)[source]¶
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:
- aarray_like
An array like object containing the sample data.
- axisint, tuple or None, optional
Axis along which to operate. Default is 0. If None, compute over the whole array a.
- ddofint, optional
Degree of freedom correction in the calculation of the geometric standard deviation. Default is 1.
- Returns:
- 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
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 isexp(std(log(a)))
. The default value for ddof is different to the default value (0) used by other ddof containing functions, such asnp.std
andnp.nanstd
.References
[1]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)